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In the philosophy of science, protoscience is a research field that has the characteristics of an undeveloped science that may ultimately develop into an established science. Philosophers use protoscience to understand the history of science and distinguish protoscience from science and pseudoscience. The word "protoscience" is a hybrid Greek-Latin compound of the roots proto- + scientia, meaning a first or primeval rational knowledge. Common examples of protoscience include alchemy, Wegener's original theory of continental drift, and political economy (the predecessor to the modern economic sciences). == History == Protoscience as a research field with the characteristics of an undeveloped science appeared in the early 20th century. In 1910, Jones described the field of political economy as it began the transition to the modern field of economics: I confess to a personal predilection for some term such as proto-science, pre-science, or nas-science, to give expression to what I conceive to be the true state of affairs, which I take to be this, that economics and kindred subjects are not sciences, but are on the way to become sciences. Thomas Kuhn later provided a more precise description, protoscience as a field that generates testable conclusions, faces “incessant criticism and continually strive for a fresh start,” but currently, like art and philosophy, appears to have failed to progress in a way similar to the progress seen in the established sciences. He applies protoscience to the fields of natural philosophy, medicine and the crafts in the past that ultimately became established sciences. Philosophers later developed more precise criteria to identify protoscience using the cognitive field concept. == Thought collective == This material is from Ludwik Fleck § Thought collective Thomas Kuhn later discovered that Fleck 1935 had voiced concepts that predated Kuhn's own work. That is, Fleck wrote that the development of truth in scientific research was an unattainable ideal as different researchers were locked into thought collectives (or thought-styles). This means "that a pure and direct observation cannot exist: in the act of perceiving objects the observer, i.e. the epistemological subject, is always influenced by the epoch and the environment to which he belongs, that is by what Fleck calls the thought style". Thought style throughout Fleck's work is closely associated with representational style. A "fact" was a relative value, expressed in the language or symbolism of the thought collective in which it belonged, and subject to the social and temporal structure of this collective. He argued, however, that within the active cultural style of a thought collective, knowledge claims or facts were constrained by passive elements arising from the observations and experience of the natural world. This passive resistance of natural experience represented within the stylized means of the thought collective could be verified by anyone adhering to the culture of the thought collective, and thus facts could be agreed upon within any particular thought style. Thus while a fact may be verifiable within its own collective, it may be unverifiable in others. He felt that the development of scientific facts and concepts was not unidirectional and does not consist of just accumulating new pieces of information, but at times required changing older concepts, methods of observations, and forms of representation. This changing of prior knowledge is difficult because a collective attains over time a specific way of investigating, bringing with it a blindness to alternative ways of observing and conceptualization. Change was especially possible when members of two thought collectives met and cooperated in observing, formulating hypothesis and ideas. He strongly advocated comparative epistemology. He also notes some features of the culture of modern natural sciences that recognize provisionality and evolution of knowledge along the value of pursuit of passive resistances. This approach anticipated later developments in social constructionism, and especially the development of critical science and technology studies. == Conceptual framework == === Cognitive field === Philosophers describe protoscience using the cognitive field concept. In every society, there are fields of knowledge (cognitive fields). The cognitive field consists of a community of individuals within a society with a domain of inquiry, a philosophical worldview, logical/mathematical tools, specific background knowledge from neighboring fields, a set of problems investigated, accumulated knowledge from the community, aims and methods. Cognitive fields are either belief fields or research fields. A cognitive research field invariably changes over time due to research; research fields include natural sciences, applied sciences, mathematics, technology, medicine, jurisprudence, social sciences and the humanities. A belief field (faith field) is "a cognitive field which either does not change at all or changes due to factors other than research (such as economic interest, political or religious pressure, or brute violence)." Belief fields include political ideology, religion, pseudodoctrines and pseudoscience. === Science field === A science field is a research field that satisfies 12 conditions: 1) all components of the science field invariably change over time from research in the field, especially logical/mathematical tools and specific background/presuppositions from other fields; 2) the research community has special training, “hold strong information links”, initiates or continues the “tradition of inquiry”; 3) researchers have autonomy to pursue research and receive support from the host society; 4) the researchers worldview is the real world as contains “lawfully changing concrete” objects, an adequate view of the scientific method, a vision of organized science achieving truthfull descriptions and explanations, ethical principles for conducting research, and the free search for truthful, deep and systematic understanding; 5) up-to-date logical/mathematical tools precisely determine and process information; 6) the domain of research are real objects/entities; 7) specific background knowledge is up-to-date, confirmed data, hypotheses and theories from relevant neighboring fields; 8) the set of problems investigated are from the domain of inquiry or within the research field; 9) the accumulated knowledge includes worldview-compatible, up-to-date testworthy/testable theories, hypotheses and data, and special knowledge previously accumlated in the research field; 10) the aims are find and apply laws and theories in the domain of inquiry, systemize acquired knonwledge, generalized information into theories, and improve research methods; 11) appropriate scientific methods are “subject to test, correction and justification”; 12) the research field is connected with a wider research field with similar capable researchers capable of “scientific inference, action and discussion”, similar hosting society, a domain of inquiry containing the domain of inquiry of the narrower field, and shared worldview, logical/mathematical tools, background knowledge, accumulated knowledge, aims and methods. === Protoscience === Philosophers define protoscience as an undeveloped science field, undeveloped meaning an incomplete or approximate science field. Mario Bunge defined a protoscience as a research field that approximately satisfies a similar set of the 12 science conditions. A protoscience that is evolving to ultimately satisfy all 12 conditions is an emerging or developing science. Bunge states, "The difference between protoscience and pseudoscience parallels that between error and deception." A protoscience may not survive or evolve to a science or pseudoscience. Kuhn was skeptical about any remedy that would reliably transform a protoscience to a science stating, “I claim no therapy to assist the transformation of a proto-science to a science, nor do I suppose anything of this sort is to be had.” Raimo Tuomela defined a protoscience as a research field that satisfies 9 of the 12 science conditions; a protoscience fails to satisfy the up-to-date conditions for logic/mathematical tools, specific background knowledge from neighboring fields, and accumulated knowledge (5, 7, 9), and there is reason to believe the protoscience will ultimately satisfy all 12 conditions. Protosciences and belief fields are both non-science fields, but only a protoscience can become a science field. Tuomela emphasizes that the cognitive field concept refers to "ideal types" and there may be some persons within a science field with non-scientific "attitudes, thinking and actions"; therefore, it may be better to apply scientific and non-scientific to "attitudes, thinking and actions" rather than directly to cognitive fields. == Developmental stages of science == Bunge stated that protoscience may occur as the second stage of a five-stage process in the development of science. Each stage has a theoretical and empirical aspect: Prescience has unchecked speculation theory and unchecked data. Protoscience has hypotheses without theory accompanied by observation and occasional measurement, but no experiment. Deuteroscience has hypotheses formulated mathematically without theory accompanied by systematic measurement, and experiment on perceptible traits of perceptible objects. Tritoscience has mathematical models accompanied by systematic measurements and experiments on perceptible and imperceptible traits of perceptible and imperceptible objects. Tetartoscience has mathematical models and comprehensive theories accompanied by precise systematic measurements and experiments on perceptible and imperceptible traits of perceptible and imperceptible objects. == Origin of protoscience == Protoscience may arise from the philosophical inquiry that anticipates science. Philosophers anticipated the development of astronomy, atomic theory, evolution and linguistics. The Greek philosopher Anaximander (610–546 BC) viewed the earth as a non-moving free-floating cylinder in space. The atomist doctrine of Democritus (460–370 BC) to Epicurus (341–270 BC) was that objects were composed of non-visible small particles. Anaximander had anticipated that humans may have developed from more primitive organisms. Wittgenstein’s study of language preceded the linguistic studies of J. L. Austin and John Searle. Popper describes how scientific theory arises from myths such as atomism and the corpuscular theory of light. Popper states that the Copernican system was "inspired by a Neo-Platonic worship of the light of the Sun who had to occupy the center because of his nobility", leading to "testable components" that ultimately became "fruitful and important." Some scholars use the term "primitive protoscience" to describe ancient myths that help explain natural phenomena at a time prior to the development of the scientific method. == Protoscience examples == === Physical science === Ancient astronomical protoscience was recorded as astronomical images and records inscribed on stones, bones and cave walls. Luigi Ferdinando Marsili (1658–1730) contributed to protoscience oceanography, describing the ocean currents of the Bosporus and physical oceanography, and Benjamin Franklin contributed by identifying the currents of the Gulf Stream. Philosophers consider physics before Galileo and Huygens, chemistry before Lavoisier, medicine before Virchow and Bernard, electricity before the mid-eighteenth century, and the study of heredity and phylogeny before the mid-nineteenth century as protosciences that eventually became established science. Prior to 1905, leading scientists, Ostwald and Mach, viewed atomic and molecular-kinetic theory as a protoscience, a theory indirectly supported by chemistry and statistical thermodynamics; however, Einstein's theory of Brownian motion, and Perrin's experimental verification led to widespread acceptance of atomic and molecular-kinetic theory as established science. The early stage of plate tectonics, beginning with Wegener's theory of continental drift, was a protoscience until experimental research confirmed the theory many years later. The initial widespread rejection of Wegener's theory is an example of the importance of not dismissing a protoscience. === Psychology === Critics state that psychology is a protoscience because some practices occur that prevent falsification of research hypotheses. Folk psychology and coaching psychology are protosciences. === Medicine === The use of scientifically invalid biomarkers to identify adverse outcomes is a protoscience practice in medicine. The process for reporting adverse medical events is a protoscience because it relies on uncorroborated data and unsystematic methods. === Technology === Hatleback describes cybersecurity as a protoscience that lacks transparency in experimentation, scientific laws, and sound experimental design in some cases; however cybersecurity has the potential to become a science. == See also == History of science Hypothesis Pseudoscience Methodical culturalism Natural philosophy Obsolete scientific theories Pathological science == Notes == == References == == External links == "Questions to help distinguish a pseudoscience from a protoscience". 7 January 2012. Archived from the original on 2012-01-07.
Wikipedia/Protoscience
A non-science is an area of study that is not scientific, especially one that is not a natural science or a social science that is an object of scientific inquiry. In this model, history, art, and religion are all examples of non-sciences. == Classifying knowledge == Since the 17th century, some writers have used the word science to exclude some areas of studies, such as the arts and the liberal arts. The word nonscience, to describe non-scientific academic disciplines, was first used in the middle of the 19th century. In some cases, it can be difficult to identify exact boundaries between science and non-science. The demarcation problem is the study of the difficulties in determining whether certain fields of study, near the boundaries of science and non-science, should be considered as one or the other. No single test has yet been devised that can clearly separate science from non-science, but some factors, taken as a whole and evaluated over time, are commonly used. In the view of Thomas Kuhn, these factors include the desire of scientists to investigate a question as if it were a puzzle. Kuhn's view of science is also focused on the process of scientific inquiry, rather than the result. Boundary-work is the process of advocating for a desired outcome in the process of classifying fields of study that are near the borders. The rewards associated with winning a particular classification suggest that the boundary between science and non-science is socially constructed and ideologically motivated rather than representing a stark natural difference between science and non-science. The belief that scientific knowledge (e.g., biology) is more valuable than other forms of knowledge (e.g., ethics) is called scientism. == Areas of non-science == Non-science includes all areas of study that are not science. Non-science encompasses all of the humanities, including: history, including the history of science, the language arts, such as literature and language learning, philosophy, ethics, and religion, and art, including music, performing arts, fine arts, and crafts. The philosopher Martin Mahner proposed calling these academic fields the parasciences, to distinguish them from disreputable forms of non-science, such as pseudoscience. Non-sciences offer information about the meaning of life, human values, the human condition, and ways of interacting with other people, including studies of cultures, morality and ethics. == Areas of disagreement == Philosophers disagree about whether areas of study involving abstract concepts, such as pure mathematics, are scientific or non-scientific. Interdisciplinary studies may cover knowledge-generating work that includes both scientific and non-scientific studies. Archaeology is an example of a field that borrows from both the natural sciences and history. Fields of inquiry may change status over time. For many centuries, alchemy was accepted as scientific: it produced some useful information, and it supported experiments and open inquiry in the pursuit of understanding the physical world. Since the 20th century, it has been considered a pseudoscience. Modern chemistry, which developed out of alchemy, is considered a major natural science. == Alternative systems == Some philosophers, such as Paul Feyerabend, object to the effort to classify knowledge into science and non-science. The distinction is artificial, as there is little or nothing that ties together all of the bodies of knowledge that are called "sciences". Some systems of organizing knowledge separate systematic knowledge from non-systematic methods of knowing or learning something, such as personal experiences, intuition, and innate knowledge. Wissenschaft is a broad concept that encompasses reliable knowledge without making a distinction between subject area. The Wissenschaft concept is more useful than the distinction between science and non-science in distinguishing between knowledge and pseudo-knowledge, as the errors made in all forms of pseudo-scholarship, from pseudohistory to pseudoscience, are similar. This Wissenschaft concept is used in the 2006 list of Fields of Science and Technology published by the Organisation for Economic Co-operation and Development, which defines "science and technology" as encompassing all humanistic disciplines, including religion and fine art. == See also == Boundary object – an item, such as an animal hide, that can be legitimately studied in different ways by different fields of study Branches of science Liberal arts Hard and soft science Carper's fundamental ways of knowing == References == == External links == Science and Non-Science in Liberal Education in The New Atlantis Why the distinction between science and non-science matters to people Science Should Not Try to Absorb Religion and Other Ways of Knowing in Scientific American
Wikipedia/Non-science
The right to science and culture is one of the economic, social and cultural rights claimed in the Universal Declaration of Human Rights and related documents of international human rights law. It recognizes that everyone has a right to freely participate in culture, to freely share in (to participate and to benefit from) science and technology, and to protection of authorship. == Recognition under international law == The right to science and culture is expressed in Article 27 of the Universal Declaration of Human Rights: (1) Everyone has the right freely to participate in the cultural life of the community, to enjoy the arts and to share in scientific advancement and its benefits. (2) Everyone has the right to the protection of the moral and material interests resulting from any scientific, literary or artistic production of which he is the author. The right to science and culture also appears in Article 15 of the International Covenant on Economic, Social and Cultural Rights: (1) The States Parties to the present Covenant recognize the right of everyone: (a) To take part in cultural life; (b) To enjoy the benefits of scientific progress and its applications; (c) To benefit from the protection of the moral and material interests resulting from any scientific, literary or artistic production of which he is the author. (2) The steps to be taken by the States Parties to the present Covenant to achieve the full realization of this right shall include those necessary for the conservation, the development and the diffusion of science and culture. (3) The States Parties to the present Covenant undertake to respect the freedom indispensable for scientific research and creative activity. (4) The States Parties to the present Covenant recognize the benefits to be derived from the encouragement and development of international contacts and co-operation in the scientific and cultural fields. == Related concepts and disambiguation == The right to science and culture is often broken into rights such as "the right to take part in cultural life" or "the right to cultural participation" or "the right to culture," and "the right to benefit from scientific progress and its applications" or "the right to benefit from science" or "the right to science" or "the right to share in science". The term "cultural rights" may be used in at least three senses. It is most often used to refer to the concept protected by Article 15 of the International Covenant on Economic, Social and Cultural Rights, which assures minority groups the right to practice and preserve their languages, religions, art forms, and ways of life. Alternatively, the term "cultural rights" may be used to group both minority rights and the right to science and culture, which have a common origin in Article 27 of the Universal Declaration. Even more broadly, "cultural rights" may refer to a larger category of economic, social and cultural rights, which may be understood to refer to the right to science and culture as well as the right to education and other rights, such as the protection of authorship. The "right to science" includes both a right to participate in science (the activity) and a right to access to the body of knowledge ("benefits" or "progress" or "advances") that is a result of science. == Scholarly interpretation and advocacy == All human rights found in the Universal Declaration of Human Rights require a process of interpretation to translate the broad principles into specific state obligations. This takes place through United Nations processes and in national courts. The process is strongly influenced by human rights scholars and human rights activists. The rights found in Article 27 in some ways remain at a relatively early stage in this process, in contrast to other human rights such as the right to health or the right to education that have already been the subject of more extensive elaboration and litigation. The right to authorship has however benefitted from very strong legal development. Common global standards for application of the right to science were set out by a UN agreement called the Recommendation on Science and Scientific Researchers, adopted by consensus of some 195 governments meeting in Paris on 13 November 2017, after four years of global consultations. Some authors particularly active in this area include: Samantha Besson, Audrey R. Chapman, Yvonne Donders, Laurence Helfer, Lea Shaver, William Schabas, Jessica Wyndham, and Peter Yu. The American Association for the Advancement of Science is active in advocacy around the right to science and culture, with a particular focus on the rights and responsibilities of professional scientists. == Official interpretations == The Committee on Economic, Social and Cultural Rights has issued two General Comments interpreting portions of the right to science and culture as it appears in the International Covenant on Economic Social and Cultural Rights (ICESCR). General Comment 17 and General Comment 21. The Special Rapporteur in the Field of Cultural Rights, Farida Shaheed, addressed the right to science and culture in several reports between 2010 and 2015. At the General Conference of UNESCO in 2017, some 195 states agreed by consensus with no abstentions to common global standards relating to the right to science, in a Recommendation on Science and Scientific Researchers, which interprets the right to science as it appears in the Universal Declaration of Human Rights. == Relationship to intellectual property == In 2000 the United Nations Economic and Social Council Sub-commission on Human Rights suggested that the Agreement on Trade-Related Aspects of Intellectual Property Rights may violate the right to science and therefore conflict with international human rights law. == See also == == References ==
Wikipedia/Right_to_science_and_culture
Science & Vie (French pronunciation: [sjɑ̃seˈvi]; Science and Life) is a monthly science magazine published in France. Its headquarters is in Paris. == History and profile == The magazine was started in 1913 with the name La Science et la Vie. In 1982, a spinoff computer magazine, Science et Vie micro (SVM) was launched. The first magazine was published at the end of 1983 and was such a success that the number of copies were insufficient on the market. Another spinoff for teenagers, Science & Vie Junior was started in 1986. It was first published by Excelsior Publications until the latter was bought by Emap Plc in 2003. In June 2006 the magazine became part of Mondadori France. In July 2019, the magazine was sold to Reworld Media. Science & Vie was divided in three sections, Science (Sciences), Technologie (Technology), Vie Pratique (Daily life). While the Science section reported on recent scientific progress, the Technology section would report on recent technical advances. Science & Vie covered technical advances in industry, but also in military technology. In particular, it featured articles on explosives, firearms, chemical weapons and nuclear weapons. The Vie Pratique section was concerned with technology in daily life. It included articles on photography, personal computers, video recording equipment or television. Besides these three sections, Science & Vie contained a section on amateur electronics by Henri-Pierre Penel, a section on amateur astronomy La Calculette de l'Astronome, and two sections on computer programming in BASIC, one on video games (first for the Sinclair ZX81, and then the ZX Spectrum) and another of elementary numerical analysis, Le Micro de l'Ingénieur (with listings for the Apple II). This made Science & Vie a more popular magazine (both in terms of circulation and in terms of the level of education of its readers) than La Recherche or Pour la Science which are only concerned with science, or Industries & Techniques which only deals with applications of technology in industry. Another important distinctive feature of Science & Vie was its willingness to tackle the issue of pseudoscience. The magazine was very critical of astrology, homeopathy, and pseudoscience. With the help of magician Gérard Majax, it has exposed the tricks used by Uri Geller to bend spoons and make small objects fly. In 1989, it strongly criticized the claims of Jacques Benveniste of having observed water memory. The magazine also uncovered the fabrication of the autopsy of an alien body supposedly discovered in Roswell, New Mexico. The magazine was also very supportive of Henri Broch's debunking of paranormal claims. In general, articles on paranormal topics were marked as Blurgs, an acronym for Balivernes lamentables à l'usage réservé des gogos ("deplorable nonsense reserved for use by the gullible"). Since being bought by Mondadori, the magazine has adopted a less skeptical line. In 2004 Science & Vie sold 361,273 copies. In 2010 the circulation of the magazine was 281,000 copies. == References == == External links == Science & Vie website (in French) Science & Vie Micro website (in French) Science & Vie Junior website (in French) Index of past issues of Science & Vie (in French) Index of past issues of Science & Vie Micro (in French)
Wikipedia/Science_&_Vie
Rhetoric of science is a body of scholarly literature exploring the notion that the practice of science is a rhetorical activity. It emerged after a number of similarly oriented topics of research and discussion during the late 20th century, including the sociology of scientific knowledge, history of science, and philosophy of science, but it is practiced most typically by rhetoricians in academic departments of English, speech, and communication. == Overview == Rhetoric is best known as a discipline that studies the means and ends (i.e., methods and goals) of persuasion. Science, meanwhile, is typically considered to be the discovery and recording of knowledge about nature. A major contention of the rhetoric of science is that the practice of science itself is, to varying degrees, persuasive. The study of science from the viewpoint of rhetoric variously examines modes of inquiry, logic, argumentation, the ethos of scientific practitioners, the structures of scientific publications, and the character of scientific discourse and debates. For instance, scientists must convince their community of scientists that their research is based on sound scientific method. In terms of rhetoric, the scientific method involves problem-solution topoi (the materials of discourse) that demonstrate observational and experimental competence (arrangement or order of discourse or method), and as a means of persuasion, offer explanatory and predictive power.: 185–193  Experimental competence is itself a persuasive topos.: 186  Rhetoric of science is a practice of suasion that is an outgrowth of some of the canons of rhetoric. == History == Since its flourishing during the 1970s, rhetoric of science has contributed to a shift of opinions concerning science to include the claim that there is not any single scientific method, but rather a plurality of methods or styles.: xvi  The rhetoric of science has included various sub-topics, as indicated by these examples. John Angus Campbell has studied the works of Charles Darwin with the intention of showing Darwin's rhetorical manipulations and strategic use of the social beliefs of his time. Carolyn Miller has emphasized genres within technology and the influence of technology on genre change. Jeanne Fahnestock has identified the use of classical rhetoric in scientific reasoning and argument. Greg Myers has studied how scientific publications, grants, and other scientific texts are the result of social processes and the pragmatics of politeness in scientific discussions. Charles Bazerman's examination of the evolution of the varieties of writing characterized as experimental report through the first century and a half of the Philosophical Transactions of the Royal Society, the formation of social roles and norms concerning the publication of this journal, the Physical Review since its founding in 1893, and the evolution of the Publication Manual of the American Psychological Association, along with scrutiny of works by Newton and Compton, and an analysis of the reading habits of physicists indicate the many social, organizational, ideological, political, theoretical, methodological, evidentiary, intertextual and intellectual factors that have influenced the character of writing and rhetoric. Bazerman's work has built upon these studies to consider the way knowledge is methodically produced and communicatively circulated in various activity systems. His work follows the lead of Ludwik Fleck on Thought Collectives and thought styles, structuration theory and phenomenology. Other rhetoricians consider the rhetoric of science effectively beginning with Thomas Kuhn'sThe Structure of Scientific Revolutions (1962). Kuhn first examines "normal" science, that is, practices which he considered routine, patterned and accessible with a specific method of problem-solving. Normal science advances by building on past knowledge, through the accretion of further discoveries in a knowledge base.: xiii  Kuhn then contrasts normal science with "revolutionary" science (new science marked by a paradigm shift in thought). When Kuhn began to teach Harvard undergraduates historical texts such as Aristotle's writings on motion, he examined case studies, and sought first to understand Aristotle in his own time, and then to locate his problems and solutions within a wider context of contemporary thought and actions. : 144  That is to say, Kuhn sought first to understand the traditions and established practices of science.: 162  In this instance, Michael Polanyi's influence on Kuhn becomes apparent; that is, his acknowledgement of the importance of inherited practices and rejection of absolute objectivity. Observing the changes in scientific thought and practices, Kuhn concluded that revolutionary changes happen through the defining notion of rhetoric: persuasion.: xiv  The critical work of Herbert W. Simons – "Are Scientists Rhetors in Disguise?" in Rhetoric in Transition (1980) – and subsequent works show that Kuhn's Structure is fully rhetorical. The work of Thomas Kuhn was extended by Richard Rorty (1979, 1989), and this work was to prove fruitful in defining the means and ends of rhetoric in scientific discourse (Jasinski "Intro" xvi). Rorty, who invented the phrase "rhetorical turn", was also interested in assessing periods of scientific stability and instability. Another component of the shift in science that occurred during the past concerns the claim that there is no single scientific method, but rather a plurality of methods or styles.: xvi  Paul Feyerabend in Against Method (1975) contends that science has found no "method that turns ideologically contaminated ideas into true and useful theories", in other words; no special method exists that can guarantee the success of science (302). As evidenced by the early theory papers after Kuhn's seminal work, the idea that rhetoric is crucial to science became much discussed. Quarterly journals in speech and rhetoric included much discussion of topics such as inquiry, logic, argument fields, ethos of scientific practitioners, argumentation, scientific text, and the character of scientific discourse and debates. Philip Wander (1976) observed, for instance, the phenomenal penetration of science (public science) in modern life. He labelled the obligation of rhetoricians to investigate science's discourse "The Rhetoric of Science" (Harris "Knowing" 164). As rhetoric of science began to flourish, discussion began of a number of topics, including: Epistemic rhetoric and the discourses on the nature of semantics, knowledge, and truth: One example is the Robert L. Scott's work on viewing rhetoric as epistemic (1967). By the 1990s, epistemic rhetoric was a point of contention in the writing of Dilip Gaonkar (see "Critique" below). The early 1970s Speech Communication Conference ("Wingspread conference") gave recognition to the fact that rhetoric, in its globalization (multidisciplinary nature), has become a universal hermeneutic (Gross Rhetorical 2–5). Much scholastic output evolved concerning the theory of interpretation (hermeneutics), the knowledge-making and truth-seeking (epistemic) potential of rhetoric of science. Argument Fields (part of the Speech Communication Association and American forensic Association program): In this domain the work of Toulmin on argument appeals is exemplary. In addition, Michael Mulkay, Barry Barnes and David Bloor, as pioneers of the "Sociology of Scientific Knowledge" (SSK) movement, fostered a growing sociobiology debate. Others as Greg Myers expressed the benefits of a collaboration between rhetoricians and sociologists. Contributors to discussion pertaining to audience – the way arguments change as they move from the scientific community to the public – include John Lyne and Henry Howe.: xxi–xxxii  Scientific Giants: The important works that investigate the suasive powers of exemplars in science include those of Alan G. Gross (Newton, Descartes, argument fields in optics), John Angus Campbell (Darwin), and Michael Halloran (Watson and Crick). J. C. Maxwell introduced differentiable vector fields E and B to express Michael Faraday's findings about an electric field E and a magnetic field B. Thomas K. Simpson has described his rhetorical methods, first with a guided study, then a literary appreciation of A Treatise on Electricity and Magnetism (1873), and with a book attending to the mathematical rhetoric. Other major themes in rhetoric of science include the investigation of the accomplishments and suasive abilities of individuals (ethos) who have become influential in their respective sciences as well as an age old concern of rhetoric of science – public science policy. Science policy involves deliberative issues, and the first rhetorical study of science policy was made in 1953 by Richard M. Weaver. Among others, Helen Longino's work on public policy implications of low-level radiation continues this tradition.: 622  The reconstitution of rhetorical theory around the lines of invention (inventio), argumentation and stylistic adaptation is occurring currently (Simons 6). The major question is whether training in rhetoric can in fact help scholars and investigators make intelligent choices between rival theories, methods or data collection, and incommensurate values (Simons 14). Rhetoric of science is also an important theoretical body for rhetoric and composition studies in higher education. This body of work examines how to best prepare communicators for participation with science, such as in the work of Michael Zerbe, Carl Herndl, and Caroline Gottschalk Druschke. Through rhetorical historiography Madison Jones seeks to unearth the influence of other disciplines, such as ecology, on the ways contemporary rhetoricians theorize and define rhetorical inquiry. Interdisciplinary and transdisciplinary collaboration in science also complicates rhetoric and composition pedagogy and provides a new emphasis on collaborative writing across scientific disciplines and with community groups and stakeholds. == Developments and trends == === Epistemic rhetoric === Considering science fin terms of texts exhibiting epistemology based on prediction and control offers new comprehensive ways to consider the function of rhetoric of science (Gross "The Origin" 91–92). Epistemic rhetoric of science, in a broader context, confronts issues pertaining to truth, relativism, and knowledge. Rhetoric of science, as a type of inquiry, does not consider natural science texts as a means of conveying knowledge, but rather it considers these texts as exhibiting persuasive structures. Although the natural sciences and humanities differ in a fundamental manner, the enterprise of science can be considered hermeneutically as a stream of texts which exhibit an epistemology based on understanding (Gross "On the Shoulders 21). Its task then is the rhetorical reconstruction of the means by which scientists convince themselves and others that their knowledge claims and assertions are an integral part of privileged activity of the community of thinkers with which they are allied (Gross "The Origin" 91). In an article titled "On Viewing Rhetoric as Epistemic" (1967), Robert L. Scott offers "that truth can arise only from cooperative critical inquiry" (Harris "Knowing" 164). Scott's probe of the issues of belief, knowledge and argumentation substantiates that rhetoric is epistemic. This train of thought goes back to Gorgias who noted that truth is a product of discourse, not a substance added to it (Harris "Knowing" 164). Scientific discourse is built on accountability of empirical fact which is presented to a scientific community. Each form of communication is a type of genre that fosters human interaction and relations. An example is the emerging form of the experimental report (Bazerman "Reporting" 171–176). The suite of genres to which the rhetoric of science comes to bear on health care and scientific communities is legion. Aristotle could never accept the unavailability of certain knowledge, although most now believe the contrary (Gross "On Shoulders" 20). That is to say, Aristotle would have rejected the main concern of rhetoric of science: knowledge.: 622  Knowing itself generates the explanation of knowing, and this is the domain of the theory of knowledge. The knowledge of knowledge compels an attitude of vigilance against the temptation of certainty (Maturana 239–245). The claim of the epistemic problematic of rhetoric of science concerns: truth - property of statements with respect to other statements knowledge - configuration of mutually supporting true statements arguments - are situational (first principle of rhetoric) (Harris "Knowing" 180–181). === Argument fields === By the 1980s, Stephen Toulmin's work on argument fields published in his book titled The Uses of Argument (1958) came to prominence through rhetorical societies such as the Speech Communication Association which adopted a sociological consideration of science. Toulmin's main contribution is his notion of argument fields that included a reinvention of the rhetorical concept topoi (topics).: xxi  Toulmin discusses at length the pattern of an argument – data and warrants to support a claim – and how they tend to vary across argument fields (Toulmin 1417–1422). He delineated two concepts of argumentation, one which relied on universal (field-invariant) appeals and strategies, and one which was field dependent, particular to disciplines, movements, and the like. For Toulmin, audience is important because one speaks to a particular audience at a particular point in time, and thus an argument must be relevant to that audience. In this instance, Toulmin echoes Feyerabend, who in his preoccupation with suasive processes, makes clear the adaptive nature of persuasion.: xxv  Toulmin's ideas pertaining to argument were a radical import to argumentation theory because, in part, he contributes a model, and because he contributes greatly to rhetoric and its subfield, rhetoric of science, by providing a model of analysis (data, warrants) to show that what is argued on a subject is in effect a structured arrangement of values that are purposive and lead to a certain line of thought. Toulmin showed in Human Understanding that the arguments that would support claims as different as the Copernican revolution and the Ptolemaic revolution would not require mediation. On the strength of argument, men of the sixteenth and seventeenth centuries converted to Copernican astronomy (Gross "The Rhetoric" 214). === Incommensurability === The rhetorical challenge presently is to find discourse that crosses disciplines without sacrificing the specifics of each discipline. The objective is to render description of these disciplines intact – that is to say, the goal of finding language that would make various scientific topics "commensurable". In contrast, incommensurability is a situation where two scientific programs are fundamentally at odds. Two important authors who applied incommensurability to historical and philosophical notions of science during the 1960s are Thomas Kuhn and Paul Feyerabend. Various strands grew out of this idea that bear on issues of communication and invention. These strands are explicated in Randy Allen Harris's four-part taxonomy that in turn emphasizes his viewpoint that "incommensurability is best understood not as a relation between systems, but as a matter of rhetorical invention and hermeneutics" (Harris "Incommensurability" 1). Incommensurability of theory at times of radical theory change is the basis of Thomas Samuel Kuhn's theory of paradigms (Bazerman 1). Kuhn's Structure of Scientific Revolutions offers a vision of scientific change that involves persuasion, and thus he brought rhetoric to the heart of scientific studies.: xiii  Kuhn's Structure provides important accounts related to the concept representation, and the key conceptual changes that occur during a revolution in science. Kuhn sought to determine ways of representing concepts and taxonomies by frames.: 224–230  Kuhn's work attempts to show that incommensurable paradigms can be rationally compared by revealing the compatibility of attribute lists of say a species outlined in a pre-Darwinian and a post-Darwinian milieu accounted for in two incommensurable taxonomies, and that this compatibility is the platform for rational comparison between rival taxonomies.: 230, 1  With a view to comparing normal science to revolutionary science, Kuhn illustrates his theory of paradigms and theory of concepts within the history of electricity, chemistry and other disciplines. He gives attention to the revolutionary changes that came about as a result of the work of Nicolaus Copernicus, Isaac Newton, Albert Einstein, Wilhelm Röntgen, and Antoine Lavoisier. Some scholars, like Thomas C. Walker, feel that Kuhn's theory of paradigms implies knowledge that is "gained in small, incremental, and almost unremarkable installments." Walker states that while "normal science is narrow, rigid, esoteric, uncritical, and conservative, Kuhn considers it to be the most efficient way to ensure a cumulation of knowledge." According to Walker, while "ignorance and intolerance toward other theoretical frameworks are regrettable features of Kuhn's normal science...meaningful conversations can only occur within a single paradigm." Kuhn's work was influential for rhetoricians, sociologists, and historians (and, in a lesser manner, philosophers) for the development of a rhetorical perspective. His opinion concerning perception, concept acquisition and language suggest, according to Paul Hoyningen-Huene's analysis of Kuhn's philosophy, a cognitive perspective.: 183  === Ethos === Scientists are not just persuaded by logos or argument. Innovative initiatives in science test scientific authority by invoking the authority of past results (initial section of a scientific paper) and the authority of procedure, which establish the scientist's credibility as an investigator (Gross Starring 26–27). Examinations of the ethos of scientists (individually and collectively) spawned significant contributions in the topic of rhetoric of science. Michael Halloran notes in "The Birth of Molecular Biology" (Rhetoric Review 3, 1984) – an essay that is a rhetorical analysis of James D. Watson and Francis H. Crick's "A Structure for Deoxyribose Nucleic Acid" – that a large part of what constitutes a scientific paradigm is the ethos of its practitioners. This ethos is about an attitude and a way of attacking problems and propagating claims.: xxxi  In "The Rhetorical Construction of Scientific Ethos," Lawrence Prelli provides a systematic analysis of ethos as a tool of scientific legitimation. Prelli's work examines the exchange of information in the court of public opinion. His work provides insight into the ways in which scientific argumentation is legitimized, and thus insight into public science policy. One of the domains of rhetoric is civic life. Rhetorical criticism of science offers much in the investigation of scientific matters that impinge directly upon public opinion and policy-making decisions.: xxxiii  === Rhetoric and language-games === Rhetoric can also be defined as the strategic use of language: each scientist tries to make those statements that - given the statements made by their colleagues, and the ones the former expects they will do in the future (e.g., accepting or rejecting the claims made by the former) - maximise the chances of the former's attaining the goals he or she has. So, game theory can be applied to study the choice of the claims one scientist makes. Zamora Bonilla argues that, when rhetoric is understood this way, it can be discussed whether the way scientists interact - e.g., through certain scientific institutions like peer review - causes them to make their claims in an efficient or an inefficient way, that is, whether the 'rhetorical games' are more analogous to invisible hand processes, or to prisoner's dilemma games. If the former is the case, then we can assert that scientific 'conversation' is organised in such a manner that the strategic use of language by scientists causes them to attain cognitive progress, and if the opposite is the case, then this would be an argument to reform scientific institutions. === Rhetorical figures in science === Corresponding to distinct lines of reasoning, figures of speech are evident in scientific arguments. The same cognitive and verbal skills that are of service to one line of inquiry – political, economic or popular – are of service to science (Fahnestock 43). This implies that there is less of a division between science and the humanities than anticipated initially. Argumentatively useful figures of speech are found everywhere in scientific writing. Theodosius Dobzhansky in Genetics and the Origin of Species offers a means of reconciliation between Mendelian mutation and Darwinian natural selection. By remaining sensitive to the interests of naturalists and geneticists, Dobzhansky – through a subtle strategy of polysemy – allowed a peaceful solution to a battle between two scientific territories. His expressed objective was to review the genetic information bearing on the problem of organic diversity.: 41, 53  The building blocks of Dobzhansky's interdisciplinary influence that included much development in two scientific camps were the result of the compositional choices he made. He uses, for instance, prolepsis to make arguments that introduced his research findings, and he provided a metaphoric map as a means to guide his audience.: 57, 8  One illustration of metaphor is his use of the term "adaptive landscapes". Considered metaphorically, this term is a way of representing how theorists of two different topics can unite.: 57  Another figure that is important as an aid to understanding and knowledge is antimetabole (refutation by reversal). Antithesis also works toward a similar end. An example of antimetabole: Antimetabole often appears in writing or visuals where the line of inquiry and experiment has been characterized by mirror-image objects, or of complementarity, reversible or equilibrium processes. Louis Pasteur's revelation that many organic compounds come in left-and right-handed versions or isomers as articulated at an 1883 lecture illustrates the use of this figure. He argues in lecture that "life is the germ and the germ is life" because all life contains unsymmetrical/asymmetrical processes (Fahnestock 137–140). === New Materialist Rhetoric of Science === A more recent trend in rhetorical studies involves participation with the broader new materialist ideas concerning philosophy and science and technology studies. This new topic of inquiry investigates the role of rhetoric and discourse as an integral part of the Materialism of scientific practice. This method considers how the methods of natural sciences came into being, and the particular role interaction among scientists and scientific institutions has to play. New materialist rhetoric of science include those proponents who consider the progress of the natural sciences as having been obtained at a high cost, a cost that limits the scope and vision of science. Work in this area often draws on scholarship by Bruno Latour, Steve Woolgar, Annemarie Mol, and other new materialist scholars from science and technology studies. Work in new materialist rhetoric of science tends to be very critical of a perceived over-reliance on language in more conservative variants of rhetoric of science and has significantly criticized long-standing areas of inquiry such as incommensurability studies. === Critique of rhetoric of science === ==== Globalization of rhetoric ==== Renewed interest today in rhetoric of science is its positioning as a hermeneutic meta-discourse rather than a substantive discourse practice.: 25  Exegesis and hermeneutics are the tools around which the idea of scientific production has been forged. Criticism of rhetoric of science is mainly limited to discussions of the concept of hermeneutics, which can be considered as follows: Rhetorical hermeneutics is about a way of reading texts as rhetoric. Rhetoric is both a discipline and a perspective from which disciplines can be viewed. As a discipline, it has a hermeneutic task and generates knowledge; as a perspective, it has the task of generating new points of view (Gross Rhetorical 111). Whether rhetorical theory can function as a general hermeneutic, a key to all texts, including scientific texts, is still today a point of interest to rhetoricians. Although natural sciences and humanities differ in fundamental ways, science as enterprise can be viewed hermeneutically as a suite of texts exhibiting a study of knowledge (epistemology) based on understanding (Gross "On Shoulders" 21). A recent critique about the rhetoric of science literature asks not if science is understood properly, but rather if rhetoric is understood properly. This dissension concerns the reading of scientific texts rhetorically; it is a quarrel about how rhetorical theory is considered as a global hermeneutic (Gross "Intro" Rhetorical 1–13). Dilip Gaonkar in "The Idea of Rhetoric in the Rhetoric of Science" examines how critics argue about rhetoric, and he unfolds the global ambitions of rhetorical theory as a general hermeneutic (a master key to all texts), with the rhetoric of science as a perfect site of analysis - a hard and fast case. In his analysis of this 'case', Gaonkar looks at rhetoric's essential character first in traditional sense (Aristotilean and Ciceronian). Then he examined at the practice of rhetoric and the model of persuasive speech from the point of agency (productive orientation) or who controls the speech (means of communication). The rhetorical tradition is one of practice, while the theory evinces practice and teaching (Gross "Intro" Rhetorical 6–11). Gaonkar asserts that rhetoric considered as a tradition (Aristotilean and Ciceronia), and from the point of view of interpretation (not production or agency), rhetorical theory is "thin." He argues that rhetoric appears as a slightly disguised language of criticism in such a way that it is applicable to almost any discourse.: 33, 69  Gaonkar believes that this type of globalization of rhetoric undermines rhetoric's self-representation as a situated practical art, and in so doing, it runs counter to a humanist tradition. It runs counter to the interpretative function of a critical metadiscourse. If there is no more substance, no anchor, no reference to which rhetoric is attached, rhetoric itself is the substance, or the supplement, and thus becomes substantial, giving rise to the question how well rhetoric functions as interpretative discourse.: 77  Dilip Gaonkar's provocations have begun a broad reaching discussion that resulted in the defense of rhetoric analyses of scientific discourse. Responses to Gaonkar's provocations are many, of which two examples follow. When Gaonkar asks if a theory grounded in practice can be translated into a theory of interpretation, Michael Leff in "The Idea of Rhetoric as Interpretative Practice: A Humanist's Response to Gaonkar" see his views as too extreme, treating as opposites two positions that are in dialectic tension (rhetoric as production and rhetoric as interpretation), and separating interpretation from practice in order to establish a causal, rather than accidental, relationship between rhetoric and the globalalization of rhetoric (Gross "Intro" Rhetorical 11). John Angus Campbell in "Strategic Readings: Rhetoric, Intention, and Interpretation" also found in Rhetorical Hermeneutics is a verification of Leff's analysis (113). He argues, however, against Gaonkar's notion of invention and the mediation between producer or writer and the audience of a text(114). The differences between Campbell and Gaonkar is one of theory, and not whether agency figures in criticism (115). ==== New Materialist Rhetoric of Science ==== The new materialist method of rhetoric of science has endorsed Goankar's criticisms of rhetoric of science more generally and seeks to overcome them through interdisciplinary engagement with science and technology studies. However, the new materialist approach, itself, has been subjected to significant criticism within the field, and identified as a radical variant. The question as to the adequacy of rhetoric in its encounter with scientific texts (natural sciences) is problematic for two reasons. The first concerns traditional rhetoric and its capacity to analyze scientific texts. Secondly, the answer to the question relies on an attack of the epistomological presuppositions of a classical rhetoric of science. For this reason, the radical critique is a demand for the renewal of rhetorical theory.: 626, 7  == See also == Contingency Demarcation problem Epistemology Falsifiability Rhetoric of health and medicine == References == == Works cited == Bazerman, Charles and René Agustin De los Santos. "Measuring Incommensurability: Are toxicology and ecotoxicology blind to what the other sees?" 9 January 2006. [1]. Bazerman, Charles. "Reporting the Experiment: The Changing Account of Scientific Doings in the Philosophical Transactions of the Royal Society, 1665-1800." In Landmark Essays on Rhetoric of Science: Case Studies. Ed. Randy Allen Harris. Mahwah: Hermagoras Press, 1997. Booth, Wayne C. The Rhetoric of Rhetoric: The Quest for Effective Communication. Malden: Blackwell Publishing, 2004. Campbell, John Angus. "Scientific Discovery and Rhetorical Invention." In The Rhetorical Turn: Inventions and Persuasion in the Conduct of Inquiry. Ed. Herbert W. Simons. Chicago: The University of Chicago Press, 1990. Dawkins, Richard. The Selfish Gene. Oxford: Oxford UP, 1989. Fahnestock, Jeanne. Rhetorical Figures in Science. New York: Oxford UP, 1999. Feyerabend, Paul. Against Method: Outline of an Anarchistic Theory of Knowledge. London: Verso, 1975. Gross, Alan G. "On the Shoulders of Giants: Seventeenth-Century Optics as an Argument Field." In Landmark Essays on Rhetoric of Science: Case Studies. Ed. Randy Allen Harris. Mahwah: Hermagoras Press, 1997. Gross, Alan G., Starring The Text: The Place of Rhetoric in Science Studies. Carbondale: Southern Illinois UP, 2006. Gross, Alan G. "The Origin of Species: Evolutionary Taxonomy as an Example of the Rhetoric of Science". In The Rhetorical Turn: Invention and Persuasion in the Conduct of Inquiry. Ed. Herbert W. Simons. Chicago: The University of Chicago Press, 1990. Gross A., and William M. Keith. Eds. "Introduction." Rhetorical Hermeneutics: Invention and Interpretation in the Age of Science. Albany: State University of New York Press, 1997. Harris, Randy Allen. "Knowing, Rhetoric, Science." In Visions and Revisions: Continuity and Change in Rhetoric and Composition. Ed. James D. Williams. Carbondale: Southern Illinois UP, 2002. Jasinski, James. "Introduction." Sourcebook on Rhetoric: Key Concepts in Contemporary Rhetorical Studies. Thousand Oaks: Sage Publications, 2001. Kuhn, Thomas S. The Structure of Scientific Revolutions. 3rd ed. Chicago: University of Chicago Press, 1996. Maturana, Humberto R., and Varela, Francisco J. The Tree of Knowledge: The Biological Roots of Human Understanding. Boston: Shambhala Publications, Inc., 1987. Toulmin, S. "The Uses of Argument." In The Rhetorical Tradition: Readings from Classical Times to the Present. 2nd ed. Eds. Bizzell, Patricia and Bruce Herzberg. Boston: Bedford, 1990. == Further reading == Bazerman, Charles. Shaping Written Knowledge: The Genre and Activity of the Experimental Article in Science. Madison: University of Wisconsin Press, 1988. [2] (online version). "Reporting the Experiment: The Changing Account of Scientific Doings in the Philosophical Transactions of the Royal Society, 1665-1800" by Charles Bazerman in Landmark Essays on Rhetoric of Science is found in chapter 3 of that text. Campbell, John Angus. "Scientific Revolution and the Grammar of Culture: The Case of Darwin's Origin." Quarterly Journal of Speech 72 (1986):351-376. doi:10.1080/00335638609383782 Gaonkar, Dilip Parameshwar. "Rhetoric and Its Double: Reflections on the Rhetorical Turn in the Human Sciences." In The Rhetorical Turn: Invention and Persuasion in the Conduct of Inquiry. Ed. Herbert W. Simons. Chicago: The University of Chicago Press, 1990. Halloran, S. Michael and Annette Norris Bradford. "Figures of Speech in the Rhetoric of Science and Technology." Essays on Classical Rhetoric and Modern Discourse. Ed. Robert J. Connors et al. Carbondale: Southern Illinois University Press, 1984. Harris, Randy Allen. Ed. Rhetoric and Incommensurability. West Lafayette: Parlor Press, 2005. Latour, Bruno and Steve Woolgar. Laboratory Life: The Social Construction of Scientific Facts. Beverly Hills: Sage, 1979. Leff, Michael. "The Idea of Rhetoric as Interpretative Practice: A Humanist Response to Gaonkar." The Southern Communication Journal 58 (1993): 296–300. doi:10.1080/10417949309372910 Miller, Carolyn. "Genre as Social Action." Quarterly Journal of Speech 70: 151–57. doi:10.1080/00335638409383686 Schryer, Catherine F. "Genre Theory, Health-Care Discourse, and Professional Identity Formation." Journal of Business and Technical Communication 19.3 (2005):249-278. Scott, R. L. "On Viewing Rhetoric as Epistemic." Central States Speech Journal (1967) 18:9-16. doi:10.1080/10510976709362856 Simpson, Thomas K. Figures of Thought: A Literary Appreciation of Maxwell's Treatise on Electricity and Magnetism, 2005, Green Lion Press, ISBN 1-888009-31-4 Stark, Ryan. Rhetoric, Science, and Magic in Seventeenth-Century England. Washington, DC: The Catholic University of America Press, 2009. Waddell, Craig. "The Role of Pathos in the Decision-Making Process: A Study in the Rhetoric of Science Policy." Quarterly Journal of Speech 76 (1990): 381–400. doi:10.1080/00335639009383932 Wander, Philip C. and Dennis Jaehne. "Prospects for 'a rhetoric of science.'" Social Epistemology 14.2/3 (2000): 211–233. 30 December. 2005. [3] (PDF file) Ziman, John (2000). Real Science: what it is, and what it means. Cambridge, Uk: Cambridge University Press.
Wikipedia/Rhetoric_of_science
Science communication encompasses a wide range of activities that connect science and society. Common goals of science communication include informing non-experts about scientific findings, raising the public awareness of and interest in science, influencing people's attitudes and behaviors, informing public policy, and engaging with diverse communities to address societal problems. The term "science communication" generally refers to settings in which audiences are not experts on the scientific topic being discussed (outreach), though some authors categorize expert-to-expert communication ("inreach" such as publication in scientific journals) as a type of science communication. Examples of outreach include science journalism and health communication. Since science has political, moral, and legal implications, science communication can help bridge gaps between different stakeholders in public policy, industry, and civil society. Science communicators are a broad group of people: scientific experts, science journalists, science artists, medical professionals, nature center educators, science advisors for policymakers, and everyone else who communicates with the public about science. They often use entertainment and persuasion techniques including humour, storytelling, and metaphors to connect with their audience's values and interests. Science communication also exists as an interdisciplinary field of social science research on topics such as misinformation, public opinion of emerging technologies, and the politicization and polarization of science. For decades, science communication research has had only limited influence on science communication practice, and vice-versa, but both communities are increasingly attempting to bridge research and practice. Historically, academic scientists were discouraged from spending time on public outreach, but that has begun to change. Research funders have raised their expectations for researchers to have broader impacts beyond publication in academic journals. An increasing number of scientists, especially younger scholars, are expressing interest in engaging the public through social media and in-person events, though they still perceive significant institutional barriers to doing so. Science communication is closely related to the fields of informal science education, citizen science, and public engagement with science, and there is no general agreement on whether or how to distinguish them. Like other aspects of society, science communication is influenced by systemic inequalities that impact both inreach and outreach. == Motivations == Writing in 1987, Geoffery Thomas and John Durant advocated various reasons to increase public understanding of science, or scientific literacy. More trained engineers and scientists could allow a nation to be more competitive economically.: 11–17  Science can also benefit individuals. Science can simply have aesthetic appeal (e.g., popular science or science fiction). Living in an increasingly technological society, background scientific knowledge can help to negotiate it. The science of happiness is an example of a field whose research can have direct and obvious implications for individuals. Governments and societies might also benefit from more scientific literacy, since an informed electorate promotes a more democratic society. Moreover, science can inform moral decision making (e.g., answering questions about whether animals can feel pain, how human activity influences climate, or even a science of morality). In 1990, Steven Hilgartner, a scholar in science and technology studies, criticized some academic research in public understanding of science. Hilgartner argued that what he called "the dominant view" of science popularization tends to imply a tight boundary around those who can articulate true, reliable knowledge. By defining a "deficient public" as recipients of knowledge, the scientists get to emphasize their own identity as experts, according to Hilgartner. Understood in this way, science communication may explicitly exist to connect scientists with the rest of society, but science communication may reinforce the boundary between the public and the experts (according to work by Brian Wynne in 1992 and Massimiano Bucchi in 1998). In 2016, the scholarly journal Public Understanding of Science ran an essay competition on the "deficit model" or "deficit concept" of science communication and published a series of articles answering the question "In science communication, why does the idea of a public deficit always return?" in different ways; for example, Carina Cortassa's essay argued that the deficit model of science communication is just a special case of an omnipresent problem studied in social epistemology of testimony, the problem of "epistemic asymmetry", which arises whenever some people know more about some things than other people. Science communication is just one kind of attempt to reduce epistemic asymmetry between people who may know more and people who may know less about a certain subject. Biologist Randy Olson said in 2009 that anti-science groups can often be so motivated, and so well funded, that the impartiality of science organizations in politics can lead to crises of public understanding of science. He cited examples of denialism (for instance, climate change denial) to support this worry. Journalist Robert Krulwich likewise argued in 2008 that the stories scientists tell compete with the efforts of people such as Turkish creationist Adnan Oktar. Krulwich explained that attractive, easy to read, and cheap creationist textbooks were sold by the thousands to schools in Turkey (despite their strong secular tradition) due to the efforts of Oktar. Astrobiologist David Morrison has spoken of repeated disruption of his work by popular anti-scientific phenomena, having been called upon to assuage public fears of an impending cataclysm involving an unseen planetary object—first in 2008, and again in 2012 and 2017. == Methods == Science popularization figures such as Carl Sagan and Neil deGrasse Tyson are partly responsible for the view of science or a specific science discipline within the general public. However, the degree of knowledge and experience a science popularizer has can vary greatly. Because of this, some science communication can depend on sensationalism. As a Forbes contributor put it, "The main job of physics popularizers is the same as it is for any celebrity: get more famous." Another point in the controversy of popular science is the idea of how public debate can affect public opinion. A relevant and highly public example of this is climate change. A science communication study appearing in The New York Times proves that "even a fractious minority wields enough power to skew a reader's perception of a [science news] story" and that even "firmly worded (but not uncivil) disagreements between commenters affected readers' perception of science." This causes some to worry about the popularizing of science in the public, questioning whether the further popularization of science will cause pressure towards generalization or sensationalism. Marine biologist and film-maker Randy Olson published Don't Be Such a Scientist: Talking Substance in an Age of Style. In the book he describes how there has been an unproductive negligence when it comes to teaching scientists to communicate. Don't be Such a Scientist is written to his fellow scientists, and he says they need to "lighten up". He adds that scientists are ultimately the most responsible for promoting and explaining science to the public and media. This, Olson says, should be done according to a good grasp of social science; scientists must use persuasive and effective means like story telling. Olson acknowledges that the stories told by scientists need not only be compelling but also accurate to modern science—and says this added challenge must simply be confronted. He points to figures like Carl Sagan as effective popularizers, partly because such figures actively cultivate a likeable image. At his commencement address to Caltech students, journalist Robert Krulwich delivered a speech entitled "Tell me a story". Krulwich says that scientists are actually given many opportunities to explain something interesting about science or their work, and that they must seize such opportunities. He says scientists must resist shunning the public, as Sir Isaac Newton did in his writing, and instead embrace metaphors the way Galileo did; Krulwich suggests that metaphors only become more important as the science gets more difficult to understand. He adds that telling stories of science in practice, of scientists' success stories and struggles, helps convey that scientists are real people. Finally, Krulwich advocates for the importance of scientific values in general, and helping the public to understand that scientific views are not mere opinions, but hard-won knowledge. Actor Alan Alda helped scientists and PhD students get more comfortable with communication with the help of drama coaches (they use the acting techniques of Viola Spolin). Matthew Nisbet described the use of opinion leaders as intermediaries between scientists and the public as a way to reach the public via trained individuals who are more closely engaged with their communities, such as "teachers, business leaders, attorneys, policymakers, neighborhood leaders, students, and media professionals". Examples of initiatives that have taken this approach include Science & Engineering Ambassadors, sponsored by the National Academy of Sciences, and Science Booster Clubs, coordinated by the National Center for Science Education. === Evidence based practices === Similar to how evidence-based medicine gained a foothold in medical communication decades ago, researchers Eric Jensen and Alexander Gerber have argued that science communication would benefit from evidence-based prescriptions since the field faces related challenges. In particular, they argued that the lack of collaboration between researchers and practitioners is a problem: "Ironically, the challenges begin with communication about science communication evidence.": 2  The overall effectiveness of the science communication field is limited by the lack of effective transfer mechanisms for practitioners to apply research in their work and perhaps even investigate, together with researchers, communication strategies, Jensen and Gerber said. Closer collaboration could enrich the spectrum of science communication research and increase the existing methodological toolbox, including more longitudinal and experimental studies. Evidence-based science communication would combine the best available evidence from systematic research, underpinned by established theory, as well as practitioners' acquired skills and expertise, reducing the double-disconnect between scholarship and practice. Neither adequately take into account the other side's priorities, needs and possible solutions, Jensen and Gerber argued; bridging the gap and fostering closer collaboration could allow for mutual learning, enhancing the overall advancements of science communication as a young field. === Imagining science's publics === In the preface of The Selfish Gene, Richard Dawkins wrote: "Three imaginary readers looked over my shoulder while I was writing, and I now dedicate the book to them. [...] First the general reader, the layman [...] second the expert [and] third the student". Many criticisms of the public understanding of science movement have emphasized that this thing they were calling the public was somewhat of an (unhelpful) black box. Approaches to the public changed with the move away from the public understanding of science. Science communication researchers and practitioners now often showcase their desire to listen to non-scientists as well as acknowledging an awareness of the fluid and complex nature of (post/late) modern social identities. At the very least, people will use plurals: publics or audiences. As the editor of the scholarly journal Public Understanding of Science put it in a special issue on publics: We have clearly moved from the old days of the deficit frame and thinking of publics as monolithic to viewing publics as active, knowledgeable, playing multiple roles, receiving as well as shaping science. (Einsiedel, 2007: 5) However, Einsiedel goes on to suggest both views of the public are "monolithic" in their own way; they both choose to declare what something called the public is. Some promoters of public understanding of science might have ridiculed publics for their ignorance, but an alternative "public engagement with science and technology" romanticizes its publics for their participatory instincts, intrinsic morality or simple collective wisdom. As Susanna Hornig Priest concluded in her 2009 introduction essay on science's contemporary audiences, the job of science communication might be to help non-scientists feel they are not excluded as opposed to always included; that they can join in if they want, rather than that there is a necessity to spend their lives engaging. The process of quantifiably surveying public opinion of science is now largely associated with the public understanding of science movement (some would say unfairly). In the US, Jon Miller is the name most associated with such work and well known for differentiating between identifiable "attentive" or "interested" publics (that is to say science fans) and those who do not care much about science and technology. Miller's work questioned whether the American public had the following four attributes of scientific literacy: knowledge of basic textbook scientific factual knowledge an understanding of scientific method appreciated the positive outcomes of science and technology rejected superstitious beliefs, such as astrology or numerology In some respects, John Durant's work surveying British public applied similar ideas to Miller. However, they were slightly more concerned with attitudes to science and technology, rather than just how much knowledge people had. They also looked at public confidence in their knowledge, considering issues such as the gender of those ticking "don't know" boxes. We can see aspects of this approach, as well as a more "public engagement with science and technology" influenced one, reflected within the Eurobarometer studies of public opinion. These have been running since 1973 to monitor public opinion in the member states, with the aim of helping the preparation of policy (and evaluation of policy). They look at a host of topics, not just science and technology but also defense, the euro, enlargement of the European Union, and culture. Eurobarometer's 2008 study of Europeans' Attitudes to Climate Change is a good example. It focuses on respondents' "subjective level of information"; asking "personally, do you think that you are well informed or not about...?" rather than checking what people knew. === Frame analysis === Science communication can be analyzed through frame analysis, a research method used to analyze how people understand situations and activities. Some features of this analysis are listed below. Public accountability: placing a blame on public actions for value, e.g. political gain in the climate change debate Runaway technology: creating a certain view of technological advancements, e.g. photos of an exploded nuclear power plant Scientific uncertainty: questioning the reliability of a scientific theory, e.g. arguing how bad global climate change can be if humans are still alive === Heuristics === People make an enormous number of decisions every day, and to approach all of them in a careful, methodical manner is impractical. They therefore often use mental shortcuts known as "heuristics" to quickly arrive at acceptable inferences. Tversky and Kahneman originally proposed three heuristics, listed below, although there are many others that have been discussed in later research. Representativeness: used to make assumptions about probability based on relevancy, e.g. how likely item A is to be a member of category B (is Kim a chef?), or that event C resulted from process D (could the sequence of coin tosses H-H-T-T have occurred randomly?). Availability: used to estimate how frequent or likely an event is based on how quickly one can conjure examples of the event. For example, if one were asked to approximate the number of people in your age group that are currently in college, your judgment would be affected by how many of your own acquaintances are in college. Anchoring and adjustment: used when making judgments with uncertainties. One will start with an anchoring point, then adjust it to reach an assumption. For example, if you are asked to estimate how many people will take Dr. Smith's biology class this spring, you may recall that 38 students took the class in the fall, and adjust your estimation based on whether the class is more popular in the spring or in the fall. The most effective science communication efforts take into account the role that heuristics play in everyday decision-making. Many outreach initiatives focus solely on increasing the public's knowledge, but studies have found little, if any, correlation between knowledge levels and attitudes towards scientific issues. === Inclusive communication and cultural differences === Inclusive science communication seeks to build equity by prioritizing communication that is built with and for marginalized groups that are not reached through typical top-down science communication. Science communication is affected by the same implicit inequities embedded in the production of science research. It has traditionally centered Western science and communicated in Western language. Māori researcher Linda Tuhiwai Smith details how scientific research is "inextricably linked to European imperialism and colonialism". The field's focus on Western science results in publicizing "discoveries" by Western scientists that have been known to Indigenous scientists and communities for generations, continuing the cycle of colonial exploitation of physical and intellectual resources. Collin Bjork notes that science communication is linked to oppression because European colonizers "employed both the English language and western science as tools for subjugating others". Today, English is still considered the international language of science and 80% of science journals in Scopus are published in English. As a result, most science journalism also communicates in English or must use English sources, limiting the audience that science communication can reach. Just as science has historically excluded communities of Black, Indigenous and people of color, LGBTQ+ communities and communities of lower socioeconomic status or education, science communication has also failed to center these audiences. Science communication cannot be inclusive or effective if these communities are not involved in both the creation and dissemination of science information. One strategy to improve inclusivity in science communication is by building philanthropic coalitions with marginalized communities. The 2018 article titled "The Civic Science Imperative" in the Stanford Social Innovation Review (SSIR) outlined how civic science could expand inclusion in science and science communication. Civic science fosters public engagement with science issues so citizens can spur meaningful policy, societal or democratic change. This article outlined the strategies of supporting effective science communication and engagement, building diverse coalitions, building flexibility to meet changing goals, centering shared values, and using research and feedback loops to increase trust. However, the authors of the 2020 SSIR article "How Science Philanthropy Can Build Equity" warned that these approaches will not combat systemic barriers of racism, sexism, ableism, xenophobia or classism without the principles of diversity, equity and inclusion (DEI). DEI in science communication can take many forms, but will always: include marginalized groups in the goal setting, design and implementation of the science communication; use experts to determine the unique values, needs and communication style of the community being reached; test to determine the best way to reach each segment of a community; and include ways to mitigate harm or stress for community members who engage with this work. Efforts to make science communication more inclusive can focus on a global, national or local community. The Metcalf Institute for Marine & Environmental Reporting at the University of Rhode Island produced a survey of these practices in 2020. "How Science Philanthropy Can Build Equity" also lists several successful civic science projects and approaches. Complementary methods for including diverse voices include the use of poetry, participatory arts, film, and games, all of which have been used to engage various publics by monitoring, deliberating, and responding to their attitudes toward science and scientific discourse. == Science in popular culture and the media == === Birth of public science === While scientific study began to emerge as a popular discourse following the Renaissance and the Enlightenment, science was not widely funded or exposed to the public until the nineteenth century. Most science prior to this was funded by individuals under private patronage and was studied in exclusive groups, like the Royal Society. Public science emerged due to a gradual social change, resulting from the rise of the middle class in the nineteenth century. As scientific inventions, like the conveyor belt and the steam locomotive entered and enhanced the lifestyle of people in the nineteenth century, scientific inventions began to be widely funded by universities and other public institutions in an effort to increase scientific research. Since scientific achievements were beneficial to society, the pursuit of scientific knowledge resulted in science as a profession. Scientific institutions, like the National Academy of Sciences or the British Association for the Advancement of Science are examples of leading platforms for the public discussion of science. David Brewster, founder of the British Association for the Advancement of Science, believed in regulated publications in order to effectively communicate their discoveries, "so that scientific students may know where to begin their labours." As the communication of science reached a wider audience, due to the professionalization of science and its introduction to the public sphere, the interest in the subject increased. === Scientific media in the 19th century === There was a change in media production in the nineteenth century. The invention of the steam-powered printing press enabled more pages to be printed per hour, which resulted in cheaper texts. Book prices gradually dropped, which gave the working classes the ability to purchase them. No longer reserved for the elite, affordable and informative texts were made available to a mass audience. Historian Aileen Fyfe noted that, as the nineteenth century experienced a set of social reforms that sought to improve the lives of those in the working classes, the availability of public knowledge was valuable for intellectual growth. As a result, there were reform efforts to further the knowledge of the less educated. The Society for the Diffusion of Useful Knowledge, led by Henry Brougham, attempted to organize a system for widespread literacy for all classes. Additionally, weekly periodicals, like the Penny Magazine, were aimed to educate the general public on scientific achievements in a comprehensive manner. As the audience for scientific texts expanded, the interest in public science did as well. "Extension lectures" were installed in some universities, like Oxford and Cambridge, which encouraged members of the public to attend lectures. In America, traveling lectures were a common occurrence in the nineteenth century and attracted hundreds of viewers. These public lectures were a part of the lyceum movement and demonstrated basic scientific experiments, which advanced scientific knowledge for both the educated and uneducated viewers. Not only did the popularization of public science enlighten the general public through mass media, but it also enhanced communication within the scientific community. Although scientists had been communicating their discoveries and achievements through print for centuries, publications with a variety of subjects decreased in popularity. Alternatively, publications in discipline-specific journals were crucial for a successful career in the sciences in the nineteenth century. As a result, scientific journals such as Nature or National Geographic possessed a large readership and received substantial funding by the end of the nineteenth century as the popularization of science continued. === Science communication in contemporary media === Science can be communicated to the public in many different ways. According to Karen Bultitude, a science communication lecturer at University College London, these can be broadly categorized into three groups: traditional journalism, live or face-to-face events, and online interaction. ==== Traditional journalism ==== Traditional journalism (for example, newspapers, magazines, television and radio) has the advantage of reaching large audiences; in the past, this is way most people regularly accessed information about science. Traditional media is also more likely to produce information that is high quality (well written or presented), as it will have been produced by professional journalists. Traditional journalism is often also responsible for setting agendas and having an impact on government policy. The traditional journalistic method of communication is one-way, so there can be no dialogue with the public, and science stories can often be reduced in scope so that there is a limited focus for a mainstream audience, who may not be able to comprehend the bigger picture from a scientific perspective. However, there is new research now available on the role of newspapers and television channels in constituting "scientific public spheres" which enable participation of a wide range of actors in public deliberations. Another disadvantage of traditional journalism is that, once a science story is taken up by mainstream media, the scientist(s) involved no longer has any direct control over how his or her work is communicated, which may lead to misunderstanding or misinformation. Research in this area demonstrates how the relationship between journalists and scientists has been strained in some instances. On one hand scientists have reported being frustrated with things like journalists oversimplifying or dramatizing of their work, while on the other hand journalists find scientists difficult to work with and ill-equipped to communicate their work to a general audience. Despite this potential tension, a comparison of scientists from several countries has shown that many scientists are pleased with their media interactions and engage often. However, the use of traditional media sources, like newspapers and television, has steadily declined as primary sources for science information, while the internet has rapidly increased in prominence. In 2016, 55% of Americans reported using the internet as their primary source to learn about science and technology, compared to 24% reporting TV and 4% reporting newspapers were their primary sources. Additionally, traditional media outlets have dramatically decreased the number of, or in some cases eliminated, science journalists and the amount of science-related content they publish. ==== Live or face-to-face events ==== The second category is live or face-to-face events, such as public lectures in museums or universities, debates, science busking, "sci-art" exhibits, Science Cafés and science festivals. Citizen science or crowd-sourced science (scientific research conducted, in whole or in part, by amateur or nonprofessional scientists) can be done with a face-to-face approach, online, or as a combination of the two to engage in science communication. Research has shown that members of the public seek out science information that is entertaining, but also helping citizens to critically participate in risk regulation and S&T governance. Therefore, it is important to bear this aspect in mind when communicating scientific information to the public (for example, through events combining science communication and comedy, such as Festival of the Spoken Nerd, or during scientific controversies). The advantages of this approach are that it is more personal and allows scientists to interact with the public, allowing for two-way dialogue. Scientists are also better able to control content using this method. Disadvantages of this method include the limited reach, it can also be resource-intensive and costly and also, it may be that only audiences with an existing interest in science will be attracted. Another opportunity for budding science communicators is through FameLab. This programme was created by Cheltenham Festivals in 2005 and is the largest science communication competition and training programme in the world. FameLab discovers, trains and promotes the best new voices in science (including social sciences), technology, engineering and maths. Participants have just three minutes to convey a scientific concept of their choice to an audience and expert panel of judges. The winner is the speaker who best demonstrates FameLab's 3 C's – Content, Clarity and Charisma. ==== Online interaction ==== The third category is online interaction; for example, websites, blogs, wikis and podcasts can be used for science communication, as can other social media or forms of artificial intelligence like AI-Chatbots. Online methods of communicating science have the potential to reach huge audiences, can allow direct interaction between scientists and the public, and the content is always accessible and can be somewhat controlled by the scientist. Additionally, online communication of science can help boost scientists' reputation through increased citations, better circulation of articles, and establishing new collaborations. Online communication also allows for both one-way and two-way communication, depending on the audience's and the author's preferences. However, there are disadvantages in that it is difficult to control how content is picked up by others, and regular attention and updating is needed. When considering whether or not to engage in science communication online, scientists should review what science communication research has shown to be the potential positive and negative outcomes. Online communication has given rise to movements like open science, which advocates for making science more accessible. However, when engaging in communication about science online, scientists should consider not publicizing or reporting findings from their research until it has been peer-reviewed and published, as journals may not accept the work after it has been circulated under the "Ingelfinger rule". Other considerations revolve around how scientists will be perceived by other scientists for engaging in communication. For example, some scholars have criticized engaged, popular scholars using concepts like the Sagan effect or Kardashian Index. Despite these criticisms, many scientists are taking to communicating their work on online platforms, a sign of potentially changing norms in the field. ==== Art ==== According to Lesen et al. (2016), art has been a tool increasingly used to attract the public to science. Either formally or in an informal context, an integration between artists and scientists could potentially raise awareness of the general public about current topics in science, technology, engineering and mathematics (STEM). The arts have the power of creating emotional links between the public and a research topic and create a collaborative atmosphere that can "activate science" in a different way. Learning through the affection domain, in contrast to the cognitive domain, increases motivation and using the arts to communicate scientific knowledge this way could increase dramatically engagement. === Social media science communication === By using Twitter, scientists and science communicators can discuss scientific topics with many types of audiences with various points of view. Studies published in 2012 by Gunther Eysenbach shed light on how Twitter not only communicates science to the public but also affects advances in the science community. Alison Bert, editor in chief of Elsevier Connect, wrote a 2014 news article titled "How to use social media for science" that reported on a panel about social media at that year's AAAS meeting, in which panelists Maggie Koerth-Baker, Kim Cobb, and Danielle N. Lee noted some potential benefits and drawbacks to scientists of sharing their research on Twitter. Koerth-Baker, for example, commented on the importance of keeping public and private personas on social media separate in order to maintain professionalism online. Interviewed in 2014, Karen Peterson, director of Scientific Career Development at Fred Hutchinson Cancer Research Center stressed the importance for scientists of using social networks such as Facebook and Twitter to establish an online presence. Kimberly Collins et al., writing in PLOS One in 2016, explained reasons why some scientists were hesitant to join Twitter. Some scientists were hesitant to use social media outlets such as Twitter due to lack of knowledge of the platform, and inexperience with how to make meaningful posts. Some scientists did not see the meaning in using Twitter as a platform to share their research or have the time to add the information into the accounts themselves. In 2016, Elena Milani created the SciHashtag Project, which is a condensed collection of Twitter hashtags about science communication. In 2017, a study done by the Pew Research Center found that about "a quarter of social media users (26%) follow science accounts" on social media. This group of users "places both more importance and comparatively more trust on science news that comes to them through social media". Scientists have also used other social media platforms, including Instagram and Reddit, to establish a connection with the public and discuss science. == The public understanding of science movement == "Public understanding of science", "public awareness of science" and "public engagement with science and technology" are all terms coined with a movement involving governments and societies in the late 20th century. During the late 19th century, science became a professional subject and influenced by governmental suggestions. Prior to this, public understanding of science was very low on the agenda. However, some well-known figures such as Michael Faraday ran lectures aimed at the non-expert public, his being the famous Christmas Lectures which began in 1825. The 20th century saw groups founded on the basis they could position science in a broader cultural context and allow scientists to communicate their knowledge in a way that could reach and be understood by the general public. In the UK, The Bodmer Report (or The Public Understanding of Science as it is more formally known) published in 1985 by The Royal Society changed the way scientists communicated their work to the public. The report was designed to "review the nature and extent of the public understanding of science in the United Kingdom and its adequacy for an advanced democracy".: 5–7  Chaired by the geneticist Sir Walter Bodmer alongside famous scientists as well as broadcaster Sir David Attenborough, the report was evidenced by all of the major sectors concerned; scientists, politicians, journalists and industrialists but not the general public.: 5–7  One of the main assumptions drawn from the report was everybody should have some grasp of science and this should be introduced from a young age by teachers who are suitably qualified in the subject area. The report also asked for further media coverage of science including via newspapers and television which has ultimately led to the establishment of platforms such as the Vega Science Trust. In both the UK and the United States following the Second World War, public views of scientists swayed from great praise to resentment. Therefore, the Bodmer Report highlighted concerns from the scientific community that their withdrawal from society was causing scientific research funding to be weak. Bodmer promoted the communication of science to a wider more general public by expressing to British scientists that it was their responsibility to publicize their research. An upshot of the publication of the report was the creation of the Committee on the Public Understanding of Science (COPUS), a collaboration between the British Association for the Advancement of Science, the Royal Society and the Royal Institution. The engagement between these individual societies caused the necessity for a public understanding of science movement to be taken seriously. COPUS also awarded grants for specific outreach activities allowing the public understanding to come to the fore. Ultimately leading to a cultural shift in the way scientists publicized their work to the wider non-expert community. Although COPUS no longer exists within the UK the name has been adopted in the US by the Coalition on the Public Understanding of Science. An organization which is funded by the US National Academy of Sciences and the National Science Foundation and focuses on popular science projects such as science cafes, festivals, magazines and citizen science schemes. In the European Union, public views on public-funded research and the role of governmental institutions in funding scientific activities were being questioned as the budget allocated was increasing. Therefore, the European Commission encouraged strongly and later obligated research organizations to communicate about their research activities and results widely and to the general public. This is being done by integrating a communication plan into their research project that increases the public visibility of the project using an accessible language and adapted channels and materials. == See also == Conversazione Hype in science List of science communicators Public awareness of science Science-to-business marketing == Notes and references == == Further reading == Bauer, M & Bucchi, M (eds) (2007). Journalism, Science and Society (London & New York: Routledge). Bucchi, M & Trench, B (eds) (2014). Handbook of Public Communication of Science and Technology (2nd ed.) (London & New York: Routledge). Cartwright, JH & Baker, B (2005). Literature and Science: Social Impact and Interaction (Santa Barbara: ABC-CLIO). Drake, JL et al. (eds) (2013). New Trends in Earth-Science Outreach and Engagement: The Nature of Communication (Cham, Switzerland: Springer). Fortenberry, RC (2018). Complete Science Communication: A Guide to Connecting with Scientists, Journalists and the Public (London: Royal Society of Chemistry). Gregory, J & Miller, S (1998). Science in Public: Communication, Culture and Credibility (New York: Plenum). Holliman, R et al. (eds) (2009). Investigating Science Communication in the Information Age: Implications for Public Engagement and Popular Media (Oxford: Oxford University Press). National Academies of Sciences, Engineering, and Medicine (2016). Communicating Science Effectively: A Research Agenda (Washington, DC: The National Academies Press). doi:10.17226/23674 Nelkin, D (1995). Selling Science: How the Press Covers Science & Technology, 2nd edition (New York: WH Freeman). Wilson, A et al. (eds.) (1998). Handbook of Science Communication (Bristol; Philadelphia: Institute of Physics).
Wikipedia/Science_communication
This timeline describes the major developments, both experimental and theoretical understanding of fluid mechanics and continuum mechanics. This timeline includes developments in: Theoretical models of hydrostatics, hydrodynamics and aerodynamics. Hydraulics Elasticity Mechanical waves and acoustics Valves and fluidics Gas laws Turbulence modeling Plasticity and rheology Quantum fluids like Bose–Einstein condensates and superfluidity Microfluidics == Prehistory and antiquity == Before 3000 BC – Civilization starts by settling around rivers, coast and lakes. 3000 BC – Irrigation techniques develop in Mesopotamia and Ancient Egypt. Indus Valley Civilisation develops city-wide drainage systems and toilet systems. Egyptians develop reed boats. 2300 BC – Construction of the Nahrawan Canal. 2000–1500 BC – First dams constructed in India to control water. 1700 BC – Windmill are used in Babylonia to pump water. 14th century BC – Water clock are developed in Egypt under the reign of Amenhotep III. Clepsydra water clock design is developed in ancient Greece. 6th century BC – Theodorus of Samos invents the water level. Ancient Rome's drainage system is designed during the reign of Tarquinius Priscus. Rome's Cloaca Maxima is constructed by lining a river bed with stone. Tunnel of Eupalinos is constructed in Samos. 4th century BC – Mencius describes how to measure an elephant using displacement of water. Development of rain gauges in India. Aqua Appia first Roman aqueduct is built in Rome. 3rd century BC – Archimedes published On Floating Bodies describing the general principle for buoyancy and hydrostatics. Archimedes develops Archimedes' screw for water extraction. 2nd century BC – The aqueduct Aqua Tepula and Aqua Marcia aqueducts are completed in Rome. Zhang Heng of Han dynasty designs the first known seismoscope. 1st century BC – Frontinus publishes his treatise De aquaeductu on Roman water engineering. Hero of Alexandria makes a series of experiments and devices with fluids, including the aeolipile steam device and wind harnessing devices. == Middle ages == 8th–13th century – Arab Agricultural Revolution 725 – Northumbrian monk Bede publishes The Reckoning of Time, which includes a quantitative description of the influence of the moon and the sun over the tides. c. 850– Abu Ma'shar al-Balkhi (Albumasar) publishes his Kitab al-madkhal al-kabir recording the Moon position and tides, he recognizes that there are two tides in day. 850 – The Book of Ingenious Devices is published by the Banū Mūsā brothers, describing a number of early automatic controls using fluid mechanics. 1206 – Ismail al-Jazari invented water-powered programmable automata/robots and water music devices. == Renaissance == 1432 – Portuguese develop caravels for long-distance ocean travel. 1450 –Nicholas of Cusa publishes his experiments with fluids in Idiota de staticis experimentis, including the first proposal to measure air moisture using wool. 1480-1510 – Leonardo da Vinci develops the first sophisticated parachute, the first descriptions of capillary action, and the first turbine water wheels designs. 1586 – Simon Stevin publishes De Beghinselen des Waterwichts ("Principles on the weight of water") on hydrostatics. He first details the hydrostatic paradox. 1596 – Galileo Galilei produces the first (Galileo) thermometer. == 17th century == 1619 – Benedetto Castelli published Della Misura dell'Acque Correnti ("On the Measurement of Running Waters"), one of the foundations of modern hydrodynamics. 1619 – William Harvey provides first model of the human circulatory system. 1624 – Jan Baptist van Helmont coins the term "gas". 1631 – René Descartes first describes the principle of the mercury barometer. 1643 – Evangelista Torricelli provides a relation between the speed of fluid flowing from an orifice to the height of fluid above the opening, given by Torricelli's law. He also builds a mercury barometer and does a series of experiments on vacuum. 1650 – Otto von Guericke invents the first vacuum pump. 1653–1663 Blaise Pascal establishes Pascal's law of hydrostatics. 1662-1678 – Robert Boyle and Edme Mariotte independently discover a gas law that describes the relationship between pressure and volume given by Boyle's law (or Boyle-Mariotte's law). 1678 – Robert Hooke publishes Hooke's law describing linear deformation of a spring. 1687 – Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), introducing the Newton's laws of motion of classical mechanics. He also introduces the concept of Newtonian fluid. == 18th century == 1713 – Antoine Parent introduces the concept of shear stress. 1714 – Daniel Gabriel Fahrenheit develops the mercury-in-glass thermometer along the Fahrenheit temperature scale. 1718–1719 – James Jurin writes the law of capillary action, known as Jurin's law. 1727 – Leonhard Euler introduces linear elasticity and the Young's modulus. 1732 – Henri Pitot discovers how to measure the pressure from the speed of a fluid using a Pitot tube. 1738 – Daniel Bernoulli publishes Hydrodynamica discussing the mathematical relation between pressure and velocity of fluids according to Bernoulli's principle. 1742 – Anders Celsius designs a thermometer with the Celsius scale. 1744 – Euler introduces the concept of deformation and strain. 1747 – Jean le Rond d'Alembert's formula for the solutions of the wave equation in a string gets published. 1752 – D'Alembert show an inconsistency of treating fluids as inviscid incompressible fluids, known as d'Alembert's paradox. 1757 – Euler introduces the Euler equations of fluid dynamics for incompressible and non-viscous flow. He also introduces the mathematical model for buckling. 1764 – James Watt develops his steam water condenser leading to efficient steam engines. 1765 – Jean-Charles de Borda experiments with whirling arm experiments. He corrects the available theories of air friction. 1766 – de Borda publishes "Mémoire sur l’Écoulement des Fluides par les Orifices des Vases" on hydraulics and resistance of fluid through orifices. He comes up with Borda–Carnot equation. 1768 – Antoine de Chézy provides a semi-empirical formula for resistance of open channel flow, described by Chézy formula. 1775 – Pierre-Simon Girard invents the water turbine. 1776 – Charles Bossut, supervised by the Marquis de Condorcet and d'Alembert, publishes Nouvelles expériences sur la resistance de fluides, a report on a series experiments to test currents theories of hydraulics. 1775-76 – Pierre-Simon Laplace introduces the mathematical theory for tidal forces on oceans. 1779 – Pierre-Louis-Georges du Buat publishes Principes de l'hydraulique ("Principles of hydraulics"), with semiempirical equations for the flow of water through pipes and open channels. 1780 – Jacques Charles discover a gas law that describes the relationship between temperature and volume, given by Charles's law. 1782 – The Montgolfier brothers invent the hot air balloon. 1785 – First theories of friction are introduced by Charles-Augustin de Coulomb. 1787 – Ernst Chladni, publishes his experiments on vibrational modes of thin solid surfaces, describing the Chladni patterns created using a violin bow, based on previous experiments by Hooke. 1797 – Giovanni Battista Venturi discovers the Venturi effect. 1799 – George Cayley introduces modern fixed wing-machines and identifies three important factors for flying machines: thrust, lift, drag, and weight. == 19th century == 1801 – Robert Fulton develops the first submarine. 1805-1806 – The development of Young–Laplace equation by Thomas Young and improved by Laplace. 1808-1809 – Joseph Louis Gay-Lussac describes the law of combining gases. 1811–1812 – Amedeo Avogadro and André-Marie Ampère independently discover a gas law relating volume and quantity of gas, given by Avogadro's law (or Avogadro-Ampère's law). 1821 – Claude-Louis Navier introduces viscosity in to Euler equations of fluids. 1821 – Sophie Germain wins a contest of the French Academy of Sciences for providing a partial theory for the vibration of an elastic surfaces. 1827 – Augustin-Louis Cauchy introduces the Cauchy stress tensor and the concept of stress in elasticity. 1827 – Robert Brown (botanist, born 1773), identifies the Brownian motion of pollen grains suspended in water. 1831– Michael Faraday first describes vibrational modes in liquids, known as Faraday waves. 1831-1833– Thomas Graham first studies the diffusion in gases. 1834 – Benoît Paul Émile Clapeyron unifies many of the empirical gas laws into the ideal gas law. 1834 – John Scott Russell first describes the observation of solitary waves. 1837 – George Green find the minimal number of elastic moduli. 1838-40 – Gotthilf Hagen and Jean Léonard Marie Poiseuille study laminar flow, independently establishing Hagen–Poiseuille equation. 1841 – George Biddell Airy publishes the first correct formulation of Airy wave theory of water waves. 1842 – Christian Doppler introduces the Doppler effect. 1842-1850 – Stokes completes the equations of motions of fluids, now referred as Navier–Stokes equations. He also extends Airy wave theory to non-linear Stokes wave theory. 1852 – Heinrich Gustav Magnus describes the Magnus effect. 1855 – Lord Kelvin calculates the thermodynamics work and energy due to elastic deformation. 1855 – Adolf Eugen Fick publishes Fick's laws of diffusion. 1857 – Henry Darcy studies flow through porous media, leading to the discovery of Darcy's law. 1857 – Rudolf Clausius introduces the first model for the kinetic theory of gases. 1859 – W. H. Besant introduces an equation for the dynamics of bubbles in an incompressible fluid. 1860 – James Clerk Maxwell introduces the Maxwell distribution of velocity of classical gas molecules. 1863 –Hermann von Helmholtz publishes Sensations of Tone on the physics of sound perception. 1864 – August Toepler invents Schlieren photography. 1865 – Lord Kelvin introduces the Kelvin material model for viscoelasticity. 1856 – Carlo Marangoni studies the tears of wine, now explained by the Marangoni effect. 1867 – Helmholtz works on Helmholtz's theorems for vortex dynamics. 1867 – James Clerk Maxwell introduces the Maxwell material model for viscoelasticity. 1868–1871 – Helmholtz and Kelvin study and develop the theory of the Kelvin–Helmholtz instability. 1870 – William Rankine develops an equation for the study of shock waves. 1871 – Francis Herbert Wenham designs and builds the first wind tunnel. 1872-1877 – Joseph Valentin Boussinesq introduces the concept of turbulence in forms of eddy viscosity, as well as Boussinesq approximation for water waves and Boussinesq approximation for buoyancy. 1873 – Johannes Diderik van der Waals introduces the Van der Waals equation. 1883 – Osborne Reynolds demonstrates the transition and differences between laminar and turbulent pipe flow. 1885 – Lord Rayleigh predicts the existence of Rayleigh surface waves. 1885 – Helmholtz describes the concept of Helmholtz resonance. 1887 – Pierre Henri Hugoniot based on the work of Rankine, introduces the Rankine–Hugoniot conditions to model shock waves. 1887 – First models of supersonic waves by Ernst Mach. He introduces the concept of Mach number. 1888 – First commercial Venturi tube by Clemens Herschel. 1888-1890 – Independently, Henry R. A. Mallock and Maurice Couette find the mathematical solution for the Couette flow. 1889 – Robert Manning produces Manning's formula for open channel flow. 1893 – Carl Barus develops the theory of the die swell in complex fluids. 1895 – Diederik Korteweg and Gustav de Vries (1895) rediscover the Korteweg–De Vries equation first treated by Boussinesq and introduce the idea of soliton solutions. == 20th century == 1902 – Martin Kutta discusses the air flow through an airfoil using the Kutta condition. 1903 – The Wright brothers carry the first successful manned airplane flight. 1903 – Walther Ritz introduces the Ritz method to study beam theory and Chladni figures. 1905 – First theory of dislocations by Vito Volterra. 1905-1906 – First successful theories of Brownian motion by Albert Einstein and Marian Smoluchowski, supporting the atomic theory of matter. 1906 – Richard Dixon Oldham identifies the separate arrival of p-waves, s-waves and surface waves on seismograms and found the first clear evidence that the Earth has a central core. 1908 – Paul Richard Heinrich Blasius introduces the concept of boundary layer. 1908 – Experimental confirmation of the theories of Brownian motion by Jean Baptiste Perrin. 1910: Harry Fielding Reid put forward the elastic rebound theory for earthquakes. Lord Rayleigh introduces the concept of Rayleigh flow. Nikolay Zhukovsky introduces the Joukowsky transform and the Kutta–Joukowski theorem based on the work of Kutta. Carl Wilhelm Oseen solves the Stokes' paradox by introducing Oseen's approximation. 1911 – Augustus Edward Hough Love predicts the existence of Love surface waves. 1915–1916 – Frederick W. Lanchester comes up with the Lanchester's laws, a set of differential equations that were practical for flying combat. 1915-1917 – George Barker Jeffery and Georg Hamel introduce the equations of Jeffery–Hamel flow. 1916 – Horace Lamb coins the term "vorticity". 1916 – Eugene C. Bingham studies Bingham plastics 1916-1923 – Lord Rayleigh, and later G. I. Taylor describe Rayleigh–Taylor instability. 1917 – Lamb introduces Lamb waves, generalizing Rayleigh's wave theory for thin metal plates. 1918 – Ludwig Prandtl develops theory of flow over airplane wings. 1919 – Jacob Bjerknes established the bases the Norwegian cyclone model. 1920 – Nikola Tesla patents the Tesla valve, opening the field of fluidics. 1920 – Bingham coins the term rheology from a suggestion by a colleague, Markus Reiner. 1921 – Theodore von Kármán introduces the turbulence model of Von Kármán swirling flow, and phenomena like Kármán vortex street. 1921 – Alan Arnold Griffith develops his theory of fracture mechanics. 1922 – Supersonic wind tunnel is invented in National Physical Laboratory (United Kingdom). 1926 – Einstein solves the tea leaf paradox. 1925 – Jakob Ackeret publishes the theory of supersonic airfoils. 1926 – Erwin Madelung relates quantum mechanics with hydrodynamics through his quantum hydrodynamics equations, known as Madelung equations. 1931 – Sylvia Skan and Victor Montague Falkner introduce the equations for the Falkner–Skan boundary layer. 1932 – The concept of quantum of sound (phonons) is introduced by Igor Tamm. 1937 – Superfluidity is discovered in helium-4 by Pyotr Kapitsa and independently by John F. Allen and Don Misener. 1938 – Philip Saffman and G. I. Taylor publish on Saffman–Taylor instability. 1937 – Lev Landau introduces Landau theory of phase transitions. 1940-1941 – László Tisza and Landau introduce the two-fluid model for helium. 1941 – Landau introduces the concept of second sound in condensed matter. 1942 – First magnetohydrodynamics descriptions of plasma by Hannes Alfvén. He also introduced the idea of Alfvén waves. 1948 – Milton S. Plesset improves on Rayleigh and Bessant equations for the dynamics of bubbles by including surface tension according to Rayleigh–Plesset equation. 1941 – Andrey Kolmogorov introduces his detailed theory of turbulence. 1947– Karl Weissenberg introduces the Weissenberg effect in non-Newtonian fluids. 1950 – James G. Oldroyd introduces the Oldroyd-B model of viscoelasticity. 1944 – Lewis Ferry Moody plots Darcy–Weisbach friction factor against Reynolds number for various values of relative roughness, leading to the first Moody chart. 1961 – Eugene P. Gross and Lev Pitaevskii introduce Gross–Pitaevskii equation for the condensation of bosons. 1963 – Alex Kaye describes the Kaye effect in viscoelastic liquids. 1972 – David Lee, Douglas Osheroff and Robert Coleman Richardson discovered two phase transitions of helium-3 along the melting curve, which were soon realized to be the two superfluid phases. 1995 – The first Bose–Einstein condensate is produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST–JILA lab, in a gas of rubidium atoms cooled to 170 nanokelvins (nK). Shortly thereafter, Wolfgang Ketterle at MIT produced a Bose–Einstein condensate in a gas of sodium atoms. == 21st century == c. 2000 – Development on the field of microfluidics. 2003 – Deborah S. Jin and her collaboration produce the first fermionic condensate. == See also == History of aviation == References ==
Wikipedia/Timeline_of_fluid_and_continuum_mechanics
Dynamism is a general name for a group of philosophical views concerning the nature of matter. However different they may be in other respects, all these views agree in making matter consist essentially of simple and indivisible units, substances, or forces. Dynamism is sometimes used to denote systems that admit not only matter and extension, but also determinations, tendencies, and forces intrinsic and essential to matter. More properly, however, it means exclusive systems that do away with the dualism of matter and force by reducing the former to the latter. The word was coined by Thomas Carlyle, who contrasted dynamism with mechanism. == Leibniz's formulation == Dynamism is the metaphysics of Gottfried Leibniz (1646–1716) that reconciles hylomorphic substance theory with mechanistic atomism by way of a pre-established harmony, and which was later developed by Christian Wolff (1679–1754) as a metaphysical cosmology. The major thesis for Leibniz follows as a consequences of his monad, that: “the nature of every substance carries a general expression of the whole universe. [The monad provides] the concept of an individual substance that contains...all its phenomena, such that nothing can happen to substance that is not generated from its own ground...but in conformity to what happens to another”... Whereby Leibniz "counters the tendency inherent in Cartesian and Spinozistic rationalism toward an “isolationist” interpretation of the ontological independence of substance... Leibniz's account of substantial force aims to furnish the complete metaphysical groundwork for a science of dynamics". In the opening paragraph of Specimen dynamicum (1692), Leibniz begins by clarifying his intention to supersede the Cartesian account of corporeal substance by asserting the priority of force over extension... This allows him to affirm that the Aristotelian principle of form is needed for the philosophical account of nature. He does this in view of four main facets of his doctrine of force: (1) the characterization of force (vis naturae) as that which is constitutive of substance itself; (2) the concern to sharply distinguish this concept of force from the Scholastic notion of potentia; (3) the correlative interpretation of force in terms of conatus or nisus, i.e., as something between mere potency and completed act; and (4) the affirmation of the fundamental correctness of Aristotle’s own concept of form as entelechy, and Leibniz’s corresponding attempt to make this concept fully intelligible. By superseding the Cartesian concept of corporeal substance and by advocating the Aristotelian principle of form, Leibniz sets the stage for an interpretation of material being in terms different from those of inert matter and externally communicated motion. Leibniz thus retains what he takes to be the rational core of the Aristotelian conception of substance. In effect, Leibniz’s theory of force involves the rehabilitation and reconstruction of the matter-form composite as the pivotal concept of the metaphysics of corporeal nature. Leibniz’s concern to revive the Aristotelian explanatory scheme by means of the concept of substantial force underlies his description of the structural and material features of the aggregation of monads and corporeal interaction. He holds that the following four ontological expressions of substantial force constitute the nature of a complete corporeal substance and supply the grounds of all corporeal interaction: primitive active force, primitive passive force, derivative active force, and derivative passive force. The analysis of primitive active force (vis activa primitiva) yields the fundamental metaphysical principle that substance perdures through all processes of phenomenally manifested corporeal interaction [and] the basis of the identity of any particular body through the alterations that it undergoes as the result of its interactions with other bodies. It also provides for the continuity and conservation of action within corporeal nature as a whole. Primitive passive force (vis passiva primitiva) is the ground of corporeal extension, by which a body appears as material mass [and capacity] to resist changes in its state of motion and to hinder penetration by other bodies... Derivative active force (vis activa derivativa) results from the modification or limitation of primitive force... that takes the form of the phenomenally manifested conflict of physical bodies... subject to distribution by virtue of this conflict. It therefore does not perdure in any single body during the course of its interaction with other corporeal substances. Since it is comprehensible as the internal action [when] acted upon by some other body or bodies, [with] the capacity to resist... penetration and changes in their states of motion. Derivative passive force (vis passiva derivativa) is the purely quantitative modification of primitive passive force [known] in terms of the measures of any material mass’s resistance to penetration and change in its state of motion. Leibniz insists that primitive force pertains solely to completely general causes. As a strictly metaphysical principle, it is the object of purely rational apprehension. It is thus not linked immediately to the actual laws of corporeal interaction in the phenomenal realm. On the other hand, derivative force does pertain directly to such observable interaction. Its analysis leads to the systematic formulation of the fundamental laws of corporeal dynamics. These are laws of action that are known not only by reason, but are also proved by the evidence of the senses. == 20th century and contemporary use == Elements of Dynamism can be found in the works of Henri Bergson, and in more contemporary works, such as the process philosophy of Alfred North Whitehead in terms of relations, as well as the systems theory of Ludwig von Bertalanffy and William Ross Ashby. The Basque philosopher Xavier Zubiri, most notably in his works, "On Essence" and "Dynamic Structure of Reality" details of several dynamisms inherent in the universe, beginning with variation, then onto alteration, selfhood, self-possession, living-together, onto Dynamism as a Mode of Being-in-the-world. It is a response to the Philosophy of Spirit via Hegel in addition to reductionists and Heidegger. This concept also has resonances with the Object-oriented ontology and Speculative Realism schools of philosophy. == References ==
Wikipedia/Dynamism_(metaphysics)
The following is a timeline of gravitational physics and general relativity. == Before 1500 == 3rd century B.C. – Aristarchus of Samos proposes the heliocentric model. == 1500s == 1543 – Nicolaus Copernicus publishes On the Revolutions of Heavenly Spheres. 1583 – Galileo Galilei deduces the period relationship of a pendulum from observations (according to later biographer). 1586 – Simon Stevin demonstrates that two objects of different mass accelerate at the same rate when dropped. 1589 – Galileo Galilei describes a hydrostatic balance for measuring specific gravity. 1590 – Galileo Galilei formulates modified Aristotelean theory of motion (later retracted) based on density rather than weight of objects. == 1600s == 1602-1608 – Galileo Galilei experiments with pendulum motion and inclined planes; deduces his law of free fall; and discovers that projectiles travel along parabolic trajectories. 1609 – Johannes Kepler announces his first two laws of planetary motion. 1610 – Johannes Kepler states the dark night paradox. 1610 – Galileo Galilei publishes The Sidereal Messenger, detailing his astronomical discoveries made with a telescope. 1619 – Johannes Kepler unveils his third law of planetary motion. 1665-66 – Isaac Newton introduces an inverse-square law of universal gravitation uniting terrestrial and celestial theories of motion and uses it to predict the orbit of the Moon and the parabolic arc of projectiles (the latter using his generalization of the binomial theorem). 1676-9 – Ole Rømer makes the first scientific determination of the speed of light. 1684 – Isaac Newton proves that planets moving under an inverse-square force law will obey Kepler's laws in a letter to Edmond Halley. 1686 – Isaac Newton uses a fixed length pendulum with weights of varying composition to test the weak equivalence principle to 1 part in 1000. 1686 – Isaac Newton publishes his Mathematical Principles of Natural Philosophy, where he develops his calculus, states his laws of motion and gravitation, proves the shell theorem, describes his rotating bucket thought experiment, explains the tides, and calculates the figure of the Earth. == 1700s == 1705 – Edmond Halley predicts the return of Halley's comet in 1758, the first use of Newton's laws by someone other than Newton himself. 1728 – Isaac Newton posthumously publishes his cannonball thought experiment. 1742 – Colin Maclaurin studies a self-gravitating uniform liquid drop at equilibrium, the Maclaurin spheroid. 1740s – Jean le Rond d'Alembert and Leonhard Euler independently examine the precession of the equinoxes and nutation of the Earth. In the process, they develop the dynamics of rigid bodies. 1740s-1750s – Leonhard Euler and Alexis Clairault independently derive the equations of motion for the three-body problem and apply them to the Moon. 1755 – Immanuel Kant advances Emanuel Swedenborg's nebular hypothesis on the origin of the Solar System. 1765 – Leonhard Euler discovers the first three Lagrange points. 1767 – Leonhard Euler solves Euler's restricted three-body problem. 1772 – Joseph-Louis Lagrange discovers the two remaining Lagrange points. 1770s-1780s – Joseph-Louis Lagrange and Pierre-Simon de Laplace investigate the stability of the Solar System. 1780s – Adrien-Marie Legendre and Pierre-Simon de Laplace study the gravitational attraction of spheroids in spherical coordinates and introduce the Legendre polynomials. 1796 – Pierre-Simon de Laplace independently introduces the nebular hypothesis. 1798 – Henry Cavendish tests Newton's law of universal gravitation using a torsion balance, leading to the first accurate value for the gravitational constant and the mean density of the Earth. == 1800s == 1846 – Urbain Le Verrier and John Couch Adams, studying Uranus' orbit, independently prove that another, farther planet must exist. Neptune was found at the predicted moment and position. 1855 – Le Verrier observes a 38 arc-second per century excess precession of Mercury's orbit and attributes it to another planet, inside Mercury's orbit. The planet, called Vulcan, was never found. Le Verrier's figure is revised by Simon Newcomb to 43 arc-second per century in 1882. 1876 – William Kingdon Clifford suggests that the motion of matter may be due to changes in the geometry of space. 1884 – William Thomson (Lord Kelvin) lectures on the issues with the wave theory of light with regards to the luminiferous ether. 1887 – Albert A. Michelson and Edward W. Morley in their famous experiment do not detect the ether drift. 1889 – Loránd Eötvös uses a torsion balance to test the weak equivalence principle to 1 part in one billion. 1887 – George Francis FitzGerald explains his hypothesis that the Michelson-Morley interferometer contracts in the direction of motion through the luminiferous ether to Oliver Lodge. 1893 – Ernst Mach states Mach's principle, the first constructive critique of the idea of Newtonian absolute space. 1897 – Henri Poincaré questions whether absolute space, absolute time, and Euclidean geometry are applicable to physics. == 1900s == 1902 – Paul Gerber explains the movement of the perihelion of Mercury using finite speed of gravity. His formula, at least approximately, matches the later model from Einstein's general relativity, but Gerber's theory was incorrect. 1902 – Henri Poincaré questions the concept of simultaneity in his book, Science and Hypothesis. 1904 – Hendrik Antoon Lorentz publishes the Lorentz transformations, so named by Henri Poincaré. 1902 – Henri Poincaré shows that the Lorentz transformations form a mathematical group, called the Lorentz group, and derives the relativistic formula for adding velocities. 1905 – Albert Einstein completes his special theory of relativity and examines relativistic aberration and the transverse Doppler effect. 1905 – Albert Einstein discovers the equivalence of mass and energy, E = m c 2 {\displaystyle E=mc^{2}} in modern form. 1906 – Max Planck coins the term Relativtheorie. Albert Einstein later uses the term Relativitätstheorie in a conversation with Paul Ehrenfest. He originally prefers calling it Invariance Theory. 1906 – Max Planck formulates a variational principle for special relativity. 1907 – Albert Einstein introduces the principle of equivalence of gravitational and inertial mass and uses it to predict gravitational lensing and gravitational redshift, historically known as the Einstein shift. 1907-8 – Hermann Minkowski introduces the Minkowski spacetime and the notion of tensors to relativity. His paper was published posthumously. 1909 – Max Born proposes his notion of rigidity. 1909 – Paul Ehrenfest states the Ehrenfest paradox. === 1910s === 1911 – Max von Laue publishes the first textbook on special relativity. 1911 – Albert Einstein explains the need to replace both special relativity and Newton's theory of gravity; he realizes that the principle of equivalence only holds locally, not globally. 1912 – Friedrich Kottler applies the notion of tensors to curved spacetime. 1915-16 – Albert Einstein completes his general theory of relativity. He explains the perihelion of Mercury and calculates gravitational lensing correctly and introduces the post-Newtonian approximation. 1915 – David Hilbert independently introduces the Einstein-Hilbert action. Hilbert also recognizes the connection between the Einstein equations and the Gauss-Bonnet theorem. 1916 – Karl Schwarzschild publishes the Schwarzschild metric about a month after Einstein published his general theory of relativity. This was the first solution to the Einstein field equations other than the trivial flat space solution. 1916 – Albert Einstein predicts gravitational waves. 1916 – Willem de Sitter predicts the geodetic effect. 1917 – Albert Einstein applies his field equations to the entire Universe. Physical cosmology is born. 1916-20 – Arthur Eddington studies the internal constitution of the stars. 1918 – Albert Einstein derives the quadrupole formula for gravitational radiation. 1918 – Emmy Noether publishes Noether's theorem and resolves the issue of local energy conservation in general relativity. 1918 – Josef Lense and Hans Thirring find the gravitomagnetic frame-dragging of gyroscopes in the equations of general relativity. 1919 – Arthur Eddington leads a solar eclipse expedition which detects gravitational deflection of light by the Sun, which, despite opinion to the contrary, survives modern scrutiny. Other teams fail for reasons of war and politics. === 1920s === 1921 – Theodor Kaluza demonstrates that a five-dimensional version of Einstein's equations unifies gravitation and electromagnetism. This idea is later extended by Oskar Klein. 1922 – Alexander Friedmann derives the Friedmann equations. 1922 – Enrico Fermi introduces the Fermi coordinates. This is developed further in 1932 by Arthur Walker into the Fermi-Walker transport. 1923 – George David Birkhoff proves Birkhoff's theorem on the uniqueness of the Schwarzschild solution. 1924 – Arthur Eddington calculates the Eddington limit. 1924 – Cornelius Lanczos discovers the van Stockum dust, later rediscovered by Willem Jacob van Stockum in 1938. 1925 – Walter Adams measures the gravitational redshift of the light emitted by the companion of Sirius B, a white dwarf. 1927 – Georges Lemaître publishes his hypothesis of the primeval atom. 1929 – Edwin Hubble published the law later named for him. === 1930s === 1931 – Subrahmanyan Chandrasekhar studies the stability of white dwarfs. 1931 – Georges Lemaître and Arthur Eddington predict the expansion of the Universe. 1931 – Albert Einstein introduces his cosmological constant. 1932 – Albert Einstein and Willem de Sitter propose the Einstein-de Sitter cosmological model. 1932 – John Cockcroft and Ernest Walton verify Einstein's mass-energy equation by an experiment artificially transmuting lithium into helium. 1934 – Dmitry Blokhintsev and F. M. Gal'perin coin the term 'graviton'. Paul Dirac reintroduces it in 1959. 1934 – Walter Baade and Fritz Zwicky predict the existence of neutron stars. Although their details are wrong, their basic idea is now accepted. 1935 – Albert Einstein and Nathan Rosen derive the Einstein-Rosen bridge, the first wormhole solution. 1935 – Howard Robertson and Arthur Walker obtain the Robertson-Walker metric. 1936 – Albert Einstein predicts that a gravitational lens brightens the light coming from a distant object to the observer. 1937 – Fritz Zwicky states that galaxies could act as gravitational lenses. 1937 – Albert Einstein and Nathan Rosen obtain the Einstein-Rosen metric, the first exact solution describing gravitational waves. 1938 – Albert Einstein, Leopold Infeld, and Banesh Hoffmann obtain the Einstein-Infeld-Hoffmann equations of motion. 1939 – Hans Bethe shows that nuclear fusion is responsible for energy production inside stars, building upon the Kelvin–Helmholtz mechanism. 1939 – Richard Tolman solves the Einstein field equations in the case of a spherical fluid drop. 1939 – Robert Serber, George Volkoff, Richard Tolman, and J. Robert Oppenheimer study the stability of neutron stars, obtaining the Tolman–Oppenheimer–Volkoff limit. 1939 – J. Robert Oppenheimer and Hartland Snyder publish the Oppenheimer-Snyder model for the continued gravitational contraction of a star. === 1940s === 1948 – Ralph Alpher and Robert Herman predict the cosmic microwave background. 1949 – Cornelius Lanczos introduces the Lanczos potential for the Weyl tensor. 1949 – Kurt Gödel discovers Gödel's solution. === 1950s === 1953 – P. C. Vaidya Newtonian time in general relativity, Nature, 171, p260. 1954 – Suraj Gupta sketches how to derive the equations of general relativity from quantum field theory for a massless spin-2 particle (the graviton). His procedure was later carried out by Stanley Deser in 1970. 1955-56 – Robert Kraichnan shows that under the appropriate assumptions, Einstein's field equations of gravitation arise from the quantum field theory of a massless spin-2 particle coupled to the stress-energy tensor. This follows from his unpublished work as an undergraduate in 1947. 1956 – Bruno Berlotti develops the post-Minkowskian expansion. 1956 – John Lighton Synge publishes the first relativity text emphasizing spacetime diagrams and geometrical methods. 1957 – Felix A. E. Pirani uses Petrov classification to understand gravitational radiation. 1957 – Richard Feynman introduces his sticky bead argument. He later derives the quadrupole formula in a letter to Victor Weisskopf (1961). 1957-8 – John Wheeler discusses the breakdown of classical general relativity near singularities and the need for quantum gravity. 1958 – David Finkelstein presents a new coordinate system that eliminates the Schwarzschild radius as a singularity. 1959 – Robert Pound and Glen Rebka propose the Pound–Rebka experiment, first precision test of gravitational redshift. The experiment relies on the Mössbauer effect. 1959 – Lluís Bel introduces Bel–Robinson tensor and the Bel decomposition of the Riemann tensor. 1959 – Arthur Komar introduces the Komar mass. 1959 – Richard Arnowitt, Stanley Deser and Charles W. Misner developed ADM formalism. === 1960s === 1960 – Martin Kruskal and George Szekeres independently introduce the Kruskal–Szekeres coordinates for the Schwarzschild vacuum. 1960 – John Graves and Dieter Brill study the causal structure of an electrically charged black hole. 1960 – Thomas Matthews and Allan R. Sandage associate 3C 48 with a point-like optical image, show radio source can be at most 15 light minutes in diameter, 1960 – Ivor M. Robinson and Andrzej Trautman discover the Robinson-Trautman null dust solution 1960 – Robert Pound and Glen Rebka test the gravitational redshift predicted by the equivalence principle to approximately 1%. 1961 –Tullio Regge introduces the Regge calculus. 1961 – Carl H. Brans and Robert H. Dicke introduce Brans–Dicke theory, the first viable alternative theory with a clear physical motivation. 1961 – Pascual Jordan and Jürgen Ehlers develop the kinematic decomposition of a timelike congruence, 1961 – Robert Dicke, Peter Roll, and R. Krotkov refine the Eötvös experiment to an accuracy of 10−11. 1962 – John Wheeler and Robert Fuller show that the Einstein-Rosen bridge is unstable. 1962 – Roger Penrose and Ezra T. Newman introduce the Newman–Penrose formalism. 1962 – Ehlers and Wolfgang Kundt classify the symmetries of Pp-wave spacetimes. 1962 –Joshua Goldberg and Rainer K. Sachs prove the Goldberg–Sachs theorem. 1962 – Ehlers introduces Ehlers transformations, a new solution generating method, 1962 – Richard Arnowitt, Stanley Deser, and Charles W. Misner introduce the ADM reformulation and global hyperbolicity, 1962 – Istvan Ozsvath and Englbert Schücking rediscover the circularly polarized monochromomatic gravitational wave. 1962 – Hans Adolph Buchdahl discovers Buchdahl's theorem. 1962 – Hermann Bondi introduces Bondi mass. 1962 – Hermann Bondi, M. G. van der Burg, A. W. Metzner, and Rainer K. Sachs introduce the asymptotic symmetry group of asymptotically flat, Lorentzian spacetimes at null (i.e., light-like) infinity. 1963 – Roy Kerr discovers the Kerr vacuum solution of Einstein's field equations, 1963 – Redshifts of 3C 273 and other quasars show they are very distant; hence very luminous, 1963 – Newman, T. Unti and L.A. Tamburino introduce the NUT vacuum solution, 1963 – Roger Penrose introduces Penrose diagrams and Penrose limits. 1963 – Maarten Schmidt and Jesse Greenstein discover quasi-stellar objects, later shown to be moving away from Earth due to the expansion of the Universe. 1963 – First Texas Symposium on Relativistic Astrophysics held in Dallas, 16–18 December. 1964 – Steven Weinberg shows that a quantum field theory of interacting massless spin-2 particles is Lorentz invariant only if it satisfies the principle of equivalence. 1964 – Subrahmanyan Chandrasekhar determines a stability criterion. 1964 – R. W. Sharp and Charles Misner introduce the Misner–Sharp mass. 1964 – Hong-Yee Chiu coins the term "'quasar" for quasi-stellar radio sources. 1964 – Sjur Refsdal suggests that the Hubble constant could be determined using gravitational lensing. 1964 – Irwin Shapiro predicts a gravitational time delay of radiation travel as a test of general relativity. 1965 – Roger Penrose proves the first singularity theorem. 1965 – Penrose discovers the structure of the light cones in gravitational plane wave spacetimes. 1965 – Ezra Newman and others introduce Kerr-Newman metric. 1965 – Arno Penzias and Robert Wilson accidentally discover the cosmic microwave background radiation. This rules out the steady-state model of Fred Hoyle and Jayant Narlikar. 1965 – Joseph Weber puts the first Weber bar gravitational wave detector into operation. 1966 – Sachs and Ronald Kantowski discover the Kantowski-Sachs dust solution. 1967 – John Archibald Wheeler popularizes "black hole" at a conference. 1967 – Jocelyn Bell and Antony Hewish discover pulsars. 1967 – Robert H. Boyer and R. W. Lindquist introduce Boyer–Lindquist coordinates for the Kerr vacuum. 1967 – Bryce DeWitt publishes on canonical quantum gravity. 1967 – Werner Israel proves a special case of the no-hair theorem and the converse of Birkhoff's theorem. 1967 – Kenneth Nordtvedt develops PPN formalism. 1967 – Mendel Sachs publishes factorization of Einstein's field equations. 1967 – Hans Stephani discovers the Stephani dust solution. 1968 – F. J. Ernst discovers the Ernst equation. 1968 – B. Kent Harrison discovers the Harrison transformation, a solution-generating method. 1968 – Brandon Carter solves the geodesic equations for Kerr–Newmann electrovacuum with Carter's constant. 1968 – Hugo D. Wahlquist discovers the Wahlquist fluid. 1968 – James Hartle and Kip Thorne obtain the Hartle–Thorne metric. 1968 – Irwin Shapiro and his colleagues present the first detection of the Shapiro delay. 1968 – Kenneth Nordtvedt studies a possible violation of the weak equivalence principle for self-gravitating bodies and proposes a new test of the weak equivalence principle based on observing the relative motion of the Earth and Moon in the Sun's gravitational field. 1969 – William B. Bonnor introduces the Bonnor beam. 1969 – Joseph Weber reports observation of gravitational waves a claim now generally discounted. 1969 – Penrose proposes the (weak) cosmic censorship hypothesis and the Penrose process, 1969 – Misner introduces the mixmaster universe. 1969 – Yvonne Choquet-Bruhat and Robert Geroch discuss global aspects of the Cauchy problem in general relativity. 1965-70 – Subrahmanyan Chandrasekhar and colleagues develops the post-Newtonian expansions. 1968-70 – Roger Penrose, Stephen Hawking, and George Ellis prove that singularities must arise in the Big Bang models. === 1970s === 1970 – Vladimir Alekseevich Belinski, Isaak Markovich Khalatnikov, and Evgeny Lifshitz introduce the BKL conjecture. 1970 – Stephen Hawking and Roger Penrose prove trapped surfaces must arise in black holes. 1971 – David Scott demonstrates that a hammer and a feather fall at the same rate on the Moon. 1971 – Alfred Goldhaber and Michael Nieto give stringent limits on the photon mass. The strictest one is m γ ≤ 4 × 10 − 51 kg {\displaystyle m_{\gamma }\leq 4\times 10^{-51}{\text{kg}}} . 1971 – Stephen Hawking proves that the area of a black hole can never decrease. 1971 – Peter C. Aichelburg and Roman U. Sexl introduce the Aichelburg–Sexl ultraboost. 1971 – Introduction of the Khan–Penrose vacuum, a simple explicit colliding plane wave spacetime. 1971 – Robert H. Gowdy introduces the Gowdy vacuum solutions (cosmological models containing circulating gravitational waves). 1971 – Cygnus X-1, the first solid black hole candidate, discovered by Uhuru satellite. 1971 – William H. Press discovers black hole ringing by numerical simulation. 1971 – Harrison and Estabrook algorithm for solving systems of PDEs. 1971 – James W. York introduces conformal method generating initial data for ADM initial value formulation. 1971 – Robert Geroch introduces Geroch group and a solution generating method. 1972 – Jacob Bekenstein proposes that black holes have a non-decreasing entropy which can be identified with the area. 1972 – Sachs introduces optical scalars and proves peeling theorem. 1972 – Rainer Weiss proposes concept of interferometric gravitational wave detector in an unpublished manuscript. 1972 – Joseph Hafele and Richard Keating perform the Hafele–Keating experiment. 1972 – Richard H. Price studies gravitational collapse with numerical simulations. 1972 – Saul Teukolsky derives the Teukolsky equation. 1972 – Yakov B. Zel'dovich predicts the transmutation of electromagnetic and gravitational radiation. 1972 – Brandon Carter, Stephen Hawking, and James M. Bardeen propose the four laws of black hole mechanics. 1972 – James Bardeen calculates the shadow of a black hole. This was later verified by the Event Horizon Telescope. 1973 – Charles W. Misner, Kip S. Thorne and John A. Wheeler publish the treatise Gravitation, a textbook that remains in use in the twenty-first century. 1973 – Stephen W. Hawking and George Ellis publish the monograph The Large Scale Structure of Space-Time. 1973 – Robert Geroch introduces the GHP formalism. 1973 – Homer Ellis obtains the Ellis drainhole, the first traversable wormhole. 1974 – Russell Hulse and Joseph Hooton Taylor, Jr. discover the Hulse–Taylor binary pulsar, 1974 – James W. York and Niall Ó Murchadha present the analysis of the initial value formulation and examine the stability of its solutions. 1974 – R. O. Hansen introduces Hansen–Geroch multipole moments. 1974 – Stephen Hawking discovers Hawking radiation. 1975 – Stephen Hawking shows that the area of a black hole is proportional to its entropy, as previously conjectured by Jacob Bekenstein. 1975 – Roberto Colella, Albert Overhauser, and Samuel Werner observe the quantum-mechanical phase shift of neutrons due to gravity. Neutron interferometry was later used to test the principle of equivalence. 1975 – Chandrasekhar and Steven Detweiler compute the effects of perturbations on a Schwarzschild black hole. 1975 – Szekeres and D. A. Szafron discover the Szekeres–Szafron dust solutions. 1976 – Penrose introduces Penrose limits (every null geodesic in a Lorentzian spacetime behaves like a plane wave), 1978 – Penrose introduces the notion of a thunderbolt, 1978 – Belinskiǐ and Zakharov show how to solve Einstein's field equations using the inverse scattering transform; the first gravitational solitons, 1979 – Dennis Walsh, Robert Carswell, and Ray Weymann discover the gravitationally lensed quasar Q0957+561. 1979 – Jean-Pierre Luminet creates an image of a black hole with an accretion disk using computer simulation. 1979 – Steven Detweiler proposes using pulsar timing arrays to detect gravitational waves. 1979-81 – Richard Schoen and Shing-Tung Yau prove the positive mass theorem. Edward Witten independently proves the same thing. === 1980s === 1980 – Vera Rubin and colleagues study the rotational properties of UGC 2885, demonstrating the prevalence of dark matter. 1980 – Gravity Probe A verifies gravitational redshift to approximately 0.007% using a space-born hydrogen maser. 1980 – James Bardeen explains structure in the Universe using cosmological perturbation theory. 1981 – Alan Guth proposes cosmic inflation in order to solve the flatness and horizon problems. 1982 – Joseph Taylor and Joel Weisberg show that the rate of energy loss from the binary pulsar PSR B1913+16 agrees with that predicted by the general relativistic quadrupole formula to within 5%. 1983 – James Hartle and Stephen Hawking propose the no-boundary wave function for the Universe. 1983-84 – RELIKT-1 observes the cosmic microwave background. 1986 – Helmut Friedrich proves that the de Sitter spacetime is stable. 1986 – Bernard Schutz shows that cosmic distances can be determined using sources of gravitational waves without references to the cosmic distance ladder. Standard-siren astronomy is born. 1988 – Mike Morris, Kip Thorne, and Yurtsever Ulvi obtain the Morris-Thorne wormhole. Morris and Thorne argue for its pedagogical value. 1989 – Steven Weinberg discusses the cosmological constant problem, the discrepancy between the measured value and those predicted by modern theories of elementary particles. 1989-93 – The Cosmic Background Explorer (COBE) identifies anisotropy in the cosmic microwave background. === 1990s === 1992 – Stephen Hawking states his chronology protection conjecture. 1993 – Demetrios Christodoulou and Sergiu Klainerman prove the non-linear stability of the Minkowski spacetime. 1995 – John F. Donoghue show that general relativity is a quantum effective field theory. This framework could be used to analyze binary systems observed by gravitational-wave observatories. 1995 – Hubble Deep Field image taken. It is a landmark in the study of cosmology. 1998 – The first complete Einstein ring, B1938+666, discovered using the Hubble Space Telescope and MERLIN. 1998-99 – Scientists discover that the expansion of the Universe is accelerating. 1999 – Alessandra Buonanno and Thibault Damour introduce the effective one-body formalism. This was later used to analyze data collected by gravitational-wave observatories. == 2000s == 2003 – Arvind Borde, Alan Guth, and Alexander Vilenkin prove the Borde–Guth–Vilenkin theorem. 2002 – First data collection of the Laser Interferometer Gravitational-Wave Observatory (LIGO). 2002 – James Williams, Slava Turyshev, and Dale Boggs conduct stringent lunar test of violations of the principle of equivalence. 2005 – Daniel Holz and Scott Hughes coin the term "standard sirens". 2009 – Gravity Probe B experiment verifies the geodetic effect to 0.5%. === 2010s === 2010 – A team at the U.S. National Institute for Standards and Technology (NIST) verifies relativistic time dilation using optical atomic clocks. 2011 – Wilkinson Microwave Anisotropy Probe (WMAP) finds no statistically significant deviations from the ΛCDM model of cosmology. 2012 – Hubble Ultra-Deep Field image released. It was created using data collected by the Hubble Space Telescope between 2003 and 2004. 2013 – NuSTAR and XMM-Newton measure the spin of the supermassive black hole at the center of the galaxy NGC 1365. 2015 – Advanced LIGO reports the first direct detections of gravitational waves, GW150914 and GW151226, mergers of stellar-mass black holes. Gravitational-wave astronomy is born. No deviations from general relativity were found. 2017 – LIGO-VIRGO collaboration detects gravitational waves emitted by a neutron-star binary, GW170817. The Fermi Gamma-ray Space Telescope and the International Gamma-ray Astrophysics Laboratory (INTEGRAL) unambiguously detect the corresponding gamma-ray burst. LIGO-VIRGO and Fermi constrain the difference between the speed of gravity and the speed of light in vacuum to 10−15. This marks the first time electromagnetic and gravitational waves are detected from a single source, and give direct evidence that some (short) gamma-ray bursts are due to colliding neutron stars. 2017 – Multi-messenger astronomy reveals neutron-star mergers to be responsible for the nucleosynthesis of some heavy elements, such as strontium, via the rapid-neutron capture or r-process. 2017 – MICROSCOPE satellite experiment verifies the principle of equivalence to 10−15 in terms of the Eötvös ratio η {\displaystyle \eta } . The final report is published in 2022. 2017 – Principle of equivalence tested to 10−9 for atoms in a coherent state of superposition. 2017 – Scientists begin using gravitational-wave sources as "standard sirens" to measure the Hubble constant, finding its value to be broadly in line with the best estimates of the time. Refinements of this technique will help resolve discrepancies between the different methods of measurements. 2017 – Neutron Star Interior Composition Explorer (NICER) arrives on the International Space Station. 2017-18 – Georgios Moschidis proves the instability of the anti-de Sitter spacetime. 2018 – Final paper by the Planck satellite collaboration. Planck operated between 2009 and 2013. 2018 – Mihalis Dafermos and Jonathan Luk disprove the strong cosmic censorship hypothesis for the Cauchy horizon of an uncharged, rotating black hole. 2018 – European Southern Observatory (ESO) observes gravitational redshift of radiation emitted by matter orbiting Sagittarius A*, the central supermassive black hole of the Milky Way, and verifies the innermost stable circular orbit for that object. 2018 – Advanced LIGO-VIRGO collaboration constrains equations of state for a neutron star using GW170817. 2018 – Luciano Rezzolla, Elias R. Most, and Lukas R. Weih used gravitational-wave data from GW170817 constrain the possible maximum mass for a neutron star to around 2.17 solar masses. 2018 – Kris Pardo, Maya Fishbach, Daniel Holz, and David Spergel limit the number of spacetime dimensions through which gravitational waves can propagate to 3 + 1, in line with general relativity and ruling out models that allow for "leakage" to higher dimensions of space. Analyses of GW170817 have also ruled out many other alternatives to general relativity, and proposals for dark energy. 2018 – Two different experimental teams report highly precise values of Newton's gravitational constant G {\displaystyle G} that slightly disagree. 2019 – Event Horizon Telescope (EHT) releases an image of supermassive black hole M87*, and measures its mass and shadow. Results are confirmed in 2024. 2019 – Advanced LIGO and VIRGO detect GW190814, the collision of a 26-solar-mass black hole and a 2.6-solar-mass object, either an extremely heavy neutron star or a very light black hole. This is the largest mass gap seen in a gravitational-wave source to-date. === 2020s === 2020 – Principle of equivalence tested for individual atoms using atomic interferometry to ~10−12. 2020 – ESO observes Schwarzschild precession of the star S2 about Sagittarius A*. 2021 – Jun Ye and his team measure gravitational redshift with an accuracy of 7.6 × 10−21 using an ultracold cloud of 100,000 strontium atoms in an optical lattice. 2021 – EHT measures the polarization of the ring of M87*, and other properties of the magnetic field in its vicinity. 2021 – EHT releases an image of Sagittarius A*, measures its shadow, and shows that it is accurately described by the Kerr metric. 2022 – Chris Overstreet and his team observe the gravitational Aharonov-Bohm effect using an experimental design from 2012. 2022 – James Webb Space Telescope (JWST) publishes its first image, a deep-field photograph of the SMACS 0723 galaxy cluster. 2022 – Neil Gehrels Swift Observatory detects GRB 221009A, the brightest gamma-ray burst recorded. 2022 – JWST identifies several candidate high-redshift objects, corresponding to just a few hundred million years after the Big Bang. 2023 – James Nightingale and colleagues detect Abell 1201, an ultramassive black hole (33 billion solar masses), using strong gravitational lensing. 2023 – Matteo Bachetti and colleagues confirm that neutron star M82 X-2 is violating the Eddington limit, making it an ultraluminous X-ray source (ULX). 2023 – Team led by Dong Sheng and Zheng-Tian Lu found a null result for the coupling between quantum spin and gravity to 10−9. 2023 – The North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the European Pulsar Timing Array (EPTA), the Parkes Pulsar Timing Array (Australia), and the Chinese Pulsar Timing Array report detection of a gravitational-wave background. 2023 – Geraint F. Lewis and Brendon Brewer present evidence of cosmological time dilation in quasars. 2024 – The Large High Altitude Air Shower Observatory (LHAASO) collaboration imposes stringent limits on violations of Lorentz invariance proposed in certain theories of quantum gravity using GRB 221009A. == See also == Timeline of black hole physics Timeline of special relativity and the speed of light List of contributors to general relativity List of scientific publications by Albert Einstein == References == == External links == Timeline of relativity and gravitation (Tomohiro Harada, Department of Physics, Rikkyo University) Timeline of General Relativity and Cosmology from 1905 2015–General Relativity's Centennial. Physical Review Journals. American Physical Society (APS).
Wikipedia/Timeline_of_gravitational_physics_and_relativity
A timeline of events in the history of thermodynamics. == Before 1800 == 1593 – Galileo Galilei invents one of the first thermoscopes, also known as Galileo thermometer 1650 – Otto von Guericke builds the first vacuum pump 1660 – Robert Boyle experimentally discovers Boyle's law, relating the pressure and volume of a gas (published 1662) 1665 – Robert Hooke published his book Micrographia, which contained the statement: "Heat being nothing else but a very brisk and vehement agitation of the parts of a body." 1667 – J. J. Becher puts forward a theory of combustion involving combustible earth in his book Physica subterranea (see Phlogiston theory). 1676–1689 – Gottfried Leibniz develops the concept of vis viva, a limited version of the conservation of energy 1679 – Denis Papin designed a steam digester which inspired the development of the piston-and-cylinder steam engine. 1694–1734 – Georg Ernst Stahl names Becher's combustible earth as phlogiston and develops the theory 1698 – Thomas Savery patents an early steam engine 1702 – Guillaume Amontons introduces the concept of absolute zero, based on observations of gases 1738 – Daniel Bernoulli publishes Hydrodynamica, initiating the kinetic theory 1749 – Émilie du Châtelet, in her French translation and commentary on Newton's Philosophiae Naturalis Principia Mathematica, derives the conservation of energy from the first principles of Newtonian mechanics. 1761 – Joseph Black discovers that ice absorbs heat without changing its temperature when melting 1772 – Black's student Daniel Rutherford discovers nitrogen, which he calls phlogisticated air, and together they explain the results in terms of the phlogiston theory 1776 – John Smeaton publishes a paper on experiments related to power, work, momentum, and kinetic energy, supporting the conservation of energy 1777 – Carl Wilhelm Scheele distinguishes heat transfer by thermal radiation from that by convection and conduction 1783 – Antoine Lavoisier discovers oxygen and develops an explanation for combustion; in his paper "Réflexions sur le phlogistique", he deprecates the phlogiston theory and proposes a caloric theory 1784 – Jan Ingenhousz describes Brownian motion of charcoal particles on water 1791 – Pierre Prévost shows that all bodies radiate heat, no matter how hot or cold they are 1798 – Count Rumford (Benjamin Thompson) publishes his paper "An Inquiry Concerning the Source of the Heat Which Is Excited by Friction" detailing measurements of the frictional heat generated in boring cannons and develops the idea that heat is a form of kinetic energy; his measurements are inconsistent with caloric theory, but are also sufficiently imprecise as to leave room for doubt. == 1800–1847 == 1802 – Joseph Louis Gay-Lussac publishes Charles's law, discovered (but unpublished) by Jacques Charles around 1787; this shows the dependency between temperature and volume. Gay-Lussac also formulates the law relating temperature with pressure (the pressure law, or Gay-Lussac's law) 1804 – Sir John Leslie observes that a matte black surface radiates heat more effectively than a polished surface, suggesting the importance of black-body radiation 1805 – William Hyde Wollaston defends the conservation of energy in On the Force of Percussion 1808 – John Dalton defends caloric theory in A New System of Chemistry and describes how it combines with matter, especially gases; he proposes that the heat capacity of gases varies inversely with atomic weight 1810 – Sir John Leslie freezes water to ice artificially 1813 – Peter Ewart supports the idea of the conservation of energy in his paper On the measure of moving force; the paper strongly influences Dalton and his pupil, James Joule 1819 – Pierre Louis Dulong and Alexis Thérèse Petit give the Dulong-Petit law for the specific heat capacity of a crystal 1820 – John Herapath develops some ideas in the kinetic theory of gases but mistakenly associates temperature with molecular momentum rather than kinetic energy; his work receives little attention other than from Joule 1822 – Joseph Fourier formally introduces the use of dimensions for physical quantities in his Théorie Analytique de la Chaleur 1822 – Marc Seguin writes to John Herschel supporting the conservation of energy and kinetic theory 1824 – Sadi Carnot analyzes the efficiency of steam engines using caloric theory; he develops the notion of a reversible process and, in postulating that no such thing exists in nature, lays the foundation for the second law of thermodynamics, and initiating the science of thermodynamics 1827 – Robert Brown discovers the Brownian motion of pollen and dye particles in water 1831 – Macedonio Melloni demonstrates that black-body radiation can be reflected, refracted, and polarised in the same way as light 1834 – Émile Clapeyron popularises Carnot's work through a graphical and analytic formulation. He also combined Boyle's law, Charles's law, and Gay-Lussac's law to produce a combined gas law. PV/T = k 1841 – Julius Robert von Mayer, an amateur scientist, writes a paper on the conservation of energy, but his lack of academic training leads to its rejection 1842 – Mayer makes a connection between work, heat, and the human metabolism based on his observations of blood made while a ship's surgeon; he calculates the mechanical equivalent of heat 1842 – William Robert Grove demonstrates the thermal dissociation of molecules into their constituent atoms, by showing that steam can be disassociated into oxygen and hydrogen, and the process reversed 1843 – John James Waterston fully expounds the kinetic theory of gases, but according to D Levermore "there is no evidence that any physical scientist read the book; perhaps it was overlooked because of its misleading title, Thoughts on the Mental Functions." 1843 – James Joule experimentally finds the mechanical equivalent of heat 1845 – Henri Victor Regnault added Avogadro's law to the combined gas law to produce the ideal gas law. PV = nRT 1846 – Grove publishes an account of the general theory of the conservation of energy in On The Correlation of Physical Forces 1847 – Hermann von Helmholtz publishes a definitive statement of the conservation of energy, the first law of thermodynamics == 1848–1899 == 1848 – William Thomson extends the concept of absolute zero from gases to all substances 1849 – William John Macquorn Rankine calculates the correct relationship between saturated vapour pressure and temperature using his hypothesis of molecular vortices 1850 – Rankine uses his vortex theory to establish accurate relationships between the temperature, pressure, and density of gases, and expressions for the latent heat of evaporation of a liquid; he accurately predicts the surprising fact that the apparent specific heat of saturated steam will be negative 1850 – Rudolf Clausius coined the term "entropy" (das Wärmegewicht, symbolized S) to denote heat lost or turned into waste. ("Wärmegewicht" translates literally as "heat-weight"; the corresponding English term stems from the Greek τρέπω, "I turn".) 1850 – Clausius gives the first clear joint statement of the first and second law of thermodynamics, abandoning the caloric theory, but preserving Carnot's principle 1851 – Thomson gives an alternative statement of the second law 1852 – Joule and Thomson demonstrate that a rapidly expanding gas cools, later named the Joule–Thomson effect or Joule–Kelvin effect 1854 – Helmholtz puts forward the idea of the heat death of the universe 1854 – Clausius establishes the importance of dQ/T (Clausius's theorem), but does not yet name the quantity 1854 – Rankine introduces his thermodynamic function, later identified as entropy 1856 – August Krönig publishes an account of the kinetic theory of gases, probably after reading Waterston's work 1857 – Clausius gives a modern and compelling account of the kinetic theory of gases in his On the nature of motion called heat 1859 – James Clerk Maxwell discovers the distribution law of molecular velocities 1859 – Gustav Kirchhoff shows that energy emission from a black body is a function of only temperature and frequency 1862 – "Disgregation", a precursor of entropy, was defined in 1862 by Clausius as the magnitude of the degree of separation of molecules of a body 1865 – Clausius introduces the modern macroscopic concept of entropy 1865 – Josef Loschmidt applies Maxwell's theory to estimate the number-density of molecules in gases, given observed gas viscosities. 1867 – Maxwell asks whether Maxwell's demon could reverse irreversible processes 1870 – Clausius proves the scalar virial theorem 1872 – Ludwig Boltzmann states the Boltzmann equation for the temporal development of distribution functions in phase space, and publishes his H-theorem 1873 - Johannes Diderik van der Waals formulates his equation of state 1874 – Thomson formally states the second law of thermodynamics 1876 – Josiah Willard Gibbs publishes the first of two papers (the second appears in 1878) which discuss phase equilibria, statistical ensembles, the free energy as the driving force behind chemical reactions, and chemical thermodynamics in general. 1876 – Loschmidt criticises Boltzmann's H theorem as being incompatible with microscopic reversibility (Loschmidt's paradox). 1877 – Boltzmann states the relationship between entropy and probability 1879 – Jožef Stefan observes that the total radiant flux from a blackbody is proportional to the fourth power of its temperature and states the Stefan–Boltzmann law 1884 – Boltzmann derives the Stefan–Boltzmann blackbody radiant flux law from thermodynamic considerations 1888 – Henri-Louis Le Chatelier states his principle that the response of a chemical system perturbed from equilibrium will be to counteract the perturbation 1889 – Walther Nernst relates the voltage of electrochemical cells to their chemical thermodynamics via the Nernst equation 1889 – Svante Arrhenius introduces the idea of activation energy for chemical reactions, giving the Arrhenius equation 1893 – Wilhelm Wien discovers the displacement law for a blackbody's maximum specific intensity == 1900–1944 == 1900 – Max Planck suggests that light may be emitted in discrete frequencies, giving his law of black-body radiation 1905 – Albert Einstein, in the first of his miracle year papers, argues that the reality of quanta would explain the photoelectric effect 1905 – Einstein mathematically analyzes Brownian motion as a result of random molecular motion in his paper On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat 1906 – Nernst presents a formulation of the third law of thermodynamics 1907 – Einstein uses quantum theory to estimate the heat capacity of an Einstein solid 1909 – Constantin Carathéodory develops an axiomatic system of thermodynamics 1910 – Einstein and Marian Smoluchowski find the Einstein–Smoluchowski formula for the attenuation coefficient due to density fluctuations in a gas 1911 – Paul Ehrenfest and Tatjana Ehrenfest–Afanassjewa publish their classical review on the statistical mechanics of Boltzmann, Begriffliche Grundlagen der statistischen Auffassung in der Mechanik 1912 – Peter Debye gives an improved heat capacity estimate by allowing low-frequency phonons 1916 – Sydney Chapman and David Enskog systematically develop the kinetic theory of gases 1916 – Einstein considers the thermodynamics of atomic spectral lines and predicts stimulated emission 1919 – James Jeans discovers that the dynamical constants of motion determine the distribution function for a system of particles 1920 – Meghnad Saha states his ionization equation 1923 – Debye and Erich Hückel publish a statistical treatment of the dissociation of electrolytes 1924 – Satyendra Nath Bose introduces Bose–Einstein statistics, in a paper translated by Einstein 1926 – Enrico Fermi and Paul Dirac introduce Fermi–Dirac statistics 1927 – John von Neumann introduces the density matrix representation, establishing quantum statistical mechanics 1928 – John B. Johnson discovers Johnson noise in a resistor 1928 – Harry Nyquist derives the fluctuation-dissipation theorem, a relationship to explain Johnson noise in a resistor 1931 – Lars Onsager publishes his groundbreaking paper deriving the Onsager reciprocal relations 1935 – Ralph H. Fowler invents the title 'the zeroth law of thermodynamics' to summarise postulates made by earlier physicists that thermal equilibrium between systems is a transitive relation 1938 – Anatoly Vlasov proposes the Vlasov equation for a correct dynamical description of ensembles of particles with collective long range interaction 1939 – Nikolay Krylov and Nikolay Bogolyubov give the first consistent microscopic derivation of the Fokker–Planck equation in the single scheme of classical and quantum mechanics 1942 – Joseph L. Doob states his theorem on Gauss–Markov processes 1944 – Lars Onsager gives an analytic solution to the 2-dimensional Ising model, including its phase transition == 1945–present == 1945–1946 – Nikolay Bogoliubov develops a general method for a microscopic derivation of kinetic equations for classical statistical systems using BBGKY hierarchy 1947 – Nikolay Bogoliubov and Kirill Gurov extend this method for a microscopic derivation of kinetic equations for quantum statistical systems 1948 – Claude Elwood Shannon establishes information theory 1957 – Aleksandr Solomonovich Kompaneets derives his Compton scattering Fokker–Planck equation 1957 – Ryogo Kubo derives the first of the Green-Kubo relations for linear transport coefficients 1957 – Edwin T. Jaynes publishes two papers detailing the MaxEnt interpretation of thermodynamics from information theory 1960–1965 – Dmitry Zubarev develops the method of non-equilibrium statistical operator, which becomes a classical tool in the statistical theory of non-equilibrium processes 1972 – Jacob Bekenstein suggests that black holes have an entropy proportional to their surface area 1974 – Stephen Hawking predicts that black holes will radiate particles with a black-body spectrum which can cause black hole evaporation 1977 – Ilya Prigogine wins the Nobel prize for his work on dissipative structures in thermodynamic systems far from equilibrium. The importation and dissipation of energy could reverse the 2nd law of thermodynamics == See also == Timeline of heat engine technology History of physics History of thermodynamics Thermodynamics Timeline of information theory List of textbooks in thermodynamics and statistical mechanics == References ==
Wikipedia/Timeline_of_thermodynamics
Universal science (German: Universalwissenschaft; Latin: scientia generalis, scientia universalis) is a branch of metaphysics, dedicated to the study of the underlying principles of all science. Instead of viewing knowledge as being separated into branches, Universalists view all knowledge as being part of a single category. Universal science is related to, but distinct from universal language. == Precursors == Logic and rationalism lie at the foundation of the ideas of universal science. In a broad sense, logic is the study of reasoning. Although there were individuals that implicitly utilized logical methods prior to Aristotle, it is generally agreed he was the originator of modern systems of logic. The Organon, Aristotle's books on logic, details this system. In Categories, Aristotle separates everything into 10 "categories": substance, quantity, quality, relation, place, time, position, state, action, and passion. In De Interpretatione, Aristotle studied propositions, detailing what he determined were the most basic propositions and the relationships between them. The Organon had several other books, which further detailed the process of constructing arguments, deducing logical consequences, and even contained the foundations of the modern scientific method. The most immediate predecessor to universal science is the system of formal logic, which is the study of the abstract notions of propositions and arguments, usually utilizing symbols to represent these structures. Formal logic differs from previous systems of logic by looking exclusively at the structure of an argument, instead of at the specific aspects of each statement. Thus, while the statements "Jeff is shorter than Jeremy and Jeremy is shorter Aidan, so Jeff is shorter than Aidan" and "Every triangle has less sides than every rectangle and every rectangle has less sides than every pentagon, so every triangle has less sides than every pentagon" deal with different specific information, they are both are equivalent in formal logic to the expression ∀ x ∈ X , y ∈ Y , z ∈ Z , x < y ∧ y < z ⟹ x < z {\displaystyle \forall x\in X,y\in Y,z\in Z,\quad x<y\wedge y<z\implies x<z} . By abstracting away from the specifics of each statement and argument, formal logic allows the overarching structure of logic to be studied. This viewpoint inspired later logicians to seek out a set of minimal size containing all of the requisite knowledge from which everything else could be derived and is the fundamental idea behind universal science. == Llull == Ramon Llull was a 13th century Catalan philosopher, mystic, and poet. He is best known for creating an "art of finding truth" with the intention of unifying all knowledge. Llull sought to unify philosophy, theology, and mysticism through a single universal model to understand reality. Llull compiled his thoughts into his work Ars Magna, which had several versions. The most thorough and complete version being the Ars Generalis Ultima, which he wrote several years before his death. The Ars Generalis Ultima consisted of several books, which explained the Ars, his universal system to understand all of reality. The books included the principles, definitions, and questions, along with ways to combine these things, which Llull thought could serve as the basis from which reality could be studied. Since he was primarily focused upon faith and Christianity, the content of these books was also mainly concerned with religious ideas and concepts. In fact, the Ars contained figures and diagrams representing ideas from Christianity, Islam, and Judaism to serve as a tool to aid philosophers from each of the three religions to discuss ideas in a logical manner. == Leibniz == Gottfried Wilhelm Leibniz was a 17th century German philosopher, mathematician, and political adviser, metaphysician, and logician, distinguished for his achievements including the independent creation of the mathematical field of Calculus. Leibniz entered the University of Leipzig in 1661, which is where he first studied the teachings of many famous scientists and philosophers, such as Rene Descartes, Galileo Galilei, Francis Bacon, and Thomas Hobbes. These individuals, together with Aristotle, influenced Leibniz's future philosophical ideas, with one major idea being the reconciliation of the ideas of modern philosophers with the thoughts of Aristotle, already demonstrating Leibniz's interest in unification. Unification played a major role in one of Leibniz's early works, Dissertatio de arte Combinatoria. Written in 1666, De arte Combinatoria was a mathematical and philosophical text that served as the basis for Leibniz's future goal for a universal science. The text starts by analysis several mathematical problems in combinatorics, the study of ways in which objects can be arranged. While the mathematics in the text was not revolutionary, the main impact came from the ideas Leibniz derived following the mathematics. Taking major influence from Ramon Llull's ideas in his Ars Magna, Leibniz argued that the solution to these combinatorial problems served as a base for all logic and reasoning, since all of human knowledge could be viewed as different permutations of some base set. Leibniz's ideas about unifying human knowledge culminated in his Characteristica universalis, which was a proposed language that would allow for logical statements and arguments to become symbolic calculations. Leibniz aimed to construct "the alphabet of human thought," which was the collection of all of the "primitives" from which all human thought could be derived through the processes described in de arte Combinatoria. == Modern Influences == Although it has never been constructed, the ideas behind Leibniz's universal science have permeated the thoughts of many modern mathematics and philosophers. George Boole, a 19th century English mathematician, expanded upon the ideas of Leibniz. He is responsible for the modern symbolic system logic, aptly called Boolean Algebra. Boole's logical system, and thus also Leibniz's logical system, served as the foundation for modern computers and electronic circuitry. The fundamental ideas of universal science can also be seen in the modern axiomatic system of mathematics, which constructs mathematical theories as consequences of a set of axioms. In this case, axioms are the primitive elements from which all further propositions can be derived. Hilbert's Program was an attempt by German mathematician David Hilbert to axiomatize all of mathematics in the above manner, and additionally to prove that these axiomatic systems are consistent. Kurt Gödel was an Austrian mathematician and logician, who furthered the investigations in logic and the foundations of mathematics began by Hilbert and Russell in the early 20th century. Gödel is most famous for his incompleteness theorems, which encompass two theorems about provability and completeness of logical systems. In his first theorem, Gödel asserts that any formal system that includes arithmetic will have a statement which cannot be proven nor disproven within the system. His second theorem stated that a formal system additionally cannot prove that it is consistent, using methods only from that system. Thus, Gödel essentially refuted Hilbert's Program, along with aspects of universal science. == See also == Architectonics Unified Science Universal Language Ars Magna Dissertatio de arte Combinatoria Characteristica universalis Mathesis universalis == References == == External links == Stephen Palmquist, Heading 6, Philosophy as the Theological Science
Wikipedia/Universal_science
The Discourse on Metaphysics (French: Discours de métaphysique, 1686) is a short treatise by Gottfried Wilhelm Leibniz in which he develops a philosophy concerning physical substance, motion and resistance of bodies, and God's role within the universe. It is one of the few texts presenting in a consistent form the earlier philosophy of Leibniz. The Discourse is closely connected to the epistolary discussion which he carried with Antoine Arnauld. However Leibniz refrained from sending the full text and it remained unpublished until the mid 19th century. Arnauld received only an abridged version in 37 points which resumed whole paragraphs and steered their discussion. == Contents == Source: == Summary == The metaphysical considerations proceed from God to the substantial world and back to the spiritual realm. The starting point for the work is the conception of God as an absolutely perfect being (I), that God is good but goodness exists independently of God (a rejection of divine command theory) (II), and that God has created the world in an ordered and perfect fashion (III–VII). At the time of its writing Discourse made the controversial claim That the opinions of... scholastic philosophers are not to be wholly despised (XI). Early work in modern philosophy during the 17th century were based on a rejection of many of the precepts of medieval philosophy. Leibniz saw the failures of scholasticism merely as one of rigor. [If] some careful and meditative mind were to take the trouble to clarify and direct their thoughts in the manner of analytic geometers, he would find a great treasure of important truths, wholly demonstrable. Leibniz claimed that God's omnipotence was in no way impugned by the thought of evil, but was rather solidified. He endorsed the view that God chose the best of all possible worlds. In other words, Leibniz believed this world (or reality) to be the best there possibly could be — taking all facts into account, no better world could be imagined, even if we believed that we could think of something more perfect. Leibniz's conception of physical substance is expanded upon in The Monadology and Principles of Nature and Grace. == See also == Problem of future contingents == Notes == == References == Leibniz, Gottfried Wilhelm. Discourse on Metaphysics and the Monadology (trans. George R. Montgomery). Prometheus Books, 1992 (first published by Open Court, 1902). == External links == Discourse on Metaphysics. A complete English translation by George R. Montgomery. Discourse on Metaphysics public domain audiobook at LibriVox
Wikipedia/Discourse_on_Metaphysics
A golden age of physics appears to have been delineated for certain periods of progress in the physics sciences, and this includes the previous and current developments of cosmology and astronomy. Each "golden age" introduces significant advancements in theoretical and experimental methods. Discernible time periods marking a "golden age" of advancements are, for example, the development of mechanics under Galileo (1564–1642) and Isaac Newton (1642–1727). Another small epoch seen as a golden age is the unification of electricity, magnetism, and optics because of 19th century notables, including Michael Faraday, James Clerk Maxwell, and others. Significant advancements in methods of investigation were introduced for celestial mechanics, which includes realizing a universal gravitational force, with the introduction of the telescope. Basing mechanics on experimental results was possible with the development of devices that could measure time, and tools for measuring distance. The advances in electromagnetism in the 19th century enamored physicists, as another golden age closed, and there was a reluctance to perceive further advancement. Hence, the progress of one era, termed a "golden age" has appeared to mark the completion of physics as a science. Yet, this perception has turned out to be erroneous. For example, around 1980, Stephen Hawking predicted the end of theoretical physics within 20 years. Around 2001, he amended his prediction to twenty years more from that year. Steven Weinberg predicts a unified physics by 2050. Tadeusz Lulek, Barbara Lulek, and A. Wal – the authors of a 2001 book – believed themselves to be at the beginning of a new "golden age of physics". Paul Davies notes that whilst "many elderly scientists" may regard the first 30 years of the 20th century as a golden age of physics, historians may well, instead, regard it to be the dawning days of "the New Physics". When Paul Dirac received the J. Robert Oppenheimer Memorial Prize in 1969, said I can thank the fact that I was born at just the right time. A few years older or younger, I would have missed the opportunity... One might call the period from 1925 onward for a few years the Golden Age of Physics when our basic ideas were developing very rapidly and there was plenty of work for everyone to do. The golden age of physics was the 19th century. According to Emilio Segrè, in Italy it came to an end in the 18th century, after the time of Alessandro Volta. He reported in his autobiography that Enrico Fermi felt that it was coming to an end in 1933. A golden age of physics began with the simultaneous discovery of the principle of the conservation of energy in the mid-19th century. A golden age of physics was the years 1925 to 1927. The golden age of nonlinear physics was the period from 1950 to 1970, encompassing the Fermi–Pasta–Ulam–Tsingou problem and others. This followed the golden age of nuclear physics, which had spanned the two decades from the mid-1930s to the mid-1950s. A golden age of physics started at the end of the 1920s. The golden age of physics cabinets was the 18th century, with the rise of such lecturer-demonstrators as John Keill, John Theophilus Desaguliers, and William Whiston, who all invented new physics apparatus for their lectures. == See also == Golden age of general relativity Golden age of cosmology Golden age (metaphor) == References == === Reference bibliography === Amaldi, Edoardo (1998). "The Case of Physics". In Giovanni Battimelli; Giovanni Paoloni (eds.). 20th century physics: essays and recollections : a selection of historical writings. World Scientific. ISBN 978-981-02-2369-4. Brenni, Paolo (2002). "Jean Antoine Nollet and Physics Instruments". In Lewis Pyenson; Jean-François Gauvin (eds.). The art of teaching physics: the eighteenth-century demonstration apparatus of Jean Antoine Nollet. Les éditions du Septentrion. ISBN 978-2-89448-320-6. Cook, Norman D. (2006). Models of the atomic nucleus: with interactive software. Vol. 1. Birkhäuser. ISBN 978-3-540-28569-4. Davies, Paul (1992). The new physics. Cambridge University Press. ISBN 978-0-521-43831-5. Mitra, Asoke Nath (2009). India in the world of physics: then and now. History of science, philosophy, and culture in Indian civilization: Theories of natural and life sciences. Vol. 1. Pearson Education India. ISBN 978-81-317-1579-6. Prigogine, Ilya; Stengers, Isabelle (1984). Order out of chaos: man's new dialogue with nature. Vol. 2. Bantam Books. ISBN 978-0-553-34082-2. Sandbothe, Mike (2001). The temporalization of time: basic tendencies in modern debate on time in philosophy and science. Rowman & Littlefield. ISBN 978-0-7425-1290-0. Segrè, Emilio (1993). A mind always in motion: the autobiography of Emilio Segrè. University of California Press. ISBN 978-0-520-07627-3. Van Name, F. W. (1962). "The Golden Age of Physics". Modern physics (2nd ed.). Prentice-Hall. Wilhelm, I (2008). "The Ethics of Research: The Responsibility of the Researcher". In S. Gunn; A. William; Michele Masellis (eds.). Concepts and Practice of Humanitarian Medicine. Springer. ISBN 978-0-387-72263-4. Lulek, Tadeusz; Lulek, Barbara; Wal, A. (May 2001). Symmetry and Structural Properties of Condensed Matter, Proceedings of the Sixth's International School of Theoretical Physics. World Scientific Publishing Company, Inc. pp. 13 to 23 (Chap. 1). ISBN 978-981-02-4569-6. Download available from Google Books.
Wikipedia/Golden_age_of_physics
Major innovations in materials technology == BC == 28,000 BC – People wear beads, bracelets, and pendants 14,500 BC – First pottery, made by the Jōmon people of Japan. 6th millennium BC – Copper metallurgy is invented and copper is used for ornamentation (see Pločnik article) 2nd millennium BC – Bronze is used for weapons and armor 16th century BC – The Hittites develop crude iron metallurgy 13th century BC – Invention of steel when iron and charcoal are combined properly 10th century BC – Glass production begins in ancient Near East 1st millennium BC – Pewter beginning to be used in China and Egypt 1000 BC – The Phoenicians introduce dyes made from the purple murex. 3rd century BC – Wootz steel, the first crucible steel, is invented in ancient India 50s BC – Glassblowing techniques flourish in Phoenicia 20s BC – Roman architect Vitruvius describes low-water-content method for mixing concrete == 1st millennium == 3rd century – Cast iron widely used in Han dynasty China 300 – Greek alchemist Zomius, summarizing the work of Egyptian alchemists, describes arsenic and lead acetate 4th century – Iron pillar of Delhi is the oldest surviving example of corrosion-resistant steel 8th century – Porcelain is invented in Tang dynasty China 8th century – Tin-glazing of ceramics invented by Muslim chemists and potters in Basra, Iraq: 1  9th century – Stonepaste ceramics invented in Iraq: 5  900 – First systematic classification of chemical substances appears in the works attributed to Jābir ibn Ḥayyān (Latin: Geber) and in those of the Persian alchemist and physician Abū Bakr al-Rāzī (c. 865–925, Latin: Rhazes) 900 – Synthesis of ammonium chloride from organic substances described in the works attributed to Jābir ibn Ḥayyān (Latin: Geber) 900 – Abū Bakr al-Rāzī describes the preparation of plaster of Paris and metallic antimony 9th century – Lustreware appears in Mesopotamia: 86–87  == 2nd millennium == 1000 – Gunpowder is developed in China 1340 – In Liège, Belgium, the first blast furnaces for the production of iron are developed 1448 – Johann Gutenberg develops type metal alloy 1450s – Cristallo, a clear soda-based glass, is invented by Angelo Barovier 1540 – Vannoccio Biringuccio publishes first systematic book on metallurgy 1556 – Georg Agricola's influential book on metallurgy 1590 – Glass lenses are developed in the Netherlands and used for the first time in microscopes and telescopes 1664 – In the pipes supplying water to the gardens at Versailles, cast iron is used === 18th century === 1717 – Abraham Darby makes iron with coke, a derivative of coal 1738 – Metallic zinc processed by distillation from calamine and charcoal patented by William Champion 1740 – Crucible steel technique developed by Benjamin Huntsman 1774 – Joseph Priestley discovers oxygen Johann Gottlieb Gahn discovers manganese Karl Wilhelm Scheele discovers chlorine 1779 – Hydraulic cement (stucco) patented by Bryan Higgins for use as an exterior plaster 1799 – Acid battery made from copper/zinc by Alessandro Volta === 19th century === 1821 – Thermocouple invented by Thomas Johann Seebeck 1824 – Portland cement patent issued to Joseph Aspdin 1825 – Metallic aluminum produced by Hans Christian Ørsted 1839 – Vulcanized rubber invented by Charles Goodyear 1839 – Silver-based photographic processes invented by Louis Daguerre and William Fox Talbot 1855 – Bessemer process for mass production of steel patented by Henry Bessemer 1861 – Color photography demonstrated by James Clerk Maxwell 1883 – First solar cells using selenium waffles made by Charles Fritts 1893 – Thermite Welding developed and soon used to weld rails === 20th century === 1902 – Synthetic rubies created by the Verneuil process developed by Auguste Verneuil 1908 – Cellophane invented by Jacques E. Brandenberger 1909 – Bakelite hard thermosetting plastic presented by Leo Baekeland 1911 – Superconductivity discovered by Heike Kamerlingh Onnes 1912 – Stainless steel invented by Harry Brearley 1916 – Method for growing single crystals of metals invented by Jan Czochralski 1919 – The merchant ship Fullagar has the first all welded hull. 1924 – Pyrex invented by scientists at Corning Incorporated, a glass with a very low coefficient of thermal expansion 1931 – synthetic rubber called neoprene developed by Julius Nieuwland (see also: E.K. Bolton, Wallace Carothers) 1931 – Nylon developed by Wallace Carothers 1935 – Langmuir–Blodgett film coating of glass was developed by Katharine Burr Blodgett, creating "invisible glass" which is >99% transmissive 1938 – The process for making poly-tetrafluoroethylene, better known as Teflon discovered by Roy Plunkett 1939 – Dislocations in metals confirmed by Robert W. Cahn 1947 – First germanium point-contact transistor invented 1947 – First commercial application of a piezoelectric ceramic: barium titanate used as a phonograph pickup 1951 – Individual atoms seen for the first time using the field ion microscope 1953 – Metallic catalysts which greatly improve the strength of polyethylene polymers discovered by Karl Ziegler 1954 – Silicon solar cells with 6% efficiency made at Bell Laboratories 1954 – Argon oxygen decarburization (AOD) refining invented by scientists at the Union Carbide Corporation 1959 – Float glass process patented by the Pilkington Brothers 1962 – SQUID superconducting quantum interference device invented 1966 – Stephanie Kwolek invented a fibre that would later become known as Kevlar 1968 – Liquid crystal display developed by RCA 1970 – Silica optical fibers grown by Corning Incorporated 1980 – Duplex stainless steels developed which resist oxidation in chlorides 1984 – Fold-forming system developed by Charles Lewton-Brain to produce complex three dimensional forms rapidly from sheet metal 1985 – The first fullerene molecule discovered by scientists at Rice University (see also: Timeline of carbon nanotubes) 1986 – The first high temperature superconductor is discovered by Georg Bednorz and K. Alex Müller == See also == Timeline of scientific discoveries Timeline of historic inventions List of inventions named after people Materials science Roman metallurgy == References ==
Wikipedia/Timeline_of_materials_technology
This article lists the main historical events in the history of condensed matter physics. This branch of physics focuses on understanding and studying the physical properties and transitions between phases of matter. Condensed matter refers to materials where particles (atoms, molecules, or ions) are closely packed together or under interaction, such as solids and liquids. This field explores a wide range of phenomena, including the electronic, magnetic, thermal, and mechanical properties of matter. This timeline includes developments in subfields of condensed matter physics such as theoretical crystallography, solid-state physics, soft matter physics, mesoscopic physics, material physics, low-temperature physics, microscopic theories of magnetism in matter and optical properties of matter and metamaterials. Even if material properties were modeled before 1900, condensed matter topics were considered as part of physics since the development of quantum mechanics and microscopic theories of matter. According to Philip W. Anderson, the term "condensed matter" appeared about 1965. For history of fluid mechanics, see timeline of fluid and continuum mechanics. == Before quantum mechanics == === Prehistory === 28,000–12,000 BP – Upper Paleolithic: earliest evidence of ceramic objects made for ritual purposes. 10,000–3300 BC – Neolithic: development of pottery, as well as early evidence of glass production and metalworking. 3300–1200 BC – Bronze Age: development of metallurgy, with copper and tin being combined to create bronze. 1200–300 BC – Iron Age: development of ferrous metallurgy, allowing iron and steel to largely replace bronze. === Antiquity === 8th century BC: first writings on the magnetic properties of lodestone in Ancient Greece. 6th century BC – Thales of Miletus observes that rubbing fur on various substances, such as amber, would cause an attraction between the two, which is now known to be caused by static electricity. 5th century BC – Leucippus and Democritus postulate the philosophy of atomism. 4th century BC – Aristotle describes the composition of matter in terms of the four classical elements, founding Aristotelian physics. 1st century AD – Pliny the Elder in his Natural History records the story of Magnes the shepherd who discovered the magnetic properties of some iron stones. 160 AD – Claudius Ptolemy writes his book Optics on reflection and refraction of light, and tabulated angles of refraction for several media. He found a refraction law valid for small angles. === Classical theories before the 19th century === 1611 – Johannes Kepler first states the Kepler conjecture about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. 1621 – Willebrord Snellius reformulates the laws of refraction and reflection of light into Snell's law. 1660 – Robert Hooke postulates the simplest equation of linear elasticity known as Hooke's law. 1687 – Isaac Newton postulates the Newton's laws of motion. 1701 – Newton studies heat, leading to Newton's law of cooling. 1729 – Scientist Stephen Gray discovers the electrical conduction of metals. 1778 – Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields. 1781 – René Just Haüy (often termed the "Father of Modern Crystallography") discovers that crystals always cleave along crystallographic planes. Based on this observation, and the fact that the inter-facial angles in each crystal species always have the same value, Haüy concluded that crystals must be periodic and composed of regularly arranged rows of tiny polyhedra (molécules intégrantes). This theory explained why all crystal planes are related by small rational numbers (the law of rational indices). === 19th century === 1800 – The Voltaic pile, the first electric battery is developed by Alessandro Volta. 1803–1808 – John Dalton reconsiders the atomic theory of matter in order to understand chemistry. 1816 – David Brewster discovers stress birefringence in diamond. 1819 – Experimentally Pierre Louis Dulong and Alexis Thérèse Petit find that the specific heat capacity of solids was close to a constant value given by Dulong–Petit law. 1821 – Thomas Johann Seebeck discovers the thermoelectric effect, related by the Seebeck coefficient. 1822 – Joseph Fourier proposes Fourier's law of thermal conduction and the heat equation. 1826 – Moritz Ludwig Frankenheim derives the 32 crystal classes by using the crystallographic restriction, consistent with Haüy's laws, that only 2, 3, 4 and 6-fold rotational axes are permitted. 1827 – Georg Ohm, publishes the proportional relation between electric current and voltage in metals, known as Ohm's law. 1834 – Jean-Charles Peltier discovers the Peltier effect: heating by an electric current at the junction of two different metals. 1839 – William Hallowes Miller invents zonal relations by projecting the faces of a crystal upon the surface of a circumscribed sphere. Miller indices are defined which form a notation system in crystallography for planes in crystal (Bravais) lattices. 1840 – James Prescott Joule formulates the equation for Joule heating quantifying the amount of heat produced in a circuit as proportional to the product of the time duration, the resistance, and the square of the current passing through it. 1845 – Michael Faraday studies the interaction of light and magnetic fields with matter (Faraday rotation). 1848 – Louis Pasteur discovers that sodium ammonium tartrate can crystallize in left- and right-handed forms and showed that the two forms can rotate polarized light in opposite directions. This was the first demonstration of molecular chirality, and also the first explanation of isomerism. 1850 – Auguste Bravais develops the concept of Bravais lattices to describe periodicity in crystals. He derives the 14 space lattices. 1853 – Discovery of Wiedemann–Franz law relating thermal and electrical conductivities, by Gustav Wiedemann and Rudolph Franz. 1854 – Lord Kelvin discovers the thermoelectric Thomson effect. 1859 – Gustav Kirchhoff introduces the concept of a blackbody and proves that its emission spectrum depends only on its temperature. 1861–1865 – James Clerk Maxwell summarizes the fundamental equations of electromagnetism into an early version of Maxwell's equations and relates electromagnetism to light in his publications On Physical Lines of Force and A Dynamical Theory of the Electromagnetic Field. 1867 – Dmitry Chernov establishes the critical temperatures of steel. 1872 – The Boltzmann transport equation, describing the statistical behaviour of a thermodynamic system not in a state of equilibrium, is devised by Ludwig Boltzmann. 1872 – Ludvig Lorenz finds the Lorenz number, the constant of the Wiedemann–Franz law. 1874 – Karl Ferdinand Braun discovered current rectification using a point-contact metal–semiconductor junction. 1875 – John Kerr discovers the double refraction of solid and liquids, now known as the Kerr effect. 1876 – Josiah Willard Gibbs introduces the concept of phase transition. 1879 – Edwin Hall discovers the Hall effect. 1879 – Leonhard Sohncke lists the 65 crystallographic point systems using rotations and reflections in addition to translations. 1880 – The first demonstration of the direct piezoelectric effect by the brothers Pierre Curie and Jacques Curie. 1883 – Thomas Edison discovers thermionic emission or the Edison effect. 1887 – Floris Osmond names the phases of steel. 1887 – Heinrich Hertz discovers the photoelectric effect. 1888–1889 – Crystalline optical properties of liquid crystals and their ability to flow are first described by Friedrich Reinitzer and confirmed by Otto Lehmann. 1891 – Derivation of the 230 space groups (by adding mirror-image symmetry to Sohncke's work) by a collaborative effort of Evgraf Fedorov and Arthur Schoenflies. 1895 – Wilhelm Conrad Röntgen discovers X-rays in experiments with electron beams in plasma. 1895 – Hendrik Lorentz derives the Lorentz force for charged particles in electric and magnetic fields. 1895 – Pierre Curie discovers empirically that the magnetic susceptibility of many materials is inversely proportional to temperature according to Curie's law. He also found that permanent magnetism was lost after a certain Curie temperature. 1896–1897 – Pieter Zeeman first observes the Zeeman splitting effect by applying a magnetic field to light sources. 1897 – J. J. Thomson's experimentation with cathode rays led him to suggest a fundamental unit more than a 1000 times smaller than an atom, based on the high charge-to-mass ratio. He called the particle a "corpuscle", but later scientists preferred the term electron. == 20th century == === Early 1900s === 1900 – Max Planck uses for the first time quantum theory to explain black-body radiation. 1900 – Paul Drude proposes the Drude model to explain thermal and electric properties of metals. 1901 – Thermionic emission is first theoretically modeled by Owen Willans Richardson 1905 – Albert Einstein's Annus mirabilis papers postulating special relativity, the theory for Brownian motion and explaining the photoelectric effect using quantum mechanics. 1905 – Paul Langevin derives the classical theory for diamagnetism. 1907: Einstein solid model predicts the deviations for the specific heat of solids from Dulong–Petit law. The first theory describing crystallographic defects is developed by Vito Volterra. Pierre Weiss introduces the magnetic domain theory of ferromagnetism. 1909 – Lorentz develops the classical Lorentz oscillator model to describe the optical response of materials. 1911 – Heike Kamerlingh Onnes and Gilles Holst discover superconductivity in mercury. 1912: Max von Laue discovers diffraction of X-rays by crystals. Peter Debye develops a model for the specific heat of solids in terms of phonons, known as Debye model. Geertruida Lorentz, applies Einstein's Brownian motion equations to noise in electrical circuits. 1913 – William Henry Bragg and Lawrence Bragg use X-rays to analyze crystals. 1917 – Weiss and Auguste Piccard first observe the magnetocaloric effect. 1919 – Walter H. Schottky introduces the concept of shot noise while studying vacuum tubes. 1919 – Hendrika Johanna van Leeuwen rediscovers the Bohr–Van Leeuwen theorem, showing that magnetic properties of matter are due to quantum mechanics. 1920: Ferroelectricity gets discovered in Rochelle salt by Joseph Valasek. Hermann Staudinger, suggest that small molecules can be link together through covalent bonds to form polymer. Wilhelm Lenz describes for the first time the Ising model as a model for magnetism in matter. 1923 – Pierre Auger discovers the Auger effect, where filling the inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom. 1923 – Louis de Broglie extends wave–particle duality to particles, postulating that electrons in motion are associated with waves. He predicts that the wavelengths are given by the Planck constant h divided by the momentum of the mv = p of the electron: λ = h / mv = h / p. 1923–1927 Electron wave diffraction is demonstrated experimentally independently by Davisson–Germer experiments and the experiments by George Paget Thomson and Alexander Reid. 1924 – Satyendra Nath Bose explains Planck's law using a new statistical law that governs bosons, and Einstein generalizes it to predict Bose–Einstein condensate. The theory becomes known as Bose–Einstein statistics. 1924 – Wolfgang Pauli outlines the Pauli exclusion principle which states that no two identical fermions may occupy the same quantum state simultaneously, a fact that explains many features of the periodic table. 1925 – Werner Heisenberg, Max Born, and Pascual Jordan develop the matrix mechanics formulation of quantum mechanics. 1925 – Ernst Ising finds the analytical solution to the 1D Ising model. 1926: Enrico Fermi discovers the spin-statistics theorem connection. Paul Dirac introduces Fermi–Dirac statistics. Erwin Schrödinger uses de Broglie's electron wave postulate (1924) to develop a Schrödinger equation; also introduces the Hamiltonian operator in quantum mechanics. Johnson–Nyquist noise is first measured by John B. Johnson at Bell Labs. He described his findings to Harry Nyquist, also at Bell Labs, who was able to explain the results. 1927: Max Born and J. Robert Oppenheimer introduce the Born–Oppenheimer approximation, which allows the quick approximation of the energy and wavefunctions of smaller molecules. Pauli models the paramagnetic contribution of itinerant electrons due to spins (Pauli paramagnetism). Walter Heitler and Fritz London introduce the concepts of valence bond theory and apply it to the hydrogen molecule. Llewellyn Thomas and Fermi develop the Thomas–Fermi model for a gas in a box. Chandrasekhara Venkata Raman studies optical photon scattering by electrons, now known as Raman spectroscopy. Walter Heitler uses Schrödinger's wave equation to show how two hydrogen atom wavefunctions join, with plus, minus, and exchange terms, to form a covalent bond. Robert S. Mulliken works, in coordination with Hund, to develop a molecular orbital theory where electrons are assigned to states that extend over an entire molecule and, in 1932, introduces many new molecular orbital terminologies, such as σ bond, π bond, and δ bond. Eugene Wigner relates degeneracies of quantum states to irreducible representations of symmetry groups. Arnold Sommerfeld, extends Drude's model using Fermi–Dirac statistics leading to the free electron model. Douglas Hartree introduced the Hartree equation for atoms. 1928–1930 – John Hasbrouck Van Vleck formalizes the quantum theory of magnetism and formulates Van Vleck paramagnetism. 1928 – Linus Pauling outlines the quantum nature of the chemical bonds. 1928 – Friedrich Hund and Robert S. Mulliken introduce the concept of molecular orbitals. 1929: Felix Bloch demonstrates Bloch's theorem. John Lennard-Jones introduces the linear combination of atomic orbitals (LCAO) approximation for the calculation of molecular orbitals. The electron hole concept is pioneered by Rudolf Peierls to understand semiconductors. Peierls coins the term Umklapp scattering. First observation of plasma oscillations by Irving Langmuir and Lewi Tonks. Egil Hylleraas finds an approximate solution to the helium atom. 1930: Léon Brillouin develops the concept of Brillouin zone. Bloch introduces the theory of spin waves and magnons, Erich Hückel introduces the Hückel molecular orbital method, which expands on orbital theory to determine the energies of orbitals of pi electrons in conjugated hydrocarbon systems. Fritz London explains van der Waals forces as due to the interacting fluctuating dipole moments between molecules. Landau formulates the concept of Landau quantization, explaining the diamagnetic contribution of a free electron gas (Landau diamagnetism) and predicting the De Haas–Van Alphen effect. This effect was measured a few months after by Wander Johannes de Haas and his student Pieter M. van Alphen. 1931: Onsager reciprocal relations are first proposed by Lars Onsager Ralph Kronig and William Penney solve the infinite periodic array of rectangular potential barriers (Kronig–Penney model). Alan Herries Wilson develops the theory of electronic band structure to describe the conduction properties of solids. He also distinguished between intrinsic and extrinsic semiconductors. The concept of excitons is proposed by Yakov Frenkel. John Lennard-Jones proposes the Lennard-Jones interatomic potential. Ernst Ruska creates the first electron microscope. 1932 – Werner Heisenberg applies perturbation theory to the two-electron problem to show how resonance arising from electron exchange can explain exchange forces. 1933: Walther Meissner and Robert Ochsenfeld discover the Meissner effect by measuring the magnetic field distribution outside superconducting tin and lead samples. Landau models antiferromagnetism for the first time. Landau introduces the concept of electron-phonon quasiparticle, termed polaron. Erich Mollwo, working with Robert Wichard Pohl concludes that color in alkali metal halides is due to the existence of F-centers (color centers). 1935: J.N. Rjabinin and Lev Shubnikov experimentally discover type-II superconductivity. The London equations get developed by brothers Fritz and Heinz London. Hartree introduces Hartree–Fock method. 1937: Landau introduces Landau theory of phase transitions. Jan Hendrik de Boer and Evert Verwey, and independently Peierls, and Nevill Francis Mott introduce the problem of the metal–insulator transition. Other developments include the discovery of the Verwey transition and the theory of the Mott insulator. Wannier functions are introduced by Gregory Wannier. Conyers Herring theorizes the possibility of Weyl semimetals. 1938 – Superfluidity is discovered by the team of Pyotr Kapitsa. 1941 – Landau introduces the concept of second sound. 1944 – Lars Onsager find an analytical solution for the 2D Ising model. 1947 – The first transistor is developed by William Shockley, John Bardeen and Walter Houser Brattain. 1947 – The theory of single layer graphite (graphene) is first published by P. R. Wallace. 1948 – Louis Néel discovers ferrimagnetism 1945–1946 – First neutron diffraction experiments are carried out by Ernest O. Wollan and independently by Clifford Shull. 1947–1948 – Hendrik Casimir and Dirk Polder at Philips Research Labs propose the existence of Casimir–Polder effect between two polarizable atoms and between such an atom and a conducting plate. After a conversation with Niels Bohr, who suggested it had something to do with zero-point energy. 1947–1948 – The formal development of quantum field theory by Richard Feynman, Julian Schwinger, Shin'ichirō Tomonaga and Freeman Dyson. 1949 – Werner Ehrenberg and Raymond E. Siday first predict Aharonov–Bohm effect. === Second half of the 20th century === 1950 – The Ginzburg–Landau theory phenomenological theory of superconductors is formulated by Vitaly Ginzburg and Landau. 1950 – Tomonaga introduces the Luttinger liquid model for electrons in 1D. 1952 – The plasmon (quantum of plasma oscillation in metals) is proposed by David Pines and David Bohm. 1952 – Friedel oscillations are first described by Jacques Friedel. 1953 – The occurrence of Van Hove singularities is first analyzed by Léon Van Hove for the case of phonon densities of states. 1953 – Charles H. Townes, James P. Gordon, and Herbert Zeiger demonstrate the first maser. 1954: Lindhard theory for electric-field screening is published by Jens Lindhard. The tight-binding method is conceived by John Clarke Slater and George Fred Koster. Bernd T. Matthias comes up with the empirical Matthias rules for finding superconductors. Herbert Fröhlich introduces the Frölich Hamiltonian for polarons. Publication of Dynamical Theory of Crystal Lattices by Max Born and Huang Kun, introducing Born–Huang approximation and Cauchy–Born rule. 1954–1957 – Malvin Ruderman and Charles Kittel develop the theory of indirect exchange interaction, later expanded by Tadao Kasuya and Kei Yosida into the RKKY theory. 1955 – Dresselhaus spin–orbit coupling is discovered by Gene Dresselhaus. 1955 – Takeo Matsubara introduces his many-body Green's function based on Matsubara frequency formalism. 1956 – Theory of interacting electrons in solids, Fermi liquid theory is developed by Landau 1957: BCS theory by Bardeen, Leon Cooper and John Robert Schrieffer. Rolf Landauer, who first suggested a version the Landauer formula. Ryogo Kubo who first presents the Kubo formula, to express the linear response of an observable quantity due to a time-dependent perturbation using quantum mechanics. Jack Kilby proposes the first integrated circuit. 1957–1959 – Kubo, Paul C. Martin and Schwinger introduced the KMS condition used it in 1959 to define thermodynamic Green's functions. 1958 – Philip W. Anderson starts developing the theory of metal-insulator transitions and Anderson localization. 1958 – John Hopfield coins the polariton in theory of Hopfield dielectric. 1958–1960 – The first laser is built by Theodore Maiman at Hughes Aircraft Company, based on a patent from Townes and Arthur Leonard Schawlow. 1959 – Rashba spin-orbit coupling is discovered by Emmanuel Rashba and Valentin I. Sheka. 1961–1964 – Schwinger, O. V. Konstantinov and Vladimir I. Perel, Leo Kadanoff and Gordon Baym, and Leonid Keldysh independently develop Keldysh formalism. 1962: Jeffrey Goldstone, Yoichiro Nambu, Abdus Salam, and Steven Weinberg develop what is now known as Goldstone's Theorem: if there is a continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must be spinless particles of zero mass, thereafter called Nambu-Goldstone bosons. Philip W. Anderson proposes a spontaneous symmetry breaking mechanism (later called Higgs mechanism) for superconductors. Josephson effect of electron tunneling in superconductors is predicted by Brian Josephson. The Little–Parks effect is discovered by William A. Little and Ronald D. Parks. 1963 – John Hubbard, Martin Gutzwiller and Junjiro Kanamori each independently propose the Hubbard model. 1964 – Jun Kondō models the resistance minimum in metals leading to the Kondo model and the prediction of the Kondo effect. The development of the density functional theory starts with the theorems of Walter Kohn and Pierre Hohenberg. 1966–1967: Mermin–Wagner theorem is proved by N. David Mermin, Herbert Wagner and independently by Pierre Hohenberg. 1966–1968 – Zhores Alferov and independently Herbert Kroemer created the first lasers based on heterostructures. 1967 – Volker Heine coins the term ''condensed matter''. 1967 – Negative-index materials are first described theoretically by Victor Veselago. 1970 – French scientist Madeleine Veyssié, coins the term soft matter (French: matière molle). 1971: The spin Hall effect is predicted by Mikhail I. Dyakonov and Vladimir I. Perel. Pierre-Gilles de Gennes introduces the reptation model for polymer physics. Polder and Michael Van Hove derive the theory for near-field radiative heat transfer between arbitrary non-magnetic media. 1971–75 – Michael Fisher, Kenneth G. Wilson, and Leo Kadanoff come up with the renormalization group. 1972 – David Lee, Douglas Osheroff and Robert Coleman Richardson discovered two phase transitions of helium-3 along the melting curve, which were soon realized to be the two superfluid phases. 1972 – The concept of Berezinskii–Kosterlitz–Thouless phase transition in the XY model is developed by Vadim Berezinskii, J. Michael Kosterlitz and David J. Thouless. 1973 – Peter Mansfield formulates the physical theory of nuclear magnetic resonance imaging (NMRI) 1979: Giorgio Parisi finds a solution to Sherrington–Kirkpatrick model for spin glasses. Su–Schrieffer–Heeger model is devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger to describe the increase of electrical conductivity of polyacetylene polymer chain when doped. Alexey Ekimov creates the first quantum dots and their quantum size effects. 1980 – The integer quantum Hall effect is discovered by Klaus von Klitzing 1980 – Richard Feynman proposes quantum computing. 1981 – The scanning tunneling microscope (STM), an instrument for imaging surfaces at the atomic level, was developed by Gerd Binnig and Heinrich Rohrer. 1982 – The fractional quantum Hall effect is discovered by Robert Laughlin, Horst Störmer, and Daniel Tsui. 1982 – First observation of a quasicrystal by Dan Shechtman. 1982 – Frank Wilczek explores the fractional statistics of quasiparticles in two dimensions and coins the term "anyon". 1985 – Fullerene C60 discovered by Richard Smalley, Robert Curl, and Harry Kroto. 1985 – Patrick A. Lee and A. Douglas Stone coin the term universal conductance fluctuations. 1986 – Binnig, Calvin Quate and Christoph Gerber invent the first atomic force microscope (AFM). 1986 – Discovery of high-temperature superconductivity by K. Alex Müller and Georg Bednorz. 1987 – Karl Alexander Müller and Georg Bednorz discover high-temperature superconductivity in ceramics. 1988 – Giant magnetoresistance is discovered by Albert Fert and Peter Grünberg. 1988 – The conductance quantum are first demonstrated in quantum point contacts. 1989 – Jainendra K. Jain proposes the concept of composite fermions. 1991 – Carbon nanotubes are discovered by Sumio Iijima 1995 – Experimental Bose–Einstein condensate is first demonstrated by Eric Cornell, Carl Wieman and Wolfgang Ketterle. 1997 – Experiment discovery of rare-earth oxides that behave as spin ice by Steven T. Bramwell, Mark Harris and collaborators, who also coined the term. 1998 – Thomas Callister Hales proves Kepler's conjecture. 1998 – Lene Hau produces slow light with a speed of 17 m/s. == 21st century == 2000 – The thermal conductance quantum is first measured. 2000 Alexei Kitaev introduces the theory of the Kitaev chain. 2001 – Attosecond pulsed sources are developed independently by Pierre Agostini and Ferenc Krausz, leading to the development of attosecond physics. 2003 – Deborah S. Jin and her collaboration produce the first fermionic condensate. 2004 – Single-layer graphene was first unambiguously produced and identified by the group of Andre Geim and Konstantin Novoselov. 2005 – Charles Kane and Gene Mele propose the quantum spin Hall effect. 2008-2010 – Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki and Andreas W. W. Ludwig; and well as Alexei Kitaev, develop the periodic table of topological matter. 2013 – The quantum anomalous Hall effect is first observed by the team of Xue Qikun. 2012 – Wilczek proposes the idea of time crystals. 2015 – M. Zahid Hasan's team demontrates the existence of Weyl semimetals. 2018 – Twisted graphene superconductivity is demonstrated by Pablo Jarillo-Herrero. 2024 – Altermagnetism is discovered in experiment. == See also == History of metamaterials Timeline of crystallography Timeline of materials technology Timeline of states of matter and phase transitions Timeline of quantum computing and communication == References ==
Wikipedia/Timeline_of_condensed_matter_physics
A timeline of atomic and subatomic physics, including particle physics. == Antiquity == 6th - 2nd Century BCE Kanada (philosopher) proposes that anu is an indestructible particle of matter, an "atom"; anu is an abstraction and not observable. 430 BCE Democritus speculates about fundamental indivisible particles—calls them "atoms" == The beginning of chemistry == 1766 Henry Cavendish discovers and studies hydrogen 1778 Carl Scheele and Antoine Lavoisier discover that air is composed mostly of nitrogen and oxygen 1781 Joseph Priestley creates water by igniting hydrogen and oxygen 1800 William Nicholson and Anthony Carlisle use electrolysis to separate water into hydrogen and oxygen 1803 John Dalton introduces atomic ideas into chemistry and states that matter is composed of atoms of different weights 1805 (approximate time) Thomas Young conducts the double-slit experiment with light 1811 Amedeo Avogadro claims that equal volumes of gases should contain equal numbers of molecules 1815 William Prout hypothesizes that all matter is built up from hydrogen, adumbrating the proton; 1832 Michael Faraday states his laws of electrolysis 1838 Richard Laming hypothesized a subatomic particle carrying electric charge; 1839 Alexandre Edmond Becquerel discovered the photovoltaic effect 1858 Julius Plücker produced cathode rays; 1871 Dmitri Mendeleyev systematically examines the periodic table and predicts the existence of gallium, scandium, and germanium 1873 Johannes van der Waals introduces the idea of weak attractive forces between molecules 1874 George Johnstone Stoney hypothesizes a minimum unit of electric charge. In 1891, he coins the word electron for it; 1885 Johann Balmer finds a mathematical expression for observed hydrogen line wavelengths 1886 Eugen Goldstein produced anode rays; 1887 Heinrich Hertz discovers the photoelectric effect 1894 Lord Rayleigh and William Ramsay discover argon by spectroscopically analyzing the gas left over after nitrogen and oxygen are removed from air 1895 William Ramsay discovers terrestrial helium by spectroscopically analyzing gas produced by decaying uranium 1896 Antoine Henri Becquerel discovers the radioactivity of uranium 1896 Pieter Zeeman studies the splitting of sodium D lines when sodium is held in a flame between strong magnetic poles 1897 J. J. Thomson discovered the electron; 1897 Emil Wiechert, Walter Kaufmann and J.J. Thomson discover the electron 1898 Marie and Pierre Curie discovered the existence of the radioactive elements radium and polonium in their research of pitchblende 1898 William Ramsay and Morris Travers discover neon, and negatively charged beta particles == The age of quantum mechanics == 1887 Heinrich Rudolf Hertz discovers the photoelectric effect that will play a very important role in the development of the quantum theory with Einstein's explanation of this effect in terms of quanta of light 1896 Wilhelm Conrad Röntgen discovers the X-rays while studying electrons in plasma; scattering X-rays—that were considered as 'waves' of high-energy electromagnetic radiation—Arthur Compton will be able to demonstrate in 1922 the 'particle' aspect of electromagnetic radiation. 1899 Ernest Rutherford discovered the alpha and beta particles emitted by uranium; 1900 Johannes Rydberg refines the expression for observed hydrogen line wavelengths 1900 Max Planck states his quantum hypothesis and blackbody radiation law 1900 Paul Villard discovers gamma-rays while studying uranium decay 1902 Philipp Lenard observes that maximum photoelectron energies are independent of illuminating intensity but depend on frequency 1905 Albert Einstein explains the photoelectric effect 1906 Charles Barkla discovers that each element has a characteristic X-ray and that the degree of penetration of these X-rays is related to the atomic weight of the element 1908-1911 Jean Perrin proves the existence of atoms and molecules with experimental work to test Einstein's theoretical explanation of Brownian motion 1909 Ernest Rutherford and Thomas Royds demonstrate that alpha particles are doubly ionized helium atoms 1909 Hans Geiger and Ernest Marsden discover large angle deflections of alpha particles by thin metal foils 1911 Ernest Rutherford explains the Geiger–Marsden experiment by invoking a nuclear atom model and derives the Rutherford cross section 1911 Ștefan Procopiu measures the magnetic dipole moment of the electron 1912 Max von Laue suggests using crystal lattices to diffract X-rays 1912 Walter Friedrich and Paul Knipping diffract X-rays in zinc blende 1913 Henry Moseley shows that nuclear charge is the real basis for numbering the elements 1913 Johannes Stark demonstrates that strong electric fields will split the Balmer spectral line series of hydrogen 1913 Niels Bohr presents his quantum model of the atom 1913 Robert Millikan measures the fundamental unit of electric charge 1913 William Henry Bragg and William Lawrence Bragg work out the Bragg condition for strong X-ray reflection 1914 Ernest Rutherford suggests that the positively charged atomic nucleus contains protons 1914 James Franck and Gustav Hertz observe atomic excitation 1915 Arnold Sommerfeld develops a modified Bohr atomic model with elliptic orbits to explain relativistic fine structure 1916 Gilbert N. Lewis and Irving Langmuir formulate an electron shell model of chemical bonding 1917 Albert Einstein introduces the idea of stimulated radiation emission 1918 Ernest Rutherford notices that, when alpha particles were shot into nitrogen gas, his scintillation detectors showed the signatures of hydrogen nuclei. 1921 Alfred Landé introduces the Landé g-factor 1922 Arthur Compton studies X-ray photon scattering by electrons demonstrating the 'particle' aspect of electromagnetic radiation. 1922 Otto Stern and Walther Gerlach show "spin quantization" 1923 Lise Meitner discovers what is now referred to as the Auger process 1924 John Lennard-Jones proposes a semiempirical interatomic force law 1924 Louis de Broglie suggests that electrons may have wavelike properties in addition to their 'particle' properties; the wave–particle duality has been later extended to all fermions and bosons. 1924 Santiago Antúnez de Mayolo proposes a neutron. 1924 Satyendra Bose and Albert Einstein introduce Bose–Einstein statistics 1925 George Uhlenbeck and Samuel Goudsmit postulate electron spin 1925 Pierre Auger discovers the Auger process (2 years after Lise Meitner) 1925 Werner Heisenberg, Max Born, and Pascual Jordan formulate quantum matrix mechanics 1925 Wolfgang Pauli states the quantum exclusion principle for electrons 1926 Enrico Fermi discovers the spin–statistics connection, for particles that are now called 'fermions', such as the electron (of spin-1/2). 1926 Erwin Schrödinger proves that the wave and matrix formulations of quantum theory are mathematically equivalent 1926 Erwin Schrödinger states his nonrelativistic quantum wave equation and formulates quantum wave mechanics 1926 Gilbert N. Lewis introduces the term "photon", thought by him to be "the carrier of radiant energy." 1926 Oskar Klein and Walter Gordon state their relativistic quantum wave equation, now the Klein–Gordon equation 1926 Paul Dirac introduces Fermi–Dirac statistics 1927 Charles Drummond Ellis (along with James Chadwick and colleagues) finally establish clearly that the beta decay spectrum is in fact continuous and not discrete, posing a problem that will later be solved by theorizing (and later discovering) the existence of the neutrino. 1927 Clinton Davisson, Lester Germer, and George Paget Thomson confirm the wavelike nature of electrons 1927 Thomas and Fermi develop the Thomas–Fermi model 1927 Max Born interprets the probabilistic nature of wavefunctions 1927 Max Born and Robert Oppenheimer introduce the Born–Oppenheimer approximation 1927 Walter Heitler and Fritz London introduce the concepts of valence bond theory and apply it to the hydrogen molecule. 1927 Werner Heisenberg states the quantum uncertainty principle 1928 Chandrasekhara Raman studies optical photon scattering by electrons 1928 Charles G. Darwin and Walter Gordon solve the Dirac equation for a Coulomb potential 1928 Friedrich Hund and Robert S. Mulliken introduce the concept of molecular orbital 1928 Paul Dirac states the Dirac equation 1929 Nevill Mott derives the Mott cross section for the Coulomb scattering of relativistic electrons 1929 Oskar Klein discovers the Klein paradox 1929 Oskar Klein and Yoshio Nishina derive the Klein–Nishina cross section for high energy photon scattering by electrons 1930 Wolfgang Pauli postulated the neutrino to explain the energy spectrum of beta decays; 1930 Erwin Schrödinger predicts the zitterbewegung motion 1930 Fritz London explains van der Waals forces as due to the interacting fluctuating dipole moments between molecules 1930 Paul Dirac introduces electron hole theory 1931 Harold Urey discovers deuterium using evaporation concentration techniques and spectroscopy 1931 Irène Joliot-Curie and Frédéric Joliot observe but misinterpret neutron scattering in paraffin 1931 John Lennard-Jones proposes the Lennard-Jones interatomic potential 1931 Linus Pauling discovers resonance bonding and uses it to explain the high stability of symmetric planar molecules 1931 Paul Dirac shows that charge quantization can be explained if magnetic monopoles exist 1931 Wolfgang Pauli puts forth the neutrino hypothesis to explain the apparent violation of energy conservation in beta decay 1932 Carl D. Anderson discovers the positron 1932 James Chadwick discovers the neutron 1932 John Cockcroft and Ernest Walton split lithium and boron nuclei using proton bombardment 1932 Werner Heisenberg presents the proton–neutron model of the nucleus and uses it to explain isotopes 1933 Ernst Stueckelberg (1932), Lev Landau (1932), and Clarence Zener discover the Landau–Zener transition 1933 Max Delbrück suggests that quantum effects will cause photons to be scattered by an external electric field 1934 Enrico Fermi publishes a very successful model of beta decay in which neutrinos were produced. 1934 Enrico Fermi suggests bombarding uranium atoms with neutrons to make a 93 proton element 1934 Irène Joliot-Curie and Frédéric Joliot bombard aluminium atoms with alpha particles to create artificially radioactive phosphorus-30 1934 Leó Szilárd realizes that nuclear chain reactions may be possible 1934 Lev Landau tells Edward Teller that non-linear molecules may have vibrational modes which remove the degeneracy of an orbitally degenerate state (Jahn–Teller effect) 1934 Pavel Cherenkov reports that light is emitted by relativistic particles traveling in a nonscintillating liquid 1935 Albert Einstein, Boris Podolsky, and Nathan Rosen put forth the EPR paradox 1935 Henry Eyring develops the transition state theory 1935 Hideki Yukawa presents a theory of the nuclear force and predicts the scalar meson 1935 Niels Bohr presents his analysis of the EPR paradox 1936 Carl D. Anderson discovered the muon while he studied cosmic radiation; 1936 Alexandru Proca formulates the relativistic quantum field equations for a massive vector meson of spin-1 as a basis for nuclear forces 1936 Eugene Wigner develops the theory of neutron absorption by atomic nuclei 1936 Hermann Arthur Jahn and Edward Teller present their systematic study of the symmetry types for which the Jahn–Teller effect is expected 1937 Carl Anderson proves experimentally the existence of the pion predicted by Yukawa's theory. 1937 Hans Hellmann finds the Hellmann–Feynman theorem 1937 Seth Neddermeyer, Carl Anderson, J.C. Street, and E.C. Stevenson discover muons using cloud chamber measurements of cosmic rays 1939 Lise Meitner and Otto Robert Frisch determine that nuclear fission is taking place in the Hahn–Strassmann experiments 1939 Otto Hahn and Fritz Strassmann bombard uranium salts with thermal neutrons and discover barium among the reaction products 1939 Richard Feynman finds the Hellmann–Feynman theorem 1942 Enrico Fermi makes the first controlled nuclear chain reaction 1942 Ernst Stueckelberg introduces the propagator to positron theory and interprets positrons as negative energy electrons moving backwards through spacetime == Quantum field theory == 1947 George Dixon Rochester and Clifford Charles Butler discovered the kaon, the first strange particle; 1947 Cecil Powell, César Lattes, and Giuseppe Occhialini discover the pi meson by studying cosmic ray tracks 1947 Richard Feynman presents his propagator approach to quantum electrodynamics 1947 Willis Lamb and Robert Retherford measure the Lamb–Retherford shift 1948 Hendrik Casimir predicts a rudimentary attractive Casimir force on a parallel plate capacitor 1951 Martin Deutsch discovers positronium 1952 David Bohm propose his interpretation of quantum mechanics 1953 Robert Wilson observes Delbruck scattering of 1.33 MeV gamma-rays by the electric fields of lead nuclei 1953 Charles H. Townes, collaborating with J. P. Gordon, and H. J. Zeiger, builds the first ammonia maser 1954 Chen Ning Yang and Robert Mills investigate a theory of hadronic isospin by demanding local gauge invariance under isotopic spin space rotations, the first non-Abelian gauge theory 1955 Owen Chamberlain, Emilio Segrè, Clyde Wiegand, and Thomas Ypsilantis discover the antiproton 1955 and 1956 Murray Gell-Mann and Kazuhiko Nishijima independently derive the Gell-Mann–Nishijima formula, which relates the baryon number, the strangeness, and the isospin of hadrons to the charge, eventually leading to the systematic categorization of hadrons and, ultimately, the quark model of hadron composition. 1956 Clyde Cowan and Frederick Reines discovered the (electron) neutrino; 1956 Chen Ning Yang and Tsung Lee propose parity violation by the weak nuclear force 1956 Chien Shiung Wu discovers parity violation by the weak force in decaying cobalt 1956 Frederick Reines and Clyde Cowan detect antineutrino 1957 Bruno Pontecorvo postulated the flavor oscillation; 1957 Gerhart Luders proves the CPT theorem 1957 Richard Feynman, Murray Gell-Mann, Robert Marshak, and E.C.G. Sudarshan propose a vector/axial vector (VA) Lagrangian for weak interactions. 1958 Marcus Sparnaay experimentally confirms the Casimir effect 1959 Yakir Aharonov and David Bohm predict the Aharonov–Bohm effect 1960 R.G. Chambers experimentally confirms the Aharonov–Bohm effect 1961 Jeffrey Goldstone considers the breaking of global phase symmetry 1961 Murray Gell-Mann and Yuval Ne'eman discover the Eightfold Way patterns, the SU(3) group 1962 Leon Lederman shows that the electron neutrino is distinct from the muon neutrino 1963 Eugene Wigner discovers the fundamental roles played by quantum symmetries in atoms and molecules == The formation and successes of the Standard Model == 1963 Nicola Cabibbo develops the mathematical matrix by which the first two (and ultimately three) generations of quarks can be predicted. 1964 Murray Gell-Mann and George Zweig propose the quark/aces model 1964 François Englert, Robert Brout, Peter Higgs, Gerald Guralnik, C. R. Hagen, and Tom Kibble postulate that a fundamental quantum field, now called the Higgs field, permeates space and, by way of the Higgs mechanism, provides mass to all the elementary subatomic particles that interact with it. While the Higgs field is postulated to confer mass on quarks and leptons, it represents only a tiny portion of the masses of other subatomic particles, such as protons and neutrons. In these, gluons that bind quarks together confer most of the particle mass. The result is obtained independently by three groups: François Englert and Robert Brout; Peter Higgs, working from the ideas of Philip Anderson; and Gerald Guralnik, C. R. Hagen, and Tom Kibble. 1964 Murray Gell-Mann and George Zweig independently propose the quark model of hadrons, predicting the arbitrarily named up, down, and strange quarks. Gell-Mann is credited with coining the term quark, which he found in James Joyce's book Finnegans Wake. 1964 Sheldon Glashow and James Bjorken predict the existence of the charm quark. The addition is proposed because it allows for a better description of the weak interaction (the mechanism that allows quarks and other particles to decay), equalizes the number of known quarks with the number of known leptons, and implies a mass formula that correctly reproduced the masses of the known mesons. 1964 John Stewart Bell shows that all local hidden variable theories must satisfy Bell's inequality 1964 Peter Higgs considers the breaking of local phase symmetry 1964 Val Fitch and James Cronin observe CP violation by the weak force in the decay of K mesons 1967 Bruno Pontecorvo postulated neutrino oscillation; 1967 Steven Weinberg and Abdus Salam publish papers in which they describe Yang–Mills theory using the SU(2) X U(1) supersymmetry group, thereby yielding a mass for the W particle of the weak interaction via spontaneous symmetry breaking. 1967 Steven Weinberg puts forth his electroweak model of leptons 1968 Stanford University: Deep inelastic scattering experiments at the Stanford Linear Accelerator Center (SLAC) show that the proton contains much smaller, point-like objects and is therefore not an elementary particle. Physicists at the time are reluctant to identify these objects with quarks, instead calling them partons — a term coined by Richard Feynman. The objects that are observed at SLAC will later be identified as up and down quarks. Nevertheless, "parton" remains in use as a collective term for the constituents of hadrons (quarks, antiquarks, and gluons). The existence of the strange quark is indirectly validated by the SLAC's scattering experiments: not only is it a necessary component of Gell-Mann and Zweig's three-quark model, but it provides an explanation for the kaon (K) and pion (π) hadrons discovered in cosmic rays in 1947. 1969 John Clauser, Michael Horne, Abner Shimony and Richard Holt propose a polarization correlation test of Bell's inequality 1970 Sheldon Glashow, John Iliopoulos, and Luciano Maiani propose the charm quark 1971 Gerard 't Hooft shows that the Glashow-Salam-Weinberg electroweak model can be renormalized 1972 Stuart Freedman and John Clauser perform the first polarization correlation test of Bell's inequality 1973 Frank Anthony Wilczek discover the quark asymptotic freedom in the theory of strong interactions; receives the Lorentz Medal in 2002, and the Nobel Prize in Physics in 2004 for his discovery and his subsequent contributions to quantum chromodynamics. 1973 Makoto Kobayashi and Toshihide Maskawa note that the experimental observation of CP violation can be explained if an additional pair of quarks exist. The two new quarks are eventually named top and bottom. 1973 David Politzer and Frank Anthony Wilczek propose the asymptotic freedom of quarks 1974 Burton Richter and Samuel Ting: Charm quarks are produced almost simultaneously by two teams in November 1974 (see November Revolution) — one at SLAC under Burton Richter, and one at Brookhaven National Laboratory under Samuel Ting. The charm quarks are observed bound with charm antiquarks in mesons. The two discovering parties independently assign the discovered meson two different symbols, J and ψ; thus, it becomes formally known as the J/ψ meson. The discovery finally convinces the physics community of the quark model's validity. 1974 Robert J. Buenker and Sigrid D. Peyerimhoff introduce the multireference configuration interaction method. 1975 Martin Perl discovers the tau lepton 1977 Leon Lederman observes the bottom quark with his team at Fermilab. This discovery is a strong indicator of the top quark's existence: without the top quark, the bottom quark would be without a partner that is required by the mathematics of the theory. 1977 Martin Lewis Perl discovered the tau lepton after a series of experiments; 1977 Steve Herb finds the upsilon resonance implying the existence of the beauty/bottom quark 1979 Gluon observed indirectly in three-jet events at DESY; 1982 Alain Aspect, J. Dalibard, and G. Roger perform a polarization correlation test of Bell's inequality that rules out conspiratorial polarizer communication 1983 Carlo Rubbia and Simon van der Meer discovered the W and Z bosons; 1983 Carlo Rubbia, Simon van der Meer, and the CERN UA-1 collaboration find the W and Z intermediate vector bosons 1989 The Z intermediate vector boson resonance width indicates three quark–lepton generations 1994 The CERN LEAR Crystal Barrel Experiment justifies the existence of glueballs (exotic meson). 1995 The top quark is finally observed by a team at Fermilab after an 18-year search. It has a mass much greater than had been previously expected — almost as great as a gold atom. 1995 The D0 and CDF experiments at the Fermilab Tevatron discover the top quark. 1998 – The Super-Kamiokande (Japan) detector facility reports experimental evidence for neutrino oscillations, implying that at least one neutrino has mass. 1998 Super-Kamiokande (Japan) observes evidence for neutrino oscillations, implying that at least one neutrino has mass. 1999 Ahmed Zewail wins the Nobel prize in chemistry for his work on femtochemistry for atoms and molecules. 2000 scientists at Fermilab announce the first direct evidence for the tau neutrino, the third kind of neutrino in particle physics. 2000 CERN announced quark-gluon plasma, a new phase of matter. 2001 the Sudbury Neutrino Observatory (Canada) confirm the existence of neutrino oscillations. Lene Hau stops a beam of light completely in a Bose–Einstein condensate. 2001 The Sudbury Neutrino Observatory (Canada) confirms the existence of neutrino oscillations. 2005 the RHIC accelerator of Brookhaven National Laboratory generates a "perfect" fluid, perhaps the quark–gluon plasma. 2010 The Large Hadron Collider at CERN begins operation with the primary goal of searching for the Higgs boson. 2012 Higgs boson-like particle discovered at CERN's Large Hadron Collider (LHC). 2014 The LHCb experiment observes particles consistent with tetraquarks and pentaquarks 2014 The T2K and OPERA experiment observe the appearance of electron neutrinos and Tau neutrinos in a muon neutrino beam == See also == Chronology of the universe History of subatomic physics History of quantum mechanics History of quantum field theory History of the molecule History of thermodynamics History of chemistry Golden age of physics Timeline of cosmological theories Timeline of particle physics technology == References == == External links == Alain Connes official website with downloadable papers. Alain Connes's Standard Model. A History of Quantum Mechanics Archived 2019-10-28 at the Wayback Machine A Brief History of Quantum Mechanics
Wikipedia/Timeline_of_atomic_and_subatomic_physics
This article discusses women who have made an important contribution to the field of physics. == International physics awards == === Nobel laureates === Five women have won the Nobel Prize in Physics, awarded annually since 1901 by the Royal Swedish Academy of Sciences. These are: 1903 Marie Curie: "in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel" 1963 Maria Goeppert Mayer: "for their discoveries concerning nuclear shell structure" 2018 Donna Strickland: "for their method high-intensity, ultra-short optical pulses" 2020 Andrea Ghez: "for the discovery of a supermassive compact object at the centre of our galaxy." 2023 Anne L'Huillier "for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter." Marie Curie was the first woman to be nominated in 1902 and to receive the prize in 1903 and shared 1/2 of the prize with her husband Pierre Curie for their joint work on radioactivity, discovered by Henri Becquerel who got the other half of the prize. Marie Curie was the first woman to also receive the Nobel Prize in Chemistry in 1911, making her the first person to win two Nobel prizes and, as of 2023, the only person to be awarded two Nobel prizes in two different scientific categories. Maria Goeppert Mayer became the second woman to win the prize in 1963, for the theoretical development of the nuclear shell model, a half of the prize shared with J. Hans D. Jensen (the other half given to Eugene Wigner). Donna Strickland shared half of the prize in 2018 with Gérard Mourou, for their work in chirped pulse amplification beginning in the 1980s (the other half given to Arthur Ashkin). Andrea Ghez was the fourth female Nobel laureate in 2020, she shared one half of the prize with Reinhard Genzel for the discovery of the supermassive compact object Sagittarius A* at the center of our galaxy (the other half given to Roger Penrose). In 2023, Anne L'Huillier shared the prize in equal parts with Pierre Agostini and Ferenc Krausz for their experimental contribution and development of attosecond physics. L'Huillier is the first female laureate to receive 1/3 of monetary award of the Nobel Prize in Physics (Curie, Goeppert–Mayer, Strickland and Ghez received 1/4). Physicists and physicochemists that won a Nobel Prize in Chemistry include Marie Curie, Irène Joliot-Curie, daughter of Marie Curie, in 1935, and Dorothy Hodgkin in 1964. Nuclear physicist Rosalyn Sussman Yalow was the second female scientist to win the Nobel Prize in Physiology or Medicine in 1977 for the development of radioimmunoassays. Human right activist and 2023 Nobel Peace Prize, Narges Mohammadi, was trained in nuclear physics. ==== Nobel nominees and nominators ==== According to the Nobel archives (updated up to 1970), other physicists that were nominated to the Nobel Prize in Physics but did not receive it, include: Lise Meitner, nominated 21 times; Chien-Shiung Wu, nominated 5 times; Marietta Blau, nominated 3 times; and Hertha Wambacher, Margaret Burbidge and Janine Connes, nominated once. Irène Joliot-Curie and Dorothy Hodgkin were also nominated for the Nobel Prize in Physics, but received a Nobel Prize in Chemistry in 1935 and 1964, respectively. Lise Meitner is the female physicist the most nominated, 16 times for Physics and 14 times for Chemistry. About 1.7% of the Nobel nominations in Physics up to 1970 were women. Aside from the named above, other physicists and physicochemists that were nominated to the Nobel Prize in Chemistry but dit not receive it, include Ida Noddack, Marguerite Perey, Alberte Pullman, and Erika Cremer. Up to 1970, eight female scientists have participated as nominators for the Nobel Prize in Physics. These are Marie Curie, Hertha Sponer, Marie-Antoinette Tonnelat, Anne Barbara Underhill, Katharina Boll-Dornberger, Maria Goeppert Mayer, Dorothy Hodgkin, and Margaret Burbidge. ==== Clarivate Citation ==== Several women have been selected as Clarivate Citation laureates in Physics, which makes an annual list of possible candidates for the Nobel Prize in Physics based on citation statistics, these include: 2008 Vera Rubin † "for her pioneering research indicating the existence of dark matter in the universe." 2012 Lene Hau "for the experimental demonstration of electromagnetically induced transparency 'slow light' (with Stephen E. Harris)." 2015 Deborah S. Jin † "for pioneering research on atomic gases at ultra-cold temperatures and the creation of the first fermionic condensate." 2018 Sandra Faber "for pioneering methods to determine the age, size and distance of galaxies and for other contributions to cosmology." 2023 Sharon Glotzer "for demonstrating the role of entropy in the self-assembly of matter and for introducing strategies to control the assembly process to engineer new materials." †: deceased, no longer eligible. === Wolf Prize === Two women have been awarded the Wolf Prize in Physics, awarded by the Wolf Foundation in Israel since 1978. They are: 1978 Chien-Shiung Wu, "for her explorations of the weak interaction, helping establish the precise form and the non-conservation of parity for this natural force." 2022 Anne L'Huillier, "for pioneering contributions to ultrafast laser science and attosecond physics". === Breakthrough Prize === Women who have been awarded the Breakthrough Prize in Fundamental Physics since 2012, include: 2018 WMAP Probe team, 27 listed members, including Hiranya Peiris, Licia Verde, Janet L. Weiland and Joanna Dunkley for "For detailed maps of the early universe that greatly improved our knowledge of the evolution of the cosmos and the fluctuations that seeded the formation of galaxies." 2018 Special recognition to Jocelyn Bell Burnell for "For fundamental contributions to the discovery of pulsars, and a lifetime of inspiring leadership in the scientific community." === Prizes only for female physicists === L'Oréal-UNESCO For Women in Science Awards, awarded bi-annually to one laureate per continent for outstanding contributions to the physical sciences. Maria Goeppert-Mayer Award of the American Physical Society awarded annually in recognition of an outstanding contribution to physics research. Jocelyn Bell Burnell Medal and Prize by the Institute of Physics in UK, for contributions to physics by a very early career physicist. Annie Jump Cannon Award in Astronomy awarded annually for outstanding contributions to astronomy within five years of earning a doctorate degree. == Topics named after female scientists == Female scientist have sometimes not been recognized in the naming of topics they discovered due to Matilda effect. Some physics phenomena that are named after female scientists include: === Physical models and theories === Birge–Sponer method, in molecular physics, partially named after Hertha Sponer. Fermi–Pasta–Ulam–Tsingou problem in chaos theory, partially named after Mary Tsingou. Frenkel–Kontorova model, in non-linear physics, partially named after Tatiana Kontorova. Kovalevskaya top in rotational dynamics, named after Sofya Kovalevskaya. Pasterski–Strominger–Zhiboedov triangle in quantum gravity, is partially named after Sabrina Gonzalez Pasterski. Peccei–Quinn theory in particle physics, partially named after Helen Quinn. Pöschl–Teller potential in quantum mechanics, partially named after Herta Pöschl. Randall–Sundrum model in theoretical physics, partially named after Lisa Randall. Falkner–Skan boundary layer in fluid mechanics, partially named after Sylvia Skan === Physical phenomena and empirical laws === Faber–Jackson relation, in astronomomy, partially named after Sandra Faber. Goos–Hänchen effect in optics, partially named after Hilda Hänchen. Leavitt's law in astronomy, named after Henrietta Swan Leavitt. Pockels point in surface physics, named after Agnes Pockels. Rubin–Ford effect in cosmology, partially named after Vera Rubin. === Physical theorems === Bohr–Van Leeuwen theorem in thermodynamics, partially named after Hendrika Johanna van Leeuwen Coffman–Kundu–Wootters inequality, in quantum information, partially named after Valerie Coffman Noether's theorem in modern physics, named after Emmy Noether === Experiments and equipment === Langmuir–Blodgett film, partially named after Katharine Burr Blodgett Curie (unit), Ci, partially named after Marie Curie Morton number (dimensionless number), Mo, used to characterize bubbles is named after Rose Morton Goeppert Mayer (unit), GM, unit of absorption cross section named after Maria Goeppert Mayer Wu experiment named after Chien-Shiung Wu == Timeline == === Antiquity === c. 150 BCE: Aglaonice became the first female astronomer to be recorded in Ancient Greece. c. 355–415 CE: Greek astronomer, mathematician and philosopher, Hypatia became renowned as a respected academic teacher, editor of Ptolemy's Almagest astronomical data, and head of her own science academy. === 16th century === 1572: astronomer Sophia Brahe assists her older brother Tycho Brahe finding a new bright object in the night sky, now known as called SN 1572 (a supernova). Sophia would help her brother in astronomy throughout his life. === 17th century === 1650: astronomer Maria Cunitz publishes Urania Propitia. 1668: After separating from her husband, French polymath Marguerite de la Sablière established a popular salon in Paris. Scientists and scholars from different countries visited the salon regularly to discuss ideas and share knowledge, and Sablière studied physics, astronomy and natural history with her guests. 1680: Astronomer Jeanne Dumée published a summary of arguments supporting the Copernican theory of heliocentrism. She wrote "between the brain of a woman and that of a man there is no difference". 1690: astronomer Elisabeth Hevelius published Prodromus Astronomiae, compiling the star catalog of 1560 stars by her and her husband Johannes Hevelius. 1693–1698: German astronomer and illustrator Maria Clara Eimmart created more than 350 detailed drawings of the moon phases. === 18th century === 1702: Maria Margaretha Kirch becomes the first woman to discover a comet. 17010: Due to her various contribution Maria Margaretha Kirch ask to enter the Royal Berlin Academy of Sciences. The request was denied. 1715: Eustachio Manfredi and his sisters Maddalena and Teresa Manfredi publish Ephemerides of Celestial Motion. The learning of the Manfredi sisters was acknowledged by Pope Benedict XIV. 1732: At the age of 20, Italian physicist Laura Bassi became the first female member of the Bologna Academy of Sciences. One month later, she publicly defended her academic theses and received a PhD. Bassi was awarded an honorary position as professor of physics at the University of Bologna. She was the first female physics professor in the world. 1738: French polymath Émilie du Châtelet became the first woman to have a paper published by the Paris Academy, following a contest on the nature of fire. 1740: Du Châtelet publishes Institutions de Physique, or Foundations of Physics, providing a metaphysical basis for Newtonian physics. 1751: 19-year-old Italian physicist Cristina Roccati received her PhD from the University of Bologna. 1755: Sculptor Jean-Jacques Caffieri makes a medallion of physicist Maria Angela Ardinghelli to be hung in French Academy of Sciences. The academy did not accept female members at the time. Ardinghelli worked as the main correspondent and translator between Paris and Naples in terms of physics discussions. 1757: Nicole-Reine Lepaute works out the return of Halley's Comet, in collaboration with Alexis Clairaut and Jérôme Lalande. 1776: At the University of Bologna, Italian physicist Laura Bassi became the first woman appointed as chair of physics at a university. 1789: astronomer Louise du Pierry becomes the first female professor at the Sorbonne. 1798: Marie-Jeanne de Lalande and Princess Charlotte of Saxe-Meiningen are the only female astronomers in the first European congress of astronomers. === 19th century === 1806: Carl Friedrich Gauss recognizes Marie-Jeanne de Lalande as the only woman he knows working in science. Unaware that his correspondent Sophie Germain was a woman. 1816: French mathematician and physicist Sophie Germain became the first women to win a prize from the Paris Academy of Sciences for her work on elasticity theory. 1828: Caroline Herschel, sister of William Herschel, becomes the first woman to publish in the Philosophical Transactions of the Royal Society and is awarded the Gold Medal of the Royal Astronomical Society. 1835: Caroline Herschel and Mary Somerville became the first female Honorary Members of the Royal Astronomical Society. 1856: Amateur scientist Eunice Newton Foote provides the first demonstration of the warming effect of the sun is greater for air with water vapour than for dry air, and the effect is even greater with carbon dioxide (greenhouse effect). 1890: Alice Everett becomes the first woman to be employed and payed at the Royal Observatory, Greenwich. 1891: Agnes Pockels, gets help from Rayleigh to publish her first paper on nature of surface tension. There she first introduces the concept of the Pockels point and pioneers the field of surface science. 1893: Alice Everett becomes the first woman to have a paper published by the Physical Society of London. 1895: Margaret Eliza Maltby becomes the first woman to earn a doctorate in the University of Göttingen. 1896: Elizabeth Stephansen becomes the first woman to complete the physics program of Zurich Polytechnic. 1897: American physicist Isabelle Stone became the first woman to receive a PhD in physics in the United States. She wrote her dissertation "On the Electrical Resistance of Thin Films" at the University of Chicago. 1898: Danish physicist Kirstine Meyer was awarded the gold medal of the Royal Danish Academy of Sciences and Letters. 1888: The Kovalevskaya top, one of a brief list of known examples of integrable rigid body motion, was discovered by Sofia Kovalevskaya. 1899: Irish physicist Edith Anne Stoney was appointed a physics lecturer at the London School of Medicine for Women, becoming the first woman medical physicist. She later became a pioneering figure in the use of x-ray machines on the front lines of World War I. 1899: American physicists Marcia Keith and Isabelle Stone became charter members of the American Physical Society. === 20th century === ==== 1900s ==== 1903: Marie Curie was the first woman to receive a Nobel Prize; she received the Nobel Prize in Physics along with her husband, Pierre Curie "for their joint researches on the radiation phenomena discovered by Professor Henri Becquerel", and Henri Becquerel, "for his discovery of spontaneous radioactivity". 1900: Physicists Marie Curie and Isabelle Stone attended the first International Congress of Physics in Paris, France. They were the only two women out of 836 participants. 1904: Annie S. D. Maunder and her husband Edward Walter Maunder publish the butterfly diagram to study sunspots. They also identify the Maunder Minimum. 1906: English physicist, mathematician and engineer Hertha Ayrton became the first female recipient of the Hughes Medal from the Royal Society of London. She received the award for her experimental research on electric arcs and sand ripples. The first woman to be nominated for the Royal Society and to give a lecture to the Society. 1907: Ayrton joins the Suffragettes and the Women's Social and Political Union (WSPU). 1909: Danish physicist Kristine Meyer became the first Danish woman to receive a doctorate degree in natural sciences. She wrote her dissertation on the topic of "the development of the temperature concept" within the history of physics. ==== 1910s ==== 1911: Marie Curie became the first woman to receive the Nobel Prize in Chemistry, which she received "[for] the discovery of the elements radium and polonium, by the isolation of radium and the study of the nature and compounds of this remarkable element". This made her the only woman to win two Nobel Prizes. 1912: Astronomer Henrietta Swan Leavitt studied the bright-dim cycle periods of Cepheid stars, then found a way to calculate the distance from such stars to Earth. 1913: Geertruida de Haas-Lorentz is the first to study of thermal noise in electric circuits, predating the discovery of the Johnson–Nyquist noise. 1918: Emmy Noether created Noether's theorem explaining the connection between symmetry and conservation laws. 1919: Hendrika Johanna van Leeuwen proves the Bohr–Van Leeuwen theorem in her thesis explaining why magnetism is an essentially quantum mechanical effect. ==== 1920s ==== 1922: the International Astronomical Union adopts the stellar classification used by Annie Jump Cannon. She came up with the first serious attempt to organize and classify stars based on their temperatures and spectral types. 1925: Annie Jump Cannon became the first woman to receive an honorary doctorate of science from Oxford University. 1925: Astrophysicist Cecilia Payne-Gaposchkin established that hydrogen is the most common element in stars, and thus the most abundant element in the universe. 1926: Katharine Burr Blodgett was the first women to earn a Ph.D. in physics from the University of Cambridge. 1926: The first application of quantum mechanics to molecular systems was done by Lucy Mensing. She studied the rotational spectrum of diatomic molecules using the methods of matrix mechanics. ==== 1930s ==== 1931: Sylvia Skan and Victor Montague Falkner publish their work on the Falkner–Skan boundary layer. 1933: Herta Pöschl (abbreviated G. Pöschl) working with Edward Teller, find that the Pöschl–Teller potential is analytically solvable in quantum mechanics. 1934: Olga N. Trapeznikowa and his husband Lev Shubnikov finish an experiment showing one of the first evidences for the existence of antiferromagnetism. 1935: Katharine Burr Blodgett improves Irving Langmuir experimental set up leading to the development of the Langmuir–Blodgett trough and the discovery of the Langmuir–Blodgett films. 1935: Grete Hermann provides the earliest refutation to John von Neumann's attempt to prove that quantum mechanics is incompatible with hidden variables. 1936: Hertha Sponer becomes the first female professor in the physics faculty in Duke University. 1937: Marietta Blau and her student Hertha Wambacher, both Austrian physicists, received the Lieben Prize of the Austrian Academy of Sciences for their work on cosmic ray observations using the technique of nuclear emulsions. 1938: Tatiana Kontorova, in collaboration with Yakov Frenkel, develops the Frenkel-Kontorova model to describe the structure and nonlinear dynamics of a crystal lattice in the vicinity of the dislocation core. 1939 Lise Meitner helped lead a small group of scientists who first discovered the nuclear fission of uranium when it absorbed an extra neutron. Nuclear physicist Marguerite Perey discovers francium. Sameera Moussa became the first woman to earn a doctorate in atomic radiation and the first woman to hold a teaching post in Cairo University. ==== 1940s ==== c. 1940: Elizabeth Alexander and Ruby Payne-Scott become the first women to work in radio astronomy. Making important results on the study of radar signals coming from the sun. 1941: Ruby Payne-Scott joined the Radio Physics Laboratory of the Australia Government's CSIRO; she was the first woman radio astronomer. 1942: Chicago Pile-1 led by Enrico Fermi, the first nuclear reactor reaches criticality. Leona Woods was the only woman in the team and she was instrumental in the construction and then use of geiger counters for analysis during experimentation. 1943: the Manhattan project hires the Calutron Girls, a large group of young girls to monitor dials and watch meters for calutrons, mass spectrometers adapted for separation of uranium isotopes, unaware of the purpose of the project. 1943: Berta Karlik discovers astatine as a product of two naturally occurring decay chains. She was awarded the Haitinger Prize of the Austrian Academy of Sciences for this discovery. 1944: Curium (atomic number 96, symbol Cm) gets discovered a gets named after Marie and Pierre Curie, the "m" in Cm as a reference to Marie. 1945: American physicists and mathematicians Frances Spence, Ruth Teitelbaum, Marlyn Meltzer, Betty Holberton, Jean Bartik and Kathleen Antonelli programmed the electronic general-purpose computer ENIAC, becoming some of the world's first computer programmers. 1947: Hilda Hänchen, in collaboration with Fritz Goos, demonstrates a new optical phenomena, now known as the Goos–Hänchen effect. 1949: Rosemary Brown (later Fowler), a student of C.F. Powell at the University of Bristol, discovers the k-meson in what Heisenberg calls "most beautiful" pictures of cosmic ray tracks from the Jungfraujoch (the 'k' track in Brown, R. et al. Nature, 163, 47 (1949). This discovery and the prior finding of a very similar particle in 1947 led to the "τ–θ puzzle", the discovery of parity violation in weak interactions, and hence the Standard Model. ==== 1950s ==== 1951: Cécile DeWitt-Morette founds the École de physique des Houches, one of the most prestigious scientific centers for international physics summer schools in Europe. 1952: Photograph 51, an X-ray diffraction image of crystallized DNA, was taken by Raymond Gosling in May 1952, working as a PhD student under the supervision of British chemist and biophysicist Rosalind Franklin; it was critical evidence in identifying the structure of DNA. 1952: Yvonne Choquet-Bruhat proves that Einstein field equations can be formulated as an initial value problem (local existence of solutions and uniqueness). 1953: Various authors, including Arianna W. Rosenbluth and Augusta H. Teller, led by Nicholas Metropolis, write the paper titled "Equation of State Calculations by Fast Computing Machines" that introduced the Metropolis–Hastings algorithm. 1953: Rose Morton and William L. Haberman identify a constant to characterize bubbles. The constant is now called the Morton number. 1954: Janine Connes pioneers the new field of Fourier transform infrared spectroscopy for astronomy. 1954: Sulamith Goldhaber, along with her husband Gerson Goldhaber, start a series of important experiments to measure the properties of the K meson. 1955: the results of the Fermi–Pasta–Ulam–Tsingou simulation is published in Los Alamos National Laboratory. It was coded by Mary Tsingou using the MANIAC I computer working with Enrico Fermi, John Pasta, and Stanislaw Ulam in the Manhattan Project. It represents one of the first computational experiments in mathematics and chaos theory. 1956: Chinese-American physicist Chien-Shiung Wu conducted a nuclear physics experiment in collaboration with the Low Temperature Group of the US National Bureau of Standards. The experiment, becoming known as the Wu experiment, showed that parity could be violated in weak interaction. 1957: Margaret Burbidge releases the landmark B2FH paper as first author along with Geoffrey Burbidge, William A. Fowler, and Fred Hoyle. The paper reviewed stellar nucleosynthesis theory and identified nucleosynthesis processes that are responsible for producing the elements heavier than iron and explained their relative abundances. 1958: Olga Ladyzhenskaya provides the first rigorous proofs of the convergence of a finite difference method for the Navier–Stokes equations. 1960: American medical physicist Rosalyn Yalow received the Nobel Prize in Physiology or Medicine "for the development of radioimmunoassays of peptide hormones" along with Roger Guillemin and Andrew V. Schally who received it "for their discoveries concerning the peptide hormone production of the brain". ==== 1960s ==== 1961: Ellen Fetter and Margaret Hamilton were collaborators with Edward Norton Lorenz in weather forecasting, establishing together modern chaos theory. 1962: French physicist Marguerite Perey became the first female Fellow elected to the Académie des Sciences. 1963: Maria Goeppert Mayer became the first American woman to receive a Nobel Prize in Physics; she shared the prize with J. Hans D. Jensen "for their discoveries concerning nuclear shell structure” and Eugene Paul Wigner "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles". 1963: Experiments by Myriam Sarachik provided the first data that confirmed the Kondo effect. 1964: Chien-Shiung Wu spoke at MIT about gender discrimination. 1967: Astrophysicist Jocelyn Bell Burnell co-discovered the first radio pulsars.: minute 8:59  1970: Astronomer Vera Rubin published the first evidence for dark matter. 1970: Madeleine Veyssié, coins the term soft matter. ==== 1970s ==== 1971 Mina Rees became the first woman president of American Association for the Advancement of Science (AAAS) founded in 1848. 1972: Willie Hobbs Moore became the first African-American woman to receive a Ph.D. in physics. 1972: Sandra Faber became the first woman to join the Lick Observatory staff at the University of California, Santa Cruz. 1973: American physicist Anna Coble became the first African-American woman to receive a PhD in biophysics, completing her dissertation at University of Illinois. 1975: Mary K. Gaillard, working with Benjamin W. Lee and Jonathan L. Rosner, predicts the mass of the charm quark before it was measured. She will later also predict the mass of the bottom quark. 1975: María Teresa Ruiz, becomes the first woman to obtain a PhD in astrophysics at Princeton University. 1976: Sandra Faber publishes her Faber–Jackson relation, providing the first empirical power-law relation between the luminosity and the central stellar velocity dispersion of elliptical galaxy. 1977: Helen Quinn develops the Peccei–Quinn theory as one of the first possible solutions to the strong CP problem, in collaboration with Roberto Peccei. 1978: Chien-Shiung Wu becomes the inaugural laureate of the Wolf Prize in Physics for her help with the development of the Standard Model. 1980: Nigerian geophysicist Deborah Ajakaiye became the first woman in any West African country to be appointed a full professor of physics. Over the course of her scientific career, she became the first female Fellow elected to the Nigerian Academy of Science, and the first female dean of science in Nigeria. 1980: Mary K. Gaillard produces a report at CERN (European Organization for Nuclear Research) addressing the fact that just 3% of the staff were women. She called for the elimination of gender discrimination through equality in promotion, maternity leave and full-day child care. ==== 1980s ==== 1981: Mary K. Gaillard becomes the first woman with a tenured position in the physics faculty at the University of California, Berkeley. 1985: Mildred Dresselhaus was appointed the first women Institute Professor at MIT 1986: Maria Goeppert Mayer Award was awarded for the first time to honor young female physicists at the beginning of their careers 1986 Jean M. Bennett became the first woman president of The Optical Society founded in 1916. ==== 1990s ==== 1991: Ana María López, graduate student of Eduardo Fradkin, develops the first Chern–Simons theory for composite fermions to explain the fractional quantum Hall effect. 1992: Claudine Hermann first woman to be appointed professor at École Polytechnique. 1995: Reva Williams works out the Penrose process for rotating black holes. 1997: Chemical element with atomic number 278 is officially named meitnerium, after Lise Meitner. 1999: Lisa Randall published the Randall–Sundrum model, with Raman Sundrum. 2000 Mildred Dresselhaus became the director of the Office of Science at the United States Department of Energy. Helen Quinn becomes the first woman to receive the Dirac Medal of the International Centre for Theoretical Physics (ICTP) "pioneering contributions to the quest for a unified theory of quarks and leptons and the strong, weak and electromagnetic interactions." Valerie Coffman, working with Joydip Kundu and William Wootters establish the concept of monogamy of entanglement for tripartite systems, using their Coffman–Kundu–Wooters inequality. === 21st century === ==== 2000s ==== 2001: Lene Hau stopped a beam of light completely 2001: Wendy Freedman and her team published the measured Hubble constant from measurements of the Hubble Space Telescope. 2003: Geophysicist Claudia Alexander oversaw the final stages of Project Galileo, a space exploration mission that ended at the planet Jupiter. Deborah S. Jin and her team were the first to condense pairs of fermionic atoms Physicists Ayşe Erzan, Karimat El-Sayed, Li Fanghua, Mariana Weissmann and Anneke Levelt Sengers win the first L'Oréal-UNESCO For Women in Science Awards in Physical Sciences. 2005: Myriam Sarachik becomes the first woman to win the Oliver E. Buckley Condensed Matter Prize for her contributions to quantum spin dynamics and spin coherence in condensed matter systems, along with David Awschalom and Gabriel Aeppli. 2007: Physicist Ibtesam Badhrees was the first Saudi Arabian woman to become a member of the European Organization for Nuclear Research (CERN). 2009: Margaret Reid becomes the first woman to win the Moyal Medal fromm Macquarie University, for her In 2019, her work on how to demonstrate the Einstein-Podolsky-Rosen paradox using squeezing and parametric down conversion. ==== 2010s ==== 2011: Taiwanese-American astrophysicist Chung-Pei Ma led a team of scientists in discovering two of the largest black holes ever observed. 2012: Mildred Dresselhaus becomes the first female laureate of the Kavli Prize in Nanosciences "for her pioneering contributions to the study of phonons, electron-phonon interactions, and thermal transport in nanostructures". 2013: Nashwa Eassa founded the NGO Sudanese Women in Sciences. 2014: American theoretical physicist Shirley Anne Jackson was awarded the National Medal of Science. Jackson had been the first African-American woman to receive a PhD from the Massachusetts Institute of Technology (MIT) during the early 1970s, and the first woman to chair the U.S. Nuclear Regulatory Commission. 2014: Amanda Barnard becomes the first woman to win the Feynman Prize in Nanotechnology for her computational simulations on diamond nanoparticles. 2015: Sabrina Gonzalez Pasterski, working with Andrew Strominger and Alexander Zhiboedov, develops the Pasterski–Strominger–Zhiboedov triangle relating soft particle theorems of quantum field theory, symmetries of space-time and memory effects in gravitational waves. 2016: Fabiola Gianotti became the first woman Director-General of CERN (European Organization for Nuclear Research) 2018: Astrophysicists Hiranya Peiris and Joanna Dunkley and Italian cosmologist Licia Verde were among 27 scientists awarded the Breakthrough Prize in Fundamental Physics for their contributions to "detailed maps of the early universe that greatly improved our knowledge of the evolution of the cosmos and the fluctuations that seeded the formation of galaxies". Astrophysicist Jocelyn Bell Burnell received the special Breakthrough Prize in Fundamental Physics for her scientific achievements and “inspiring leadership”, worth $3 million. She donated the entirety of the prize money towards the creation of scholarships to assist women, underrepresented minorities and refugees who are pursuing the study of physics. Physicist Donna Strickland received the Nobel Prize in Physics "for groundbreaking inventions in the field of laser physics"; she shared it with Arthur Ashkin and Gérard Mourou. For the first time in history, women received the Nobel Prize in Chemistry and the Nobel Prize in Physics in the same year. Human right activist and physicist Narges Mohammadi wins the Andrei Sakharov prize by the American Physical Society, "for her leadership in campaigning for peace, justice, and the abolition of the death penalty and for her unwavering efforts to promote the human rights and freedoms of the Iranian people, despite persecution that has forced her to suspend her scientific pursuits and endure lengthy incarceration." Ewine van Dishoeck becomes the first female laureate of the Kavli Prize in Astrophysics for "for her combined contributions to observational, theoretical, and laboratory astrochemistry, elucidating the life cycle of interstellar clouds and the formation of stars and planets" 2019: Mathematician Karen Uhlenbeck became the first woman to win the Abel Prize for "her pioneering achievements in geometric partial differential equations, gauge theory, and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics." 2020: Andrea M. Ghez received the Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy." She shared half of the prize with Reinhard Genzel, while the other half was awarded to Roger Penrose. Geoscientist Ingeborg Levin was the first woman to receive the Alfred Wegener medal from the European Geosciences Union "for fundamental contributions to our present knowledge and understanding of greenhouse gases in the atmosphere, including the global carbon cycle." Françoise Combes becomes the first female astrophysicist to win the CNRS Gold Medal, highest degree in research by the French government. ==== 2020s ==== 2022: Anne L’Huillier becomes the second female scientist to receive the Wolf Prize in Physics “for pioneering contributions to ultrafast laser science and attosecond physics”. 2022: Astronomer Ewine van Dishoeck is awarded the UNESCO Niels Bohr Medal. 2023: Professor Polina Bayvel becomes the first woman to win the Rumford Medal by the Royal Society. 2023: Anne l'Huillier receives the 2023 Nobel Prize in Physics for "for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter" shared with Pierre Agostini and Ferenc Krausz. == See also == Timeline of women in science Timeline of women in science in the United States Women in NASA Women in science Women in the workforce == References ==
Wikipedia/Women_in_physics
The following timeline starts with the invention of the modern computer in the late interwar period. == 1930s == John Vincent Atanasoff and Clifford Berry create the first electronic non-programmable, digital computing device, the Atanasoff–Berry Computer, that lasted from 1937 to 1942. == 1940s == Nuclear bomb and ballistics simulations at Los Alamos National Laboratory and Ballistic Research Laboratory (BRL), respectively. Monte Carlo simulation (voted one of the top 10 algorithms of the 20th century by Jack Dongarra and Francis Sullivan in the 2000 issue of Computing in Science and Engineering) is invented at Los Alamos National Laboratory by John von Neumann, Stanislaw Ulam and Nicholas Metropolis. First hydrodynamic simulations performed at Los Alamos National Laboratory. Ulam and von Neumann introduce the notion of cellular automata. == 1950s == Equations of State Calculations by Fast Computing Machines introduces the Metropolis–Hastings algorithm. Also, important earlier independent work by Berni Alder and Stan Frankel. Enrico Fermi, Ulam and John Pasta with help from Mary Tsingou, discover the Fermi–Pasta–Ulam-Tsingou problem. Research initiated into percolation theory. Molecular dynamics is formulated by Alder and Tom E. Wainwright. == 1960s == Using computational investigations of the 3-body problem, Michael Minovitch formulates the gravity assist method. Glauber dynamics is invented for the Ising model by Roy J. Glauber. Edward Lorenz discovers the butterfly effect on a computer, attracting interest in chaos theory. Molecular dynamics is independently invented by Aneesur Rahman. Walter Kohn instigates the development of density functional theory (with L.J. Sham and Pierre Hohenberg), for which he shared the Nobel Chemistry Prize (1998). Martin Kruskal and Norman Zabusky follow up the Fermi–Pasta–Ulam problem with further numerical experiments, and coin the term "soliton". Kawasaki dynamics is invented for the Ising model. Loup Verlet (re)discovers a numerical integration algorithm, (first used in 1791 by Jean Baptiste Delambre, by P. H. Cowell and A. C. C. Crommelin in 1909, and by Carl Fredrik Störmer in 1907, hence the alternative names Störmer's method or the Verlet-Störmer method) for dynamics, and the Verlet list. == 1970s == Computer algebra replicates the work of Boris Delaunay in Lunar theory. Martinus Veltman's calculations at CERN lead him and Gerard 't Hooft to valuable insights into renormalizability of electroweak theory. The computation has been cited as a key reason for the award of the Nobel Physics Prize that has been given to both. Jean Hardy, Yves Pomeau and Olivier de Pazzis introduce the first lattice gas model, abbreviated as the HPP model after its authors. These later evolved into lattice Boltzmann models. Kenneth G. Wilson shows that continuum quantum chromodynamics (QCD) is recovered for an infinitely large lattice with its sites infinitesimally close to one another, thereby beginning lattice QCD. == 1980s == Italian physicists Roberto Car and Michele Parrinello invent the Car–Parrinello method. Swendsen–Wang algorithm is invented in the field of Monte Carlo simulations. Fast multipole method is invented by Vladimir Rokhlin and Leslie Greengard (voted one of the top 10 algorithms of the 20th century). Ullli Wolff invents the Wolff algorithm for statistical physics and Monte Carlo simulation. == See also == Timeline of scientific computing Computational physics Important publications in computational physics == References == == External links == The Monte Carlo Method: Classic Papers Monte Carlo Landmark Papers
Wikipedia/Timeline_of_computational_physics
Single-layer graphene was first unambiguously produced and identified in 2004, by the group of Andre Geim and Konstantin Novoselov, though they credit Hanns-Peter Boehm and his co-workers for the experimental discovery of graphene in 1962; while it had been explored theoretically by P. R. Wallace in 1947. Boehm et al. introduced the term graphene in 1986. == Early history == In 1859, Benjamin Collins Brodie became aware of the highly lamellar structure of thermally reduced graphite oxide. The structure of graphite was identified in 1916 by the related method of powder diffraction. It was studied in detail by Kohlschütter and Haenni in 1918, who described the properties of graphite oxide paper. Its structure was determined from single-crystal diffraction in 1924. The theory of graphene was first explored by P. R. Wallace in 1947 as a starting point for understanding the electronic properties of 3D graphite. The emergent massless Dirac equation was first pointed out by Gordon W. Semenoff, David DiVincenzo and Eugene J. Mele. Semenoff emphasized the occurrence in a magnetic field of an electronic Landau level precisely at the Dirac point. This level is responsible for the anomalous integer quantum Hall effect. The earliest TEM images of few-layer graphite were published by G. Ruess and F. Vogt in 1948. Later, single graphene layers were observed directly by electron microscopy. Before 2004 intercalated graphite compounds were studied under a transmission electron microscope (TEM). Researchers occasionally observed thin graphitic flakes ("few-layer graphene") and possibly even individual layers. An early, detailed study on few-layer graphite dates to 1962 when Boehm reported producing monolayer flakes of reduced graphene oxide. Starting in the 1970s single layers of graphite were grown epitaxially on top of other materials. This "epitaxial graphene" consists of a single-atom-thick hexagonal lattice of sp2-bonded carbon atoms, as in free-standing graphene. However, significant charge transfers from the substrate to the epitaxial graphene, and in some cases, the d-orbitals of the substrate atoms hybridize with the π orbitals of graphene, which significantly alters the electronic structure of epitaxial graphene. Single layers of graphite were observed by TEM within bulk materials, in particular inside soot obtained by chemical exfoliation. Efforts to make thin films of graphite by mechanical exfoliation started in 1990, but nothing thinner than 50 to 100 layers was produced before 2004. == Naming == The term graphene was introduced in 1986 by chemists Hanns-Peter Boehm, Ralph Setton and Eberhard Stumpp. It is a combination of the word graphite and the suffix -ene, referring to polycyclic aromatic hydrocarbons. == Discovery == Initial attempts to make atomically thin graphitic films employed exfoliation techniques similar to the drawing method. Multilayer samples down to 10 nm in thickness were obtained. Earlier researchers tried to isolate graphene starting with intercalated compounds, producing very thin graphitic fragments (possibly monolayers). Neither of the earlier observations was sufficient to launch the "graphene gold rush" that awaited macroscopic samples of extracted atomic planes. One of the first patents pertaining to the production of graphene was filed in October 2002 and granted in 2006. It detailed one of the first large scale graphene production processes. Two years later, in 2004 Geim and Novoselov extracted single-atom-thick crystallites from bulk graphite. They pulled graphene layers from graphite and transferred them onto thin silicon dioxide (SiO2) on a silicon wafer in a process called either micromechanical cleavage or the Scotch tape technique. The SiO2 electrically isolated the graphene and weakly interacted with it, providing nearly charge-neutral graphene layers. The silicon beneath the SiO2 could be used as a "back gate" electrode to vary the charge density in the graphene over a wide range. US patent 6667100, filed in 2002, describes how to process expanded graphite to achieve a graphite thickness of one hundred-thousandth of an inch (0.25 nm). The key to success was high-throughput visual recognition of graphene on a properly chosen substrate that provides a small but noticeable optical contrast. The cleavage technique led directly to the first observation of the anomalous quantum Hall effect in graphene, which provided direct evidence of graphene's theoretically predicted Berry's phase of massless Dirac fermions. The effect was reported by Geim's group and by Kim and Zhang, whose papers appeared in Nature in 2005. Before these experiments other researchers had looked for the quantum Hall effect and Dirac fermions in bulk graphite. Geim and Novoselov received awards for their pioneering research on graphene, notably the 2010 Nobel Prize in Physics. == Commercialization == In 2014, the National Graphene Institute was announced to support applied research and development in partnership with other research organizations and industry. Commercialization of graphene proceeded rapidly once commercial scale production was demonstrated. In 2014 two North East England commercial manufacturers, Applied Graphene Materials and Thomas Swan Limited (with Trinity College, Dublin researchers), began manufacturing. In East Anglia Cambridge Nanosystems operates a graphene powder production facility. By 2017, 13 years after creation of the first laboratory graphene electronic device, an integrated graphene electronics chip was produced commercially and marketed to pharmaceutical researchers by Nanomedical Diagnostics in San Diego. == References ==
Wikipedia/Discovery_of_graphene
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.} For a function f : X → Y {\displaystyle f\colon X\to Y} , its inverse f − 1 : Y → X {\displaystyle f^{-1}\colon Y\to X} admits an explicit description: it sends each element y ∈ Y {\displaystyle y\in Y} to the unique element x ∈ X {\displaystyle x\in X} such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result. To undo this, one adds 7 to the input, then divides the result by 5. Therefore, the inverse of f is the function f − 1 : R → R {\displaystyle f^{-1}\colon \mathbb {R} \to \mathbb {R} } defined by f − 1 ( y ) = y + 7 5 . {\displaystyle f^{-1}(y)={\frac {y+7}{5}}.} == Definitions == Let f be a function whose domain is the set X, and whose codomain is the set Y. Then f is invertible if there exists a function g from Y to X such that g ( f ( x ) ) = x {\displaystyle g(f(x))=x} for all x ∈ X {\displaystyle x\in X} and f ( g ( y ) ) = y {\displaystyle f(g(y))=y} for all y ∈ Y {\displaystyle y\in Y} . If f is invertible, then there is exactly one function g satisfying this property. The function g is called the inverse of f, and is usually denoted as f −1, a notation introduced by John Frederick William Herschel in 1813. The function f is invertible if and only if it is bijective. This is because the condition g ( f ( x ) ) = x {\displaystyle g(f(x))=x} for all x ∈ X {\displaystyle x\in X} implies that f is injective, and the condition f ( g ( y ) ) = y {\displaystyle f(g(y))=y} for all y ∈ Y {\displaystyle y\in Y} implies that f is surjective. The inverse function f −1 to f can be explicitly described as the function f − 1 ( y ) = ( the unique element x ∈ X such that f ( x ) = y ) {\displaystyle f^{-1}(y)=({\text{the unique element }}x\in X{\text{ such that }}f(x)=y)} . === Inverses and composition === Recall that if f is an invertible function with domain X and codomain Y, then f − 1 ( f ( x ) ) = x {\displaystyle f^{-1}\left(f(x)\right)=x} , for every x ∈ X {\displaystyle x\in X} and f ( f − 1 ( y ) ) = y {\displaystyle f\left(f^{-1}(y)\right)=y} for every y ∈ Y {\displaystyle y\in Y} . Using the composition of functions, this statement can be rewritten to the following equations between functions: f − 1 ∘ f = id X {\displaystyle f^{-1}\circ f=\operatorname {id} _{X}} and f ∘ f − 1 = id Y , {\displaystyle f\circ f^{-1}=\operatorname {id} _{Y},} where idX is the identity function on the set X; that is, the function that leaves its argument unchanged. In category theory, this statement is used as the definition of an inverse morphism. Considering function composition helps to understand the notation f −1. Repeatedly composing a function f: X→X with itself is called iteration. If f is applied n times, starting with the value x, then this is written as f n(x); so f 2(x) = f (f (x)), etc. Since f −1(f (x)) = x, composing f −1 and f n yields f n−1, "undoing" the effect of one application of f. === Notation === While the notation f −1(x) might be misunderstood, (f(x))−1 certainly denotes the multiplicative inverse of f(x) and has nothing to do with the inverse function of f. The notation f ⟨ − 1 ⟩ {\displaystyle f^{\langle -1\rangle }} might be used for the inverse function to avoid ambiguity with the multiplicative inverse. In keeping with the general notation, some English authors use expressions like sin−1(x) to denote the inverse of the sine function applied to x (actually a partial inverse; see below). Other authors feel that this may be confused with the notation for the multiplicative inverse of sin (x), which can be denoted as (sin (x))−1. To avoid any confusion, an inverse trigonometric function is often indicated by the prefix "arc" (for Latin arcus). For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin(x). Similarly, the inverse of a hyperbolic function is indicated by the prefix "ar" (for Latin ārea). For instance, the inverse of the hyperbolic sine function is typically written as arsinh(x). The expressions like sin−1(x) can still be useful to distinguish the multivalued inverse from the partial inverse: sin − 1 ⁡ ( x ) = { ( − 1 ) n arcsin ⁡ ( x ) + π n : n ∈ Z } {\displaystyle \sin ^{-1}(x)=\{(-1)^{n}\arcsin(x)+\pi n:n\in \mathbb {Z} \}} . Other inverse special functions are sometimes prefixed with the prefix "inv", if the ambiguity of the f −1 notation should be avoided. == Examples == === Squaring and square root functions === The function f: R → [0,∞) given by f(x) = x2 is not injective because ( − x ) 2 = x 2 {\displaystyle (-x)^{2}=x^{2}} for all x ∈ R {\displaystyle x\in \mathbb {R} } . Therefore, f is not invertible. If the domain of the function is restricted to the nonnegative reals, that is, we take the function f : [ 0 , ∞ ) → [ 0 , ∞ ) ; x ↦ x 2 {\displaystyle f\colon [0,\infty )\to [0,\infty );\ x\mapsto x^{2}} with the same rule as before, then the function is bijective and so, invertible. The inverse function here is called the (positive) square root function and is denoted by x ↦ x {\displaystyle x\mapsto {\sqrt {x}}} . === Standard inverse functions === The following table shows several standard functions and their inverses: === Formula for the inverse === Many functions given by algebraic formulas possess a formula for their inverse. This is because the inverse f − 1 {\displaystyle f^{-1}} of an invertible function f : R → R {\displaystyle f\colon \mathbb {R} \to \mathbb {R} } has an explicit description as f − 1 ( y ) = ( the unique element x ∈ R such that f ( x ) = y ) {\displaystyle f^{-1}(y)=({\text{the unique element }}x\in \mathbb {R} {\text{ such that }}f(x)=y)} . This allows one to easily determine inverses of many functions that are given by algebraic formulas. For example, if f is the function f ( x ) = ( 2 x + 8 ) 3 {\displaystyle f(x)=(2x+8)^{3}} then to determine f − 1 ( y ) {\displaystyle f^{-1}(y)} for a real number y, one must find the unique real number x such that (2x + 8)3 = y. This equation can be solved: y = ( 2 x + 8 ) 3 y 3 = 2 x + 8 y 3 − 8 = 2 x y 3 − 8 2 = x . {\displaystyle {\begin{aligned}y&=(2x+8)^{3}\\{\sqrt[{3}]{y}}&=2x+8\\{\sqrt[{3}]{y}}-8&=2x\\{\dfrac {{\sqrt[{3}]{y}}-8}{2}}&=x.\end{aligned}}} Thus the inverse function f −1 is given by the formula f − 1 ( y ) = y 3 − 8 2 . {\displaystyle f^{-1}(y)={\frac {{\sqrt[{3}]{y}}-8}{2}}.} Sometimes, the inverse of a function cannot be expressed by a closed-form formula. For example, if f is the function f ( x ) = x − sin ⁡ x , {\displaystyle f(x)=x-\sin x,} then f is a bijection, and therefore possesses an inverse function f −1. The formula for this inverse has an expression as an infinite sum: f − 1 ( y ) = ∑ n = 1 ∞ y n / 3 n ! lim θ → 0 ( d n − 1 d θ n − 1 ( θ θ − sin ⁡ ( θ ) 3 ) n ) . {\displaystyle f^{-1}(y)=\sum _{n=1}^{\infty }{\frac {y^{n/3}}{n!}}\lim _{\theta \to 0}\left({\frac {\mathrm {d} ^{\,n-1}}{\mathrm {d} \theta ^{\,n-1}}}\left({\frac {\theta }{\sqrt[{3}]{\theta -\sin(\theta )}}}\right)^{n}\right).} == Properties == Since a function is a special type of binary relation, many of the properties of an inverse function correspond to properties of converse relations. === Uniqueness === If an inverse function exists for a given function f, then it is unique. This follows since the inverse function must be the converse relation, which is completely determined by f. === Symmetry === There is a symmetry between a function and its inverse. Specifically, if f is an invertible function with domain X and codomain Y, then its inverse f −1 has domain Y and image X, and the inverse of f −1 is the original function f. In symbols, for functions f:X → Y and f−1:Y → X, f − 1 ∘ f = id X {\displaystyle f^{-1}\circ f=\operatorname {id} _{X}} and f ∘ f − 1 = id Y . {\displaystyle f\circ f^{-1}=\operatorname {id} _{Y}.} This statement is a consequence of the implication that for f to be invertible it must be bijective. The involutory nature of the inverse can be concisely expressed by ( f − 1 ) − 1 = f . {\displaystyle \left(f^{-1}\right)^{-1}=f.} The inverse of a composition of functions is given by ( g ∘ f ) − 1 = f − 1 ∘ g − 1 . {\displaystyle (g\circ f)^{-1}=f^{-1}\circ g^{-1}.} Notice that the order of g and f have been reversed; to undo f followed by g, we must first undo g, and then undo f. For example, let f(x) = 3x and let g(x) = x + 5. Then the composition g ∘ f is the function that first multiplies by three and then adds five, ( g ∘ f ) ( x ) = 3 x + 5. {\displaystyle (g\circ f)(x)=3x+5.} To reverse this process, we must first subtract five, and then divide by three, ( g ∘ f ) − 1 ( x ) = 1 3 ( x − 5 ) . {\displaystyle (g\circ f)^{-1}(x)={\tfrac {1}{3}}(x-5).} This is the composition (f −1 ∘ g −1)(x). === Self-inverses === If X is a set, then the identity function on X is its own inverse: id X − 1 = id X . {\displaystyle {\operatorname {id} _{X}}^{-1}=\operatorname {id} _{X}.} More generally, a function f : X → X is equal to its own inverse, if and only if the composition f ∘ f is equal to idX. Such a function is called an involution. === Graph of the inverse === If f is invertible, then the graph of the function y = f − 1 ( x ) {\displaystyle y=f^{-1}(x)} is the same as the graph of the equation x = f ( y ) . {\displaystyle x=f(y).} This is identical to the equation y = f(x) that defines the graph of f, except that the roles of x and y have been reversed. Thus the graph of f −1 can be obtained from the graph of f by switching the positions of the x and y axes. This is equivalent to reflecting the graph across the line y = x. === Inverses and derivatives === By the inverse function theorem, a continuous function of a single variable f : A → R {\displaystyle f\colon A\to \mathbb {R} } (where A ⊆ R {\displaystyle A\subseteq \mathbb {R} } ) is invertible on its range (image) if and only if it is either strictly increasing or decreasing (with no local maxima or minima). For example, the function f ( x ) = x 3 + x {\displaystyle f(x)=x^{3}+x} is invertible, since the derivative f′(x) = 3x2 + 1 is always positive. If the function f is differentiable on an interval I and f′(x) ≠ 0 for each x ∈ I, then the inverse f −1 is differentiable on f(I). If y = f(x), the derivative of the inverse is given by the inverse function theorem, ( f − 1 ) ′ ( y ) = 1 f ′ ( x ) . {\displaystyle \left(f^{-1}\right)^{\prime }(y)={\frac {1}{f'\left(x\right)}}.} Using Leibniz's notation the formula above can be written as d x d y = 1 d y / d x . {\displaystyle {\frac {dx}{dy}}={\frac {1}{dy/dx}}.} This result follows from the chain rule (see the article on inverse functions and differentiation). The inverse function theorem can be generalized to functions of several variables. Specifically, a continuously differentiable multivariable function f : Rn → Rn is invertible in a neighborhood of a point p as long as the Jacobian matrix of f at p is invertible. In this case, the Jacobian of f −1 at f(p) is the matrix inverse of the Jacobian of f at p. == Real-world examples == Let f be the function that converts a temperature in degrees Celsius to a temperature in degrees Fahrenheit, F = f ( C ) = 9 5 C + 32 ; {\displaystyle F=f(C)={\tfrac {9}{5}}C+32;} then its inverse function converts degrees Fahrenheit to degrees Celsius, C = f − 1 ( F ) = 5 9 ( F − 32 ) , {\displaystyle C=f^{-1}(F)={\tfrac {5}{9}}(F-32),} since f − 1 ( f ( C ) ) = f − 1 ( 9 5 C + 32 ) = 5 9 ( ( 9 5 C + 32 ) − 32 ) = C , for every value of C , and f ( f − 1 ( F ) ) = f ( 5 9 ( F − 32 ) ) = 9 5 ( 5 9 ( F − 32 ) ) + 32 = F , for every value of F . {\displaystyle {\begin{aligned}f^{-1}(f(C))={}&f^{-1}\left({\tfrac {9}{5}}C+32\right)={\tfrac {5}{9}}\left(({\tfrac {9}{5}}C+32)-32\right)=C,\\&{\text{for every value of }}C,{\text{ and }}\\[6pt]f\left(f^{-1}(F)\right)={}&f\left({\tfrac {5}{9}}(F-32)\right)={\tfrac {9}{5}}\left({\tfrac {5}{9}}(F-32)\right)+32=F,\\&{\text{for every value of }}F.\end{aligned}}} Suppose f assigns each child in a family its birth year. An inverse function would output which child was born in a given year. However, if the family has children born in the same year (for instance, twins or triplets, etc.) then the output cannot be known when the input is the common birth year. As well, if a year is given in which no child was born then a child cannot be named. But if each child was born in a separate year, and if we restrict attention to the three years in which a child was born, then we do have an inverse function. For example, f ( Allan ) = 2005 , f ( Brad ) = 2007 , f ( Cary ) = 2001 f − 1 ( 2005 ) = Allan , f − 1 ( 2007 ) = Brad , f − 1 ( 2001 ) = Cary {\displaystyle {\begin{aligned}f({\text{Allan}})&=2005,\quad &f({\text{Brad}})&=2007,\quad &f({\text{Cary}})&=2001\\f^{-1}(2005)&={\text{Allan}},\quad &f^{-1}(2007)&={\text{Brad}},\quad &f^{-1}(2001)&={\text{Cary}}\end{aligned}}} Let R be the function that leads to an x percentage rise of some quantity, and F be the function producing an x percentage fall. Applied to $100 with x = 10%, we find that applying the first function followed by the second does not restore the original value of $100, demonstrating the fact that, despite appearances, these two functions are not inverses of each other. The formula to calculate the pH of a solution is pH = −log10[H+]. In many cases we need to find the concentration of acid from a pH measurement. The inverse function [H+] = 10−pH is used. == Generalizations == === Partial inverses === Even if a function f is not one-to-one, it may be possible to define a partial inverse of f by restricting the domain. For example, the function f ( x ) = x 2 {\displaystyle f(x)=x^{2}} is not one-to-one, since x2 = (−x)2. However, the function becomes one-to-one if we restrict to the domain x ≥ 0, in which case f − 1 ( y ) = y . {\displaystyle f^{-1}(y)={\sqrt {y}}.} (If we instead restrict to the domain x ≤ 0, then the inverse is the negative of the square root of y.) === Full inverses === Alternatively, there is no need to restrict the domain if we are content with the inverse being a multivalued function: f − 1 ( y ) = ± y . {\displaystyle f^{-1}(y)=\pm {\sqrt {y}}.} Sometimes, this multivalued inverse is called the full inverse of f, and the portions (such as √x and −√x) are called branches. The most important branch of a multivalued function (e.g. the positive square root) is called the principal branch, and its value at y is called the principal value of f −1(y). For a continuous function on the real line, one branch is required between each pair of local extrema. For example, the inverse of a cubic function with a local maximum and a local minimum has three branches (see the adjacent picture). === Trigonometric inverses === The above considerations are particularly important for defining the inverses of trigonometric functions. For example, the sine function is not one-to-one, since sin ⁡ ( x + 2 π ) = sin ⁡ ( x ) {\displaystyle \sin(x+2\pi )=\sin(x)} for every real x (and more generally sin(x + 2πn) = sin(x) for every integer n). However, the sine is one-to-one on the interval [−⁠π/2⁠, ⁠π/2⁠], and the corresponding partial inverse is called the arcsine. This is considered the principal branch of the inverse sine, so the principal value of the inverse sine is always between −⁠π/2⁠ and ⁠π/2⁠. The following table describes the principal branch of each inverse trigonometric function: === Left and right inverses === Function composition on the left and on the right need not coincide. In general, the conditions "There exists g such that g(f(x))=x" and "There exists g such that f(g(x))=x" imply different properties of f. For example, let f: R → [0, ∞) denote the squaring map, such that f(x) = x2 for all x in R, and let g: [0, ∞) → R denote the square root map, such that g(x) = √x for all x ≥ 0. Then f(g(x)) = x for all x in [0, ∞); that is, g is a right inverse to f. However, g is not a left inverse to f, since, e.g., g(f(−1)) = 1 ≠ −1. ==== Left inverses ==== If f: X → Y, a left inverse for f (or retraction of f ) is a function g: Y → X such that composing f with g from the left gives the identity function g ∘ f = id X ⁡ . {\displaystyle g\circ f=\operatorname {id} _{X}{\text{.}}} That is, the function g satisfies the rule If f(x)=y, then g(y)=x. The function g must equal the inverse of f on the image of f, but may take any values for elements of Y not in the image. A function f with nonempty domain is injective if and only if it has a left inverse. An elementary proof runs as follows: If g is the left inverse of f, and f(x) = f(y), then g(f(x)) = g(f(y)) = x = y. If nonempty f: X → Y is injective, construct a left inverse g: Y → X as follows: for all y ∈ Y, if y is in the image of f, then there exists x ∈ X such that f(x) = y. Let g(y) = x; this definition is unique because f is injective. Otherwise, let g(y) be an arbitrary element of X.For all x ∈ X, f(x) is in the image of f. By construction, g(f(x)) = x, the condition for a left inverse. In classical mathematics, every injective function f with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics. For instance, a left inverse of the inclusion {0,1} → R of the two-element set in the reals violates indecomposability by giving a retraction of the real line to the set {0,1}. ==== Right inverses ==== A right inverse for f (or section of f ) is a function h: Y → X such that f ∘ h = id Y . {\displaystyle f\circ h=\operatorname {id} _{Y}.} That is, the function h satisfies the rule If h ( y ) = x {\displaystyle \displaystyle h(y)=x} , then f ( x ) = y . {\displaystyle \displaystyle f(x)=y.} Thus, h(y) may be any of the elements of X that map to y under f. A function f has a right inverse if and only if it is surjective (though constructing such an inverse in general requires the axiom of choice). If h is the right inverse of f, then f is surjective. For all y ∈ Y {\displaystyle y\in Y} , there is x = h ( y ) {\displaystyle x=h(y)} such that f ( x ) = f ( h ( y ) ) = y {\displaystyle f(x)=f(h(y))=y} . If f is surjective, f has a right inverse h, which can be constructed as follows: for all y ∈ Y {\displaystyle y\in Y} , there is at least one x ∈ X {\displaystyle x\in X} such that f ( x ) = y {\displaystyle f(x)=y} (because f is surjective), so we choose one to be the value of h(y). ==== Two-sided inverses ==== An inverse that is both a left and right inverse (a two-sided inverse), if it exists, must be unique. In fact, if a function has a left inverse and a right inverse, they are both the same two-sided inverse, so it can be called the inverse. If g {\displaystyle g} is a left inverse and h {\displaystyle h} a right inverse of f {\displaystyle f} , for all y ∈ Y {\displaystyle y\in Y} , g ( y ) = g ( f ( h ( y ) ) = h ( y ) {\displaystyle g(y)=g(f(h(y))=h(y)} . A function has a two-sided inverse if and only if it is bijective. A bijective function f is injective, so it has a left inverse (if f is the empty function, f : ∅ → ∅ {\displaystyle f\colon \varnothing \to \varnothing } is its own left inverse). f is surjective, so it has a right inverse. By the above, the left and right inverse are the same. If f has a two-sided inverse g, then g is a left inverse and right inverse of f, so f is injective and surjective. === Preimages === If f: X → Y is any function (not necessarily invertible), the preimage (or inverse image) of an element y ∈ Y is defined to be the set of all elements of X that map to y: f − 1 ( y ) = { x ∈ X : f ( x ) = y } . {\displaystyle f^{-1}(y)=\left\{x\in X:f(x)=y\right\}.} The preimage of y can be thought of as the image of y under the (multivalued) full inverse of the function f. The notion can be generalized to subsets of the range. Specifically, if S is any subset of Y, the preimage of S, denoted by f − 1 ( S ) {\displaystyle f^{-1}(S)} , is the set of all elements of X that map to S: f − 1 ( S ) = { x ∈ X : f ( x ) ∈ S } . {\displaystyle f^{-1}(S)=\left\{x\in X:f(x)\in S\right\}.} For example, take the function f: R → R; x ↦ x2. This function is not invertible as it is not bijective, but preimages may be defined for subsets of the codomain, e.g. f − 1 ( { 1 , 4 , 9 , 16 } ) = { − 4 , − 3 , − 2 , − 1 , 1 , 2 , 3 , 4 } {\displaystyle f^{-1}(\left\{1,4,9,16\right\})=\left\{-4,-3,-2,-1,1,2,3,4\right\}} . The original notion and its generalization are related by the identity f − 1 ( y ) = f − 1 ( { y } ) , {\displaystyle f^{-1}(y)=f^{-1}(\{y\}),} The preimage of a single element y ∈ Y – a singleton set {y}  – is sometimes called the fiber of y. When Y is the set of real numbers, it is common to refer to f −1({y}) as a level set. == See also == Lagrange inversion theorem, gives the Taylor series expansion of the inverse function of an analytic function Integral of inverse functions Inverse Fourier transform Reversible computing == Notes == == References == == Bibliography == Briggs, William; Cochran, Lyle (2011). Calculus / Early Transcendentals Single Variable. Addison-Wesley. ISBN 978-0-321-66414-3. Devlin, Keith J. (2004). Sets, Functions, and Logic / An Introduction to Abstract Mathematics (3 ed.). Chapman & Hall / CRC Mathematics. ISBN 978-1-58488-449-1. Fletcher, Peter; Patty, C. Wayne (1988). Foundations of Higher Mathematics. PWS-Kent. ISBN 0-87150-164-3. Lay, Steven R. (2006). Analysis / With an Introduction to Proof (4 ed.). Pearson / Prentice Hall. ISBN 978-0-13-148101-5. Smith, Douglas; Eggen, Maurice; St. Andre, Richard (2006). A Transition to Advanced Mathematics (6 ed.). Thompson Brooks/Cole. ISBN 978-0-534-39900-9. Thomas Jr., George Brinton (1972). Calculus and Analytic Geometry Part 1: Functions of One Variable and Analytic Geometry (Alternate ed.). Addison-Wesley. Wolf, Robert S. (1998). Proof, Logic, and Conjecture / The Mathematician's Toolbox. W. H. Freeman and Co. ISBN 978-0-7167-3050-7. == Further reading == Amazigo, John C.; Rubenfeld, Lester A. (1980). "Implicit Functions; Jacobians; Inverse Functions". Advanced Calculus and its Applications to the Engineering and Physical Sciences. New York: Wiley. pp. 103–120. ISBN 0-471-04934-4. Binmore, Ken G. (1983). "Inverse Functions". Calculus. New York: Cambridge University Press. pp. 161–197. ISBN 0-521-28952-1. Spivak, Michael (1994). Calculus (3 ed.). Publish or Perish. ISBN 0-914098-89-6. Stewart, James (2002). Calculus (5 ed.). Brooks Cole. ISBN 978-0-534-39339-7. == External links == "Inverse function", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Wikipedia/Inverse_functions
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. It assigns a tensor to each point of a Riemannian manifold (i.e., it is a tensor field). It is a local invariant of Riemannian metrics that measures the failure of the second covariant derivatives to commute. A Riemannian manifold has zero curvature if and only if it is flat, i.e. locally isometric to the Euclidean space. The curvature tensor can also be defined for any pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection. It is a central mathematical tool in the theory of general relativity, the modern theory of gravity. The curvature of spacetime is in principle observable via the geodesic deviation equation. The curvature tensor represents the tidal force experienced by a rigid body moving along a geodesic in a sense made precise by the Jacobi equation. == Definition == Let ( M , g ) {\displaystyle (M,g)} be a Riemannian or pseudo-Riemannian manifold, and X ( M ) {\displaystyle {\mathfrak {X}}(M)} be the space of all vector fields on M {\displaystyle M} . We define the Riemann curvature tensor as a map X ( M ) × X ( M ) × X ( M ) → X ( M ) {\displaystyle {\mathfrak {X}}(M)\times {\mathfrak {X}}(M)\times {\mathfrak {X}}(M)\rightarrow {\mathfrak {X}}(M)} by the following formula where ∇ {\displaystyle \nabla } is the Levi-Civita connection: R ( X , Y ) Z = ∇ X ∇ Y Z − ∇ Y ∇ X Z − ∇ [ X , Y ] Z {\displaystyle R(X,Y)Z=\nabla _{X}\nabla _{Y}Z-\nabla _{Y}\nabla _{X}Z-\nabla _{[X,Y]}Z} or equivalently R ( X , Y ) = [ ∇ X , ∇ Y ] − ∇ [ X , Y ] {\displaystyle R(X,Y)=[\nabla _{X},\nabla _{Y}]-\nabla _{[X,Y]}} where [ X , Y ] {\displaystyle [X,Y]} is the Lie bracket of vector fields and [ ∇ X , ∇ Y ] {\displaystyle [\nabla _{X},\nabla _{Y}]} is a commutator of differential operators. It turns out that the right-hand side actually only depends on the value of the vector fields X , Y , Z {\displaystyle X,Y,Z} at a given point, which is notable since the covariant derivative of a vector field also depends on the field values in a neighborhood of the point. Hence, R {\displaystyle R} is a ( 1 , 3 ) {\displaystyle (1,3)} -tensor field. For fixed X , Y {\displaystyle X,Y} , the linear transformation Z ↦ R ( X , Y ) Z {\displaystyle Z\mapsto R(X,Y)Z} is also called the curvature transformation or endomorphism. Occasionally, the curvature tensor is defined with the opposite sign. The curvature tensor measures noncommutativity of the covariant derivative, and as such is the integrability obstruction for the existence of an isometry with Euclidean space (called, in this context, flat space). Since the Levi-Civita connection is torsion-free, its curvature can also be expressed in terms of the second covariant derivative ∇ X , Y 2 Z = ∇ X ∇ Y Z − ∇ ∇ X Y Z {\textstyle \nabla _{X,Y}^{2}Z=\nabla _{X}\nabla _{Y}Z-\nabla _{\nabla _{X}Y}Z} which depends only on the values of X , Y {\displaystyle X,Y} at a point. The curvature can then be written as R ( X , Y ) = ∇ X , Y 2 − ∇ Y , X 2 {\displaystyle R(X,Y)=\nabla _{X,Y}^{2}-\nabla _{Y,X}^{2}} Thus, the curvature tensor measures the noncommutativity of the second covariant derivative. In abstract index notation, R d c a b Z c = ∇ a ∇ b Z d − ∇ b ∇ a Z d . {\displaystyle R^{d}{}_{cab}Z^{c}=\nabla _{a}\nabla _{b}Z^{d}-\nabla _{b}\nabla _{a}Z^{d}.} The Riemann curvature tensor is also the commutator of the covariant derivative of an arbitrary covector A ν {\displaystyle A_{\nu }} with itself: A ν ; ρ σ − A ν ; σ ρ = A β R β ν ρ σ . {\displaystyle A_{\nu ;\rho \sigma }-A_{\nu ;\sigma \rho }=A_{\beta }R^{\beta }{}_{\nu \rho \sigma }.} This formula is often called the Ricci identity. This is the classical method used by Ricci and Levi-Civita to obtain an expression for the Riemann curvature tensor. This identity can be generalized to get the commutators for two covariant derivatives of arbitrary tensors as follows ∇ δ ∇ γ T α 1 ⋯ α r β 1 ⋯ β s − ∇ γ ∇ δ T α 1 ⋯ α r β 1 ⋯ β s = R α 1 ρ δ γ T ρ α 2 ⋯ α r β 1 ⋯ β s + … + R α r ρ δ γ T α 1 ⋯ α r − 1 ρ β 1 ⋯ β s − R σ β 1 δ γ T α 1 ⋯ α r σ β 2 ⋯ β s − … − R σ β s δ γ T α 1 ⋯ α r β 1 ⋯ β s − 1 σ {\displaystyle {\begin{aligned}&\nabla _{\delta }\nabla _{\gamma }T^{\alpha _{1}\cdots \alpha _{r}}{}_{\beta _{1}\cdots \beta _{s}}-\nabla _{\gamma }\nabla _{\delta }T^{\alpha _{1}\cdots \alpha _{r}}{}_{\beta _{1}\cdots \beta _{s}}\\[3pt]={}&R^{\alpha _{1}}{}_{\rho \delta \gamma }T^{\rho \alpha _{2}\cdots \alpha _{r}}{}_{\beta _{1}\cdots \beta _{s}}+\ldots +R^{\alpha _{r}}{}_{\rho \delta \gamma }T^{\alpha _{1}\cdots \alpha _{r-1}\rho }{}_{\beta _{1}\cdots \beta _{s}}-R^{\sigma }{}_{\beta _{1}\delta \gamma }T^{\alpha _{1}\cdots \alpha _{r}}{}_{\sigma \beta _{2}\cdots \beta _{s}}-\ldots -R^{\sigma }{}_{\beta _{s}\delta \gamma }T^{\alpha _{1}\cdots \alpha _{r}}{}_{\beta _{1}\cdots \beta _{s-1}\sigma }\end{aligned}}} This formula also applies to tensor densities without alteration, because for the Levi-Civita (not generic) connection one gets: ∇ μ ( g ) ≡ ( g ) ; μ = 0 , {\displaystyle \nabla _{\mu }\left({\sqrt {g}}\right)\equiv \left({\sqrt {g}}\right)_{;\mu }=0,} where g = | det ( g μ ν ) | . {\displaystyle g=\left|\det \left(g_{\mu \nu }\right)\right|.} It is sometimes convenient to also define the purely covariant version of the curvature tensor by R σ μ ν ρ = g ρ ζ R ζ σ μ ν . {\displaystyle R_{\sigma \mu \nu \rho }=g_{\rho \zeta }R^{\zeta }{}_{\sigma \mu \nu }.} == Geometric meaning == === Informally === One can see the effects of curved space by comparing a tennis court and the Earth. Start at the lower right corner of the tennis court, with a racket held out towards north. Then while walking around the outline of the court, at each step make sure the tennis racket is maintained in the same orientation, parallel to its previous positions. Once the loop is complete the tennis racket will be parallel to its initial starting position. This is because tennis courts are built so the surface is flat. On the other hand, the surface of the Earth is curved: we can complete a loop on the surface of the Earth. Starting at the equator, point a tennis racket north along the surface of the Earth. Once again the tennis racket should always remain parallel to its previous position, using the local plane of the horizon as a reference. For this path, first walk to the north pole, then walk sideways (i.e. without turning), then down to the equator, and finally walk backwards to your starting position. Now the tennis racket will be pointing towards the west, even though when you began your journey it pointed north and you never turned your body. This process is akin to parallel transporting a vector along the path and the difference identifies how lines which appear "straight" are only "straight" locally. Each time a loop is completed the tennis racket will be deflected further from its initial position by an amount depending on the distance and the curvature of the surface. It is possible to identify paths along a curved surface where parallel transport works as it does on flat space. These are the geodesics of the space, for example any segment of a great circle of a sphere. The concept of a curved space in mathematics differs from conversational usage. For example, if the above process was completed on a cylinder one would find that it is not curved overall as the curvature around the cylinder cancels with the flatness along the cylinder, which is a consequence of Gaussian curvature and Gauss's Theorema Egregium. A familiar example of this is a floppy pizza slice, which will remain rigid along its length if it is curved along its width. The Riemann curvature tensor is a way to capture a measure of the intrinsic curvature. When you write it down in terms of its components (like writing down the components of a vector), it consists of a multi-dimensional array of sums and products of partial derivatives (some of those partial derivatives can be thought of as akin to capturing the curvature imposed upon someone walking in straight lines on a curved surface). === Formally === When a vector in a Euclidean space is parallel transported around a loop, it will again point in the initial direction after returning to its original position. However, this property does not hold in the general case. The Riemann curvature tensor directly measures the failure of this in a general Riemannian manifold. This failure is known as the non-holonomy of the manifold. Let x t {\displaystyle x_{t}} be a curve in a Riemannian manifold M {\displaystyle M} . Denote by τ x t : T x 0 M → T x t M {\displaystyle \tau _{x_{t}}:T_{x_{0}}M\to T_{x_{t}}M} the parallel transport map along x t {\displaystyle x_{t}} . The parallel transport maps are related to the covariant derivative by ∇ x ˙ 0 Y = lim h → 0 1 h ( τ x h − 1 ( Y x h ) − Y x 0 ) = d d t ( τ x t − 1 ( Y x t ) ) | t = 0 {\displaystyle \nabla _{{\dot {x}}_{0}}Y=\lim _{h\to 0}{\frac {1}{h}}\left(\tau _{x_{h}}^{-1}\left(Y_{x_{h}}\right)-Y_{x_{0}}\right)=\left.{\frac {d}{dt}}\left(\tau _{x_{t}}^{-1}(Y_{x_{t}})\right)\right|_{t=0}} for each vector field Y {\displaystyle Y} defined along the curve. Suppose that X {\displaystyle X} and Y {\displaystyle Y} are a pair of commuting vector fields. Each of these fields generates a one-parameter group of diffeomorphisms in a neighborhood of x 0 {\displaystyle x_{0}} . Denote by τ t X {\displaystyle \tau _{tX}} and τ t Y {\displaystyle \tau _{tY}} , respectively, the parallel transports along the flows of X {\displaystyle X} and Y {\displaystyle Y} for time t {\displaystyle t} . Parallel transport of a vector Z ∈ T x 0 M {\displaystyle Z\in T_{x_{0}}M} around the quadrilateral with sides t Y {\displaystyle tY} , s X {\displaystyle sX} , − t Y {\displaystyle -tY} , − s X {\displaystyle -sX} is given by τ s X − 1 τ t Y − 1 τ s X τ t Y Z . {\displaystyle \tau _{sX}^{-1}\tau _{tY}^{-1}\tau _{sX}\tau _{tY}Z.} The difference between this and Z {\displaystyle Z} measures the failure of parallel transport to return Z {\displaystyle Z} to its original position in the tangent space T x 0 M {\displaystyle T_{x_{0}}M} . Shrinking the loop by sending s , t → 0 {\displaystyle s,t\to 0} gives the infinitesimal description of this deviation: d d s d d t τ s X − 1 τ t Y − 1 τ s X τ t Y Z | s = t = 0 = ( ∇ X ∇ Y − ∇ Y ∇ X − ∇ [ X , Y ] ) Z = R ( X , Y ) Z {\displaystyle \left.{\frac {d}{ds}}{\frac {d}{dt}}\tau _{sX}^{-1}\tau _{tY}^{-1}\tau _{sX}\tau _{tY}Z\right|_{s=t=0}=\left(\nabla _{X}\nabla _{Y}-\nabla _{Y}\nabla _{X}-\nabla _{[X,Y]}\right)Z=R(X,Y)Z} where R {\displaystyle R} is the Riemann curvature tensor. == Coordinate expression == Converting to the tensor index notation, the Riemann curvature tensor is given by R ρ σ μ ν = d x ρ ( R ( ∂ μ , ∂ ν ) ∂ σ ) {\displaystyle R^{\rho }{}_{\sigma \mu \nu }=dx^{\rho }\left(R\left(\partial _{\mu },\partial _{\nu }\right)\partial _{\sigma }\right)} where ∂ μ = ∂ / ∂ x μ {\displaystyle \partial _{\mu }=\partial /\partial x^{\mu }} are the coordinate vector fields. The above expression can be written using Christoffel symbols: R ρ σ μ ν = ∂ μ Γ ρ ν σ − ∂ ν Γ ρ μ σ + Γ ρ μ λ Γ λ ν σ − Γ ρ ν λ Γ λ μ σ {\displaystyle R^{\rho }{}_{\sigma \mu \nu }=\partial _{\mu }\Gamma ^{\rho }{}_{\nu \sigma }-\partial _{\nu }\Gamma ^{\rho }{}_{\mu \sigma }+\Gamma ^{\rho }{}_{\mu \lambda }\Gamma ^{\lambda }{}_{\nu \sigma }-\Gamma ^{\rho }{}_{\nu \lambda }\Gamma ^{\lambda }{}_{\mu \sigma }} (See also List of formulas in Riemannian geometry). == Symmetries and identities == The Riemann curvature tensor has the following symmetries and identities: where the bracket ⟨ , ⟩ {\displaystyle \langle ,\rangle } refers to the inner product on the tangent space induced by the metric tensor and the brackets and parentheses on the indices denote the antisymmetrization and symmetrization operators, respectively. If there is nonzero torsion, the Bianchi identities involve the torsion tensor. The first (algebraic) Bianchi identity was discovered by Ricci, but is often called the first Bianchi identity or algebraic Bianchi identity, because it looks similar to the differential Bianchi identity. The first three identities form a complete list of symmetries of the curvature tensor, i.e. given any tensor which satisfies the identities above, one can find a Riemannian manifold with such a curvature tensor at some point. Simple calculations show that such a tensor has n 2 ( n 2 − 1 ) / 12 {\displaystyle n^{2}\left(n^{2}-1\right)/12} independent components. Interchange symmetry follows from these. The algebraic symmetries are also equivalent to saying that R belongs to the image of the Young symmetrizer corresponding to the partition 2+2. On a Riemannian manifold one has the covariant derivative ∇ u R {\displaystyle \nabla _{u}R} and the Bianchi identity (often called the second Bianchi identity or differential Bianchi identity) takes the form of the last identity in the table. == Ricci curvature == The Ricci curvature tensor is the contraction of the first and third indices of the Riemann tensor. R a b ⏟ Ricci ≡ R c a c b = g c d R c a d b ⏟ Riemann {\displaystyle \underbrace {R_{ab}} _{\text{Ricci}}\equiv R^{c}{}_{acb}=g^{cd}\underbrace {R_{cadb}} _{\text{Riemann}}} == Special cases == === Surfaces === For a two-dimensional surface, the Bianchi identities imply that the Riemann tensor has only one independent component, which means that the Ricci scalar completely determines the Riemann tensor. There is only one valid expression for the Riemann tensor which fits the required symmetries: R a b c d = f ( R ) ( g a c g d b − g a d g c b ) {\displaystyle R_{abcd}=f(R)\left(g_{ac}g_{db}-g_{ad}g_{cb}\right)} and by contracting with the metric twice we find the explicit form: R a b c d = K ( g a c g d b − g a d g c b ) , {\displaystyle R_{abcd}=K\left(g_{ac}g_{db}-g_{ad}g_{cb}\right),} where g a b {\displaystyle g_{ab}} is the metric tensor and K = R / 2 {\displaystyle K=R/2} is a function called the Gaussian curvature and a {\displaystyle a} , b {\displaystyle b} , c {\displaystyle c} and d {\displaystyle d} take values either 1 or 2. The Riemann tensor has only one functionally independent component. The Gaussian curvature coincides with the sectional curvature of the surface. It is also exactly half the scalar curvature of the 2-manifold, while the Ricci curvature tensor of the surface is simply given by R a b = K g a b . {\displaystyle R_{ab}=Kg_{ab}.} === Space forms === A Riemannian manifold is a space form if its sectional curvature is equal to a constant K {\displaystyle K} . The Riemann tensor of a space form is given by R a b c d = K ( g a c g d b − g a d g c b ) . {\displaystyle R_{abcd}=K\left(g_{ac}g_{db}-g_{ad}g_{cb}\right).} Conversely, except in dimension 2, if the curvature of a Riemannian manifold has this form for some function K {\displaystyle K} , then the Bianchi identities imply that K {\displaystyle K} is constant and thus that the manifold is (locally) a space form. == See also == Introduction to the mathematics of general relativity Decomposition of the Riemann curvature tensor Curvature of Riemannian manifolds Ricci curvature tensor == Citations == == References ==
Wikipedia/Riemann_tensor
In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually denoted by I I {\displaystyle \mathrm {I\!I} } (read "two"). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth immersed submanifold in a Riemannian manifold. == Surface in R3 == === Motivation === The second fundamental form of a parametric surface S in R3 was introduced and studied by Gauss. First suppose that the surface is the graph of a twice continuously differentiable function, z = f(x,y), and that the plane z = 0 is tangent to the surface at the origin. Then f and its partial derivatives with respect to x and y vanish at (0,0). Therefore, the Taylor expansion of f at (0,0) starts with quadratic terms: z = L x 2 2 + M x y + N y 2 2 + higher order terms , {\displaystyle z=L{\frac {x^{2}}{2}}+Mxy+N{\frac {y^{2}}{2}}+{\text{higher order terms}}\,,} and the second fundamental form at the origin in the coordinates (x,y) is the quadratic form L d x 2 + 2 M d x d y + N d y 2 . {\displaystyle L\,dx^{2}+2M\,dx\,dy+N\,dy^{2}\,.} For a smooth point P on S, one can choose the coordinate system so that the plane z = 0 is tangent to S at P, and define the second fundamental form in the same way. === Classical notation === The second fundamental form of a general parametric surface is defined as follows. Let r = r(u,v) be a regular parametrization of a surface in R3, where r is a smooth vector-valued function of two variables. It is common to denote the partial derivatives of r with respect to u and v by ru and rv. Regularity of the parametrization means that ru and rv are linearly independent for any (u,v) in the domain of r, and hence span the tangent plane to S at each point. Equivalently, the cross product ru × rv is a nonzero vector normal to the surface. The parametrization thus defines a field of unit normal vectors n: n = r u × r v | r u × r v | . {\displaystyle \mathbf {n} ={\frac {\mathbf {r} _{u}\times \mathbf {r} _{v}}{|\mathbf {r} _{u}\times \mathbf {r} _{v}|}}\,.} The second fundamental form is usually written as I I = L d u 2 + 2 M d u d v + N d v 2 , {\displaystyle \mathrm {I\!I} =L\,du^{2}+2M\,du\,dv+N\,dv^{2}\,,} its matrix in the basis {ru, rv} of the tangent plane is [ L M M N ] . {\displaystyle {\begin{bmatrix}L&M\\M&N\end{bmatrix}}\,.} The coefficients L, M, N at a given point in the parametric uv-plane are given by the projections of the second partial derivatives of r at that point onto the normal line to S and can be computed with the aid of the dot product as follows: L = r u u ⋅ n , M = r u v ⋅ n , N = r v v ⋅ n . {\displaystyle L=\mathbf {r} _{uu}\cdot \mathbf {n} \,,\quad M=\mathbf {r} _{uv}\cdot \mathbf {n} \,,\quad N=\mathbf {r} _{vv}\cdot \mathbf {n} \,.} For a signed distance field of Hessian H, the second fundamental form coefficients can be computed as follows: L = − r u ⋅ H ⋅ r u , M = − r u ⋅ H ⋅ r v , N = − r v ⋅ H ⋅ r v . {\displaystyle L=-\mathbf {r} _{u}\cdot \mathbf {H} \cdot \mathbf {r} _{u}\,,\quad M=-\mathbf {r} _{u}\cdot \mathbf {H} \cdot \mathbf {r} _{v}\,,\quad N=-\mathbf {r} _{v}\cdot \mathbf {H} \cdot \mathbf {r} _{v}\,.} === Physicist's notation === The second fundamental form of a general parametric surface S is defined as follows. Let r = r(u1,u2) be a regular parametrization of a surface in R3, where r is a smooth vector-valued function of two variables. It is common to denote the partial derivatives of r with respect to uα by rα, α = 1, 2. Regularity of the parametrization means that r1 and r2 are linearly independent for any (u1,u2) in the domain of r, and hence span the tangent plane to S at each point. Equivalently, the cross product r1 × r2 is a nonzero vector normal to the surface. The parametrization thus defines a field of unit normal vectors n: n = r 1 × r 2 | r 1 × r 2 | . {\displaystyle \mathbf {n} ={\frac {\mathbf {r} _{1}\times \mathbf {r} _{2}}{|\mathbf {r} _{1}\times \mathbf {r} _{2}|}}\,.} The second fundamental form is usually written as I I = b α β d u α d u β . {\displaystyle \mathrm {I\!I} =b_{\alpha \beta }\,du^{\alpha }\,du^{\beta }\,.} The equation above uses the Einstein summation convention. The coefficients bαβ at a given point in the parametric u1u2-plane are given by the projections of the second partial derivatives of r at that point onto the normal line to S and can be computed in terms of the normal vector n as follows: b α β = r , α β γ n γ . {\displaystyle b_{\alpha \beta }=r_{,\alpha \beta }^{\ \ \,\gamma }n_{\gamma }\,.} == Hypersurface in a Riemannian manifold == In Euclidean space, the second fundamental form is given by I I ( v , w ) = − ⟨ d ν ( v ) , w ⟩ ν {\displaystyle \mathrm {I\!I} (v,w)=-\langle d\nu (v),w\rangle \nu } where ν {\displaystyle \nu } is the Gauss map, and d ν {\displaystyle d\nu } the differential of ν {\displaystyle \nu } regarded as a vector-valued differential form, and the brackets denote the metric tensor of Euclidean space. More generally, on a Riemannian manifold, the second fundamental form is an equivalent way to describe the shape operator (denoted by S) of a hypersurface, I I ( v , w ) = ⟨ S ( v ) , w ⟩ = − ⟨ ∇ v n , w ⟩ = ⟨ n , ∇ v w ⟩ , {\displaystyle \mathrm {I} \!\mathrm {I} (v,w)=\langle S(v),w\rangle =-\langle \nabla _{v}n,w\rangle =\langle n,\nabla _{v}w\rangle \,,} where ∇vw denotes the covariant derivative of the ambient manifold and n a field of normal vectors on the hypersurface. (If the affine connection is torsion-free, then the second fundamental form is symmetric.) The sign of the second fundamental form depends on the choice of direction of n (which is called a co-orientation of the hypersurface - for surfaces in Euclidean space, this is equivalently given by a choice of orientation of the surface). === Generalization to arbitrary codimension === The second fundamental form can be generalized to arbitrary codimension. In that case it is a quadratic form on the tangent space with values in the normal bundle and it can be defined by I I ( v , w ) = ( ∇ v w ) ⊥ , {\displaystyle \mathrm {I\!I} (v,w)=(\nabla _{v}w)^{\bot }\,,} where ( ∇ v w ) ⊥ {\displaystyle (\nabla _{v}w)^{\bot }} denotes the orthogonal projection of covariant derivative ∇ v w {\displaystyle \nabla _{v}w} onto the normal bundle. In Euclidean space, the curvature tensor of a submanifold can be described by the following formula: ⟨ R ( u , v ) w , z ⟩ = I I ( u , z ) I I ( v , w ) − I I ( u , w ) I I ( v , z ) . {\displaystyle \langle R(u,v)w,z\rangle =\mathrm {I} \!\mathrm {I} (u,z)\mathrm {I} \!\mathrm {I} (v,w)-\mathrm {I} \!\mathrm {I} (u,w)\mathrm {I} \!\mathrm {I} (v,z).} This is called the Gauss equation, as it may be viewed as a generalization of Gauss's Theorema Egregium. For general Riemannian manifolds one has to add the curvature of ambient space; if N is a manifold embedded in a Riemannian manifold (M,g) then the curvature tensor RN of N with induced metric can be expressed using the second fundamental form and RM, the curvature tensor of M: ⟨ R N ( u , v ) w , z ⟩ = ⟨ R M ( u , v ) w , z ⟩ + ⟨ I I ( u , z ) , I I ( v , w ) ⟩ − ⟨ I I ( u , w ) , I I ( v , z ) ⟩ . {\displaystyle \langle R_{N}(u,v)w,z\rangle =\langle R_{M}(u,v)w,z\rangle +\langle \mathrm {I} \!\mathrm {I} (u,z),\mathrm {I} \!\mathrm {I} (v,w)\rangle -\langle \mathrm {I} \!\mathrm {I} (u,w),\mathrm {I} \!\mathrm {I} (v,z)\rangle \,.} == See also == First fundamental form Gaussian curvature Gauss–Codazzi equations Shape operator Third fundamental form Tautological one-form == References == Guggenheimer, Heinrich (1977). "Chapter 10. Surfaces". Differential Geometry. Dover. ISBN 0-486-63433-7. Kobayashi, Shoshichi & Nomizu, Katsumi (1996). Foundations of Differential Geometry, Vol. 2 (New ed.). Wiley-Interscience. ISBN 0-471-15732-5. Spivak, Michael (1999). A Comprehensive introduction to differential geometry (Volume 3). Publish or Perish. ISBN 0-914098-72-1. == External links == Steven Verpoort (2008) Geometry of the Second Fundamental Form: Curvature Properties and Variational Aspects from Katholieke Universiteit Leuven.
Wikipedia/Shape_tensor
Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom. One motivation for the development of the Lagrangian formalism on fields, and more generally, for classical field theory, is to provide a clear mathematical foundation for quantum field theory, which is infamously beset by formal difficulties that make it unacceptable as a mathematical theory. The Lagrangians presented here are identical to their quantum equivalents, but, in treating the fields as classical fields, instead of being quantized, one can provide definitions and obtain solutions with properties compatible with the conventional formal approach to the mathematics of partial differential equations. This enables the formulation of solutions on spaces with well-characterized properties, such as Sobolev spaces. It enables various theorems to be provided, ranging from proofs of existence to the uniform convergence of formal series to the general settings of potential theory. In addition, insight and clarity is obtained by generalizations to Riemannian manifolds and fiber bundles, allowing the geometric structure to be clearly discerned and disentangled from the corresponding equations of motion. A clearer view of the geometric structure has in turn allowed highly abstract theorems from geometry to be used to gain insight, ranging from the Chern–Gauss–Bonnet theorem and the Riemann–Roch theorem to the Atiyah–Singer index theorem and Chern–Simons theory. == Overview == In field theory, the independent variable is replaced by an event in spacetime (x, y, z, t), or more generally still by a point s on a Riemannian manifold. The dependent variables are replaced by the value of a field at that point in spacetime φ ( x , y , z , t ) {\displaystyle \varphi (x,y,z,t)} so that the equations of motion are obtained by means of an action principle, written as: δ S δ φ i = 0 , {\displaystyle {\frac {\delta {\mathcal {S}}}{\delta \varphi _{i}}}=0,} where the action, S {\displaystyle {\mathcal {S}}} , is a functional of the dependent variables φ i ( s ) {\displaystyle \varphi _{i}(s)} , their derivatives and s itself S [ φ i ] = ∫ L ( φ i ( s ) , { ∂ φ i ( s ) ∂ s α } , { s α } ) d n s , {\displaystyle {\mathcal {S}}\left[\varphi _{i}\right]=\int {{\mathcal {L}}\left(\varphi _{i}(s),\left\{{\frac {\partial \varphi _{i}(s)}{\partial s^{\alpha }}}\right\},\{s^{\alpha }\}\right)\,\mathrm {d} ^{n}s},} where the brackets denote { ⋅ ∀ α } {\displaystyle \{\cdot ~\forall \alpha \}} ; and s = {sα} denotes the set of n independent variables of the system, including the time variable, and is indexed by α = 1, 2, 3, ..., n. The calligraphic typeface, L {\displaystyle {\mathcal {L}}} , is used to denote the density, and d n s {\displaystyle \mathrm {d} ^{n}s} is the volume form of the field function, i.e., the measure of the domain of the field function. In mathematical formulations, it is common to express the Lagrangian as a function on a fiber bundle, wherein the Euler–Lagrange equations can be interpreted as specifying the geodesics on the fiber bundle. Abraham and Marsden's textbook provided the first comprehensive description of classical mechanics in terms of modern geometrical ideas, i.e., in terms of tangent manifolds, symplectic manifolds and contact geometry. Bleecker's textbook provided a comprehensive presentation of field theories in physics in terms of gauge invariant fiber bundles. Such formulations were known or suspected long before. Jost continues with a geometric presentation, clarifying the relation between Hamiltonian and Lagrangian forms, describing spin manifolds from first principles, etc. Current research focuses on non-rigid affine structures, (sometimes called "quantum structures") wherein one replaces occurrences of vector spaces by tensor algebras. This research is motivated by the breakthrough understanding of quantum groups as affine Lie algebras (Lie groups are, in a sense "rigid", as they are determined by their Lie algebra. When reformulated on a tensor algebra, they become "floppy", having infinite degrees of freedom; see e.g., Virasoro algebra.) == Definitions == In Lagrangian field theory, the Lagrangian as a function of generalized coordinates is replaced by a Lagrangian density, a function of the fields in the system and their derivatives, and possibly the space and time coordinates themselves. In field theory, the independent variable t is replaced by an event in spacetime (x, y, z, t) or still more generally by a point s on a manifold. Often, a "Lagrangian density" is simply referred to as a "Lagrangian". === Scalar fields === For one scalar field φ {\displaystyle \varphi } , the Lagrangian density will take the form: L ( φ , ∇ φ , ∂ φ / ∂ t , x , t ) {\displaystyle {\mathcal {L}}(\varphi ,{\boldsymbol {\nabla }}\varphi ,\partial \varphi /\partial t,\mathbf {x} ,t)} For many scalar fields L ( φ 1 , ∇ φ 1 , ∂ φ 1 / ∂ t , … , φ n , ∇ φ n , ∂ φ n / ∂ t , … , x , t ) {\displaystyle {\mathcal {L}}(\varphi _{1},{\boldsymbol {\nabla }}\varphi _{1},\partial \varphi _{1}/\partial t,\ldots ,\varphi _{n},{\boldsymbol {\nabla }}\varphi _{n},\partial \varphi _{n}/\partial t,\ldots ,\mathbf {x} ,t)} In mathematical formulations, the scalar fields are understood to be coordinates on a fiber bundle, and the derivatives of the field are understood to be sections of the jet bundle. === Vector fields, tensor fields, spinor fields === The above can be generalized for vector fields, tensor fields, and spinor fields. In physics, fermions are described by spinor fields. Bosons are described by tensor fields, which include scalar and vector fields as special cases. For example, if there are m {\displaystyle m} real-valued scalar fields, φ 1 , … , φ m {\displaystyle \varphi _{1},\dots ,\varphi _{m}} , then the field manifold is R m {\displaystyle \mathbb {R} ^{m}} . If the field is a real vector field, then the field manifold is isomorphic to R n {\displaystyle \mathbb {R} ^{n}} . === Action === The time integral of the Lagrangian is called the action denoted by S. In field theory, a distinction is occasionally made between the Lagrangian L, of which the time integral is the action S = ∫ L d t , {\displaystyle {\mathcal {S}}=\int L\,\mathrm {d} t\,,} and the Lagrangian density L {\displaystyle {\mathcal {L}}} , which one integrates over all spacetime to get the action: S [ φ ] = ∫ L ( φ , ∇ φ , ∂ φ / ∂ t , x , t ) d 3 x d t . {\displaystyle {\mathcal {S}}[\varphi ]=\int {\mathcal {L}}(\varphi ,{\boldsymbol {\nabla }}\varphi ,\partial \varphi /\partial t,\mathbf {x} ,t)\,\mathrm {d} ^{3}\mathbf {x} \,\mathrm {d} t.} The spatial volume integral of the Lagrangian density is the Lagrangian; in 3D, L = ∫ L d 3 x . {\displaystyle L=\int {\mathcal {L}}\,\mathrm {d} ^{3}\mathbf {x} \,.} The action is often referred to as the "action functional", in that it is a function of the fields (and their derivatives). === Volume form === In the presence of gravity or when using general curvilinear coordinates, the Lagrangian density L {\displaystyle {\mathcal {L}}} will include a factor of g {\textstyle {\sqrt {g}}} . This ensures that the action is invariant under general coordinate transformations. In mathematical literature, spacetime is taken to be a Riemannian manifold M {\displaystyle M} and the integral then becomes the volume form S = ∫ M | g | d x 1 ∧ ⋯ ∧ d x m L {\displaystyle {\mathcal {S}}=\int _{M}{\sqrt {|g|}}dx^{1}\wedge \cdots \wedge dx^{m}{\mathcal {L}}} Here, the ∧ {\displaystyle \wedge } is the wedge product and | g | {\textstyle {\sqrt {|g|}}} is the square root of the determinant | g | {\displaystyle |g|} of the metric tensor g {\displaystyle g} on M {\displaystyle M} . For flat spacetime (e.g., Minkowski spacetime), the unit volume is one, i.e. | g | = 1 {\textstyle {\sqrt {|g|}}=1} and so it is commonly omitted, when discussing field theory in flat spacetime. Likewise, the use of the wedge-product symbols offers no additional insight over the ordinary concept of a volume in multivariate calculus, and so these are likewise dropped. Some older textbooks, e.g., Landau and Lifschitz write − g {\textstyle {\sqrt {-g}}} for the volume form, since the minus sign is appropriate for metric tensors with signature (+−−−) or (−+++) (since the determinant is negative, in either case). When discussing field theory on general Riemannian manifolds, the volume form is usually written in the abbreviated notation ∗ ( 1 ) {\displaystyle *(1)} where ∗ {\displaystyle *} is the Hodge star. That is, ∗ ( 1 ) = | g | d x 1 ∧ ⋯ ∧ d x m {\displaystyle *(1)={\sqrt {|g|}}dx^{1}\wedge \cdots \wedge dx^{m}} and so S = ∫ M ∗ ( 1 ) L {\displaystyle {\mathcal {S}}=\int _{M}*(1){\mathcal {L}}} Not infrequently, the notation above is considered to be entirely superfluous, and S = ∫ M L {\displaystyle {\mathcal {S}}=\int _{M}{\mathcal {L}}} is frequently seen. Do not be misled: the volume form is implicitly present in the integral above, even if it is not explicitly written. === Euler–Lagrange equations === The Euler–Lagrange equations describe the geodesic flow of the field φ {\displaystyle \varphi } as a function of time. Taking the variation with respect to φ {\displaystyle \varphi } , one obtains 0 = δ S δ φ = ∫ M ∗ ( 1 ) ( − ∂ μ ( ∂ L ∂ ( ∂ μ φ ) ) + ∂ L ∂ φ ) . {\displaystyle 0={\frac {\delta {\mathcal {S}}}{\delta \varphi }}=\int _{M}*(1)\left(-\partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\varphi )}}\right)+{\frac {\partial {\mathcal {L}}}{\partial \varphi }}\right).} Solving, with respect to the boundary conditions, one obtains the Euler–Lagrange equations: ∂ L ∂ φ = ∂ μ ( ∂ L ∂ ( ∂ μ φ ) ) . {\displaystyle {\frac {\partial {\mathcal {L}}}{\partial \varphi }}=\partial _{\mu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\mu }\varphi )}}\right).} === Lagrangian terms === Often the Lagrangian consists of a sum of polynomial terms, with the symmetries of the theory and the fields involved dictating the types of terms that are allowed. For example, in relativistic theories, each term must be Lorentz invariant while in a theory with a gauge field, they must be gauge invariant. Terms that contain two fields and no derivatives are known as mass terms, with these giving mass to the fields. For example, a single real scalar field ϕ ( x ) {\displaystyle \phi (x)} of mass m {\displaystyle m} has a mass term given by L m = − 1 2 m 2 ϕ 2 ( x ) . {\displaystyle {\mathcal {L}}_{m}=-{\frac {1}{2}}m^{2}\phi ^{2}(x).} The other terms that have two fields, those with at least one derivative, are known as kinetic terms. They make fields dynamical, with most theories requiring a restriction of at most two derivatives in kinetic terms to preserve probabililties in a quantum theory. They are also usually positive-definite to ensure positive energies. For example, the kinetic term for a relativistic real scalar field is given by L k = 1 2 ∂ μ ϕ ∂ μ ϕ . {\displaystyle {\mathcal {L}}_{k}={\frac {1}{2}}\partial _{\mu }\phi \partial ^{\mu }\phi .} Fields with no kinetic terms can also be found, playing the role of auxiliary fields, background fields, or currents. Theories with only kinetic and mass terms, form free field theories. Any term with more than two fields per term is known as an interaction term. The presence of these gives rise to interacting theories where particles can scatter off each other. The coefficients in front of these terms are known as coupling constants and they dictate the strength of the interaction. For example, a quartic interaction in a real scalar field theory is given by L i = − g 4 ! ϕ 4 , {\displaystyle {\mathcal {L}}_{i}=-{\frac {g}{4!}}\phi ^{4},} where g {\displaystyle g} is its coupling constant. This term gives rise to scattering processes whereby two scalar fields can scatter off each other. Interacting terms can have any number of derivatives, with each derivative providing a momentum dependence to the scattering term as can be seen by going into momentum space. Terms with only one field are known as tadpole terms since they give rise to tadpole Feynman diagrams.: 415  In theories with translational symmetries, such terms can usually be eliminated by redefining some of the fields though a shift. Constant terms, those with no fields, have no physical consequences in non-gravitational theories. In classical field theories, the equations of motion only depend on variations of the Lagrangian, so constant terms play no role. In quantum field theories they only provide an irrelevant overall multiplicative term to the partition function, so again play no role. Physically this is because in these theories there is no absolute energy scale as the potential energy can always be shifted by an arbitrary constant without altering the physics. However, in gravitational systems the constant terms are multiplied by the metric determinant, coupling them to the spacetime. They play the role of the cosmological constant, directly affecting the dynamics of the theory at both a classical and quantum level. Polynomial terms are often expressed with certain canonical normalizations, used to simplify the Feynman rules that are derived from them. Usually one divides by the product of the factorial of the multipicity of the fields. For example, in a theory with two real scalar fields, a term of the form g ϕ n φ m {\displaystyle g\phi ^{n}\varphi ^{m}} term would be divided by n ! m ! {\displaystyle n!m!} . Particles and antiparticles are distinguished in this counting, so that a complex scalar field term of the form g ′ ϕ ¯ p ϕ p {\displaystyle g'{\bar {\phi }}^{p}\phi ^{p}} is divided by p ! p ! {\displaystyle p!p!} rather than ( 2 p ) ! {\displaystyle (2p)!} . == Examples == A large variety of physical systems have been formulated in terms of Lagrangians over fields. Below is a sampling of some of the most common ones found in physics textbooks on field theory. === Newtonian gravity === The Lagrangian density for Newtonian gravity is: L ( x , t ) = − 1 8 π G ( ∇ Φ ( x , t ) ) 2 − ρ ( x , t ) Φ ( x , t ) {\displaystyle {\mathcal {L}}(\mathbf {x} ,t)=-{1 \over 8\pi G}(\nabla \Phi (\mathbf {x} ,t))^{2}-\rho (\mathbf {x} ,t)\Phi (\mathbf {x} ,t)} where Φ is the gravitational potential, ρ is the mass density, and G in m3·kg−1·s−2 is the gravitational constant. The density L {\displaystyle {\mathcal {L}}} has units of J·m−3. Here the interaction term involves a continuous mass density ρ in kg·m−3. This is necessary because using a point source for a field would result in mathematical difficulties. This Lagrangian can be written in the form of L = T − V {\displaystyle {\mathcal {L}}=T-V} , with the T = − ( ∇ Φ ) 2 / 8 π G {\displaystyle T=-(\nabla \Phi )^{2}/8\pi G} providing a kinetic term, and the interaction V = ρ Φ {\displaystyle V=\rho \Phi } the potential term. See also Nordström's theory of gravitation for how this could be modified to deal with changes over time. This form is reprised in the next example of a scalar field theory. The variation of the integral with respect to Φ is: δ L ( x , t ) = − ρ ( x , t ) δ Φ ( x , t ) − 2 8 π G ( ∇ Φ ( x , t ) ) ⋅ ( ∇ δ Φ ( x , t ) ) . {\displaystyle \delta {\mathcal {L}}(\mathbf {x} ,t)=-\rho (\mathbf {x} ,t)\delta \Phi (\mathbf {x} ,t)-{2 \over 8\pi G}(\nabla \Phi (\mathbf {x} ,t))\cdot (\nabla \delta \Phi (\mathbf {x} ,t)).} After integrating by parts, discarding the total integral, and dividing out by δΦ the formula becomes: 0 = − ρ ( x , t ) + 1 4 π G ∇ ⋅ ∇ Φ ( x , t ) {\displaystyle 0=-\rho (\mathbf {x} ,t)+{\frac {1}{4\pi G}}\nabla \cdot \nabla \Phi (\mathbf {x} ,t)} which is equivalent to: 4 π G ρ ( x , t ) = ∇ 2 Φ ( x , t ) {\displaystyle 4\pi G\rho (\mathbf {x} ,t)=\nabla ^{2}\Phi (\mathbf {x} ,t)} which yields Gauss's law for gravity. === Scalar field theory === The Lagrangian for a scalar field moving in a potential V ( ϕ ) {\displaystyle V(\phi )} can be written as L = 1 2 ∂ μ ϕ ∂ μ ϕ − V ( ϕ ) = 1 2 ∂ μ ϕ ∂ μ ϕ − 1 2 m 2 ϕ 2 − ∑ n = 3 ∞ 1 n ! g n ϕ n {\displaystyle {\mathcal {L}}={\frac {1}{2}}\partial ^{\mu }\phi \partial _{\mu }\phi -V(\phi )={\frac {1}{2}}\partial ^{\mu }\phi \partial _{\mu }\phi -{\frac {1}{2}}m^{2}\phi ^{2}-\sum _{n=3}^{\infty }{\frac {1}{n!}}g_{n}\phi ^{n}} It is not at all an accident that the scalar theory resembles the undergraduate textbook Lagrangian L = T − V {\displaystyle L=T-V} for the kinetic term of a free point particle written as T = m v 2 / 2 {\displaystyle T=mv^{2}/2} . The scalar theory is the field-theory generalization of a particle moving in a potential. When the V ( ϕ ) {\displaystyle V(\phi )} is the Mexican hat potential, the resulting fields are termed the Higgs fields. === Sigma model Lagrangian === The sigma model describes the motion of a scalar point particle constrained to move on a Riemannian manifold, such as a circle or a sphere. It generalizes the case of scalar and vector fields, that is, fields constrained to move on a flat manifold. The Lagrangian is commonly written in one of three equivalent forms: L = 1 2 d ϕ ∧ ∗ d ϕ {\displaystyle {\mathcal {L}}={\frac {1}{2}}\mathrm {d} \phi \wedge {*\mathrm {d} \phi }} where the d {\displaystyle \mathrm {d} } is the differential. An equivalent expression is L = 1 2 ∑ i = 1 n ∑ j = 1 n g i j ( ϕ ) ∂ μ ϕ i ∂ μ ϕ j {\displaystyle {\mathcal {L}}={\frac {1}{2}}\sum _{i=1}^{n}\sum _{j=1}^{n}g_{ij}(\phi )\;\partial ^{\mu }\phi _{i}\partial _{\mu }\phi _{j}} with g i j {\displaystyle g_{ij}} the Riemannian metric on the manifold of the field; i.e. the fields ϕ i {\displaystyle \phi _{i}} are just local coordinates on the coordinate chart of the manifold. A third common form is L = 1 2 t r ( L μ L μ ) {\displaystyle {\mathcal {L}}={\frac {1}{2}}\mathrm {tr} \left(L_{\mu }L^{\mu }\right)} with L μ = U − 1 ∂ μ U {\displaystyle L_{\mu }=U^{-1}\partial _{\mu }U} and U ∈ S U ( N ) {\displaystyle U\in \mathrm {SU} (N)} , the Lie group SU(N). This group can be replaced by any Lie group, or, more generally, by a symmetric space. The trace is just the Killing form in hiding; the Killing form provides a quadratic form on the field manifold, the lagrangian is then just the pullback of this form. Alternately, the Lagrangian can also be seen as the pullback of the Maurer–Cartan form to the base spacetime. In general, sigma models exhibit topological soliton solutions. The most famous and well-studied of these is the Skyrmion, which serves as a model of the nucleon that has withstood the test of time. === Electromagnetism in special relativity === Consider a point particle, a charged particle, interacting with the electromagnetic field. The interaction terms − q ϕ ( x ( t ) , t ) + q x ˙ ( t ) ⋅ A ( x ( t ) , t ) {\displaystyle -q\phi (\mathbf {x} (t),t)+q{\dot {\mathbf {x} }}(t)\cdot \mathbf {A} (\mathbf {x} (t),t)} are replaced by terms involving a continuous charge density ρ in A·s·m−3 and current density j {\displaystyle \mathbf {j} } in A·m−2. The resulting Lagrangian density for the electromagnetic field is: L ( x , t ) = − ρ ( x , t ) ϕ ( x , t ) + j ( x , t ) ⋅ A ( x , t ) + ϵ 0 2 E 2 ( x , t ) − 1 2 μ 0 B 2 ( x , t ) . {\displaystyle {\mathcal {L}}(\mathbf {x} ,t)=-\rho (\mathbf {x} ,t)\phi (\mathbf {x} ,t)+\mathbf {j} (\mathbf {x} ,t)\cdot \mathbf {A} (\mathbf {x} ,t)+{\epsilon _{0} \over 2}{E}^{2}(\mathbf {x} ,t)-{1 \over {2\mu _{0}}}{B}^{2}(\mathbf {x} ,t).} Varying this with respect to ϕ, we get 0 = − ρ ( x , t ) + ϵ 0 ∇ ⋅ E ( x , t ) {\displaystyle 0=-\rho (\mathbf {x} ,t)+\epsilon _{0}\nabla \cdot \mathbf {E} (\mathbf {x} ,t)} which yields Gauss' law. Varying instead with respect to A {\displaystyle \mathbf {A} } , we get 0 = j ( x , t ) + ϵ 0 E ˙ ( x , t ) − 1 μ 0 ∇ × B ( x , t ) {\displaystyle 0=\mathbf {j} (\mathbf {x} ,t)+\epsilon _{0}{\dot {\mathbf {E} }}(\mathbf {x} ,t)-{1 \over \mu _{0}}\nabla \times \mathbf {B} (\mathbf {x} ,t)} which yields Ampère's law. Using tensor notation, we can write all this more compactly. The term − ρ ϕ ( x , t ) + j ⋅ A {\displaystyle -\rho \phi (\mathbf {x} ,t)+\mathbf {j} \cdot \mathbf {A} } is actually the inner product of two four-vectors. We package the charge density into the current 4-vector and the potential into the potential 4-vector. These two new vectors are j μ = ( ρ , j ) and A μ = ( − ϕ , A ) {\displaystyle j^{\mu }=(\rho ,\mathbf {j} )\quad {\text{and}}\quad A_{\mu }=(-\phi ,\mathbf {A} )} We can then write the interaction term as − ρ ϕ + j ⋅ A = j μ A μ {\displaystyle -\rho \phi +\mathbf {j} \cdot \mathbf {A} =j^{\mu }A_{\mu }} Additionally, we can package the E and B fields into what is known as the electromagnetic tensor F μ ν {\displaystyle F_{\mu \nu }} . We define this tensor as F μ ν = ∂ μ A ν − ∂ ν A μ {\displaystyle F_{\mu \nu }=\partial _{\mu }A_{\nu }-\partial _{\nu }A_{\mu }} The term we are looking out for turns out to be ϵ 0 2 E 2 − 1 2 μ 0 B 2 = − 1 4 μ 0 F μ ν F μ ν = − 1 4 μ 0 F μ ν F ρ σ η μ ρ η ν σ {\displaystyle {\epsilon _{0} \over 2}{E}^{2}-{1 \over {2\mu _{0}}}{B}^{2}=-{\frac {1}{4\mu _{0}}}F_{\mu \nu }F^{\mu \nu }=-{\frac {1}{4\mu _{0}}}F_{\mu \nu }F_{\rho \sigma }\eta ^{\mu \rho }\eta ^{\nu \sigma }} We have made use of the Minkowski metric to raise the indices on the EMF tensor. In this notation, Maxwell's equations are ∂ μ F μ ν = − μ 0 j ν and ϵ μ ν λ σ ∂ ν F λ σ = 0 {\displaystyle \partial _{\mu }F^{\mu \nu }=-\mu _{0}j^{\nu }\quad {\text{and}}\quad \epsilon ^{\mu \nu \lambda \sigma }\partial _{\nu }F_{\lambda \sigma }=0} where ε is the Levi-Civita tensor. So the Lagrange density for electromagnetism in special relativity written in terms of Lorentz vectors and tensors is L ( x ) = j μ ( x ) A μ ( x ) − 1 4 μ 0 F μ ν ( x ) F μ ν ( x ) {\displaystyle {\mathcal {L}}(x)=j^{\mu }(x)A_{\mu }(x)-{\frac {1}{4\mu _{0}}}F_{\mu \nu }(x)F^{\mu \nu }(x)} In this notation it is apparent that classical electromagnetism is a Lorentz-invariant theory. By the equivalence principle, it becomes simple to extend the notion of electromagnetism to curved spacetime. === Electromagnetism and the Yang–Mills equations === Using differential forms, the electromagnetic action S in vacuum on a (pseudo-) Riemannian manifold M {\displaystyle {\mathcal {M}}} can be written (using natural units, c = ε0 = 1) as S [ A ] = − ∫ M ( 1 2 F ∧ ∗ F − A ∧ ∗ J ) . {\displaystyle {\mathcal {S}}[\mathbf {A} ]=-\int _{\mathcal {M}}\left({\frac {1}{2}}\,\mathbf {F} \wedge \ast \mathbf {F} -\mathbf {A} \wedge \ast \mathbf {J} \right).} Here, A stands for the electromagnetic potential 1-form, J is the current 1-form, F is the field strength 2-form and the star denotes the Hodge star operator. This is exactly the same Lagrangian as in the section above, except that the treatment here is coordinate-free; expanding the integrand into a basis yields the identical, lengthy expression. Note that with forms, an additional integration measure is not necessary because forms have coordinate differentials built in. Variation of the action leads to d ∗ F = ∗ J . {\displaystyle \mathrm {d} {\ast }\mathbf {F} ={\ast }\mathbf {J} .} These are Maxwell's equations for the electromagnetic potential. Substituting F = dA immediately yields the equation for the fields, d F = 0 {\displaystyle \mathrm {d} \mathbf {F} =0} because F is an exact form. The A field can be understood to be the affine connection on a U(1)-fiber bundle. That is, classical electrodynamics, all of its effects and equations, can be completely understood in terms of a circle bundle over Minkowski spacetime. The Yang–Mills equations can be written in exactly the same form as above, by replacing the Lie group U(1) of electromagnetism by an arbitrary Lie group. In the Standard model, it is conventionally taken to be S U ( 3 ) × S U ( 2 ) × U ( 1 ) {\displaystyle \mathrm {SU} (3)\times \mathrm {SU} (2)\times \mathrm {U} (1)} although the general case is of general interest. In all cases, there is no need for any quantization to be performed. Although the Yang–Mills equations are historically rooted in quantum field theory, the above equations are purely classical. === Chern–Simons functional === In the same vein as the above, one can consider the action in one dimension less, i.e. in a contact geometry setting. This gives the Chern–Simons functional. It is written as S [ A ] = ∫ M t r ( A ∧ d A + 2 3 A ∧ A ∧ A ) . {\displaystyle {\mathcal {S}}[\mathbf {A} ]=\int _{\mathcal {M}}\mathrm {tr} \left(\mathbf {A} \wedge d\mathbf {A} +{\frac {2}{3}}\mathbf {A} \wedge \mathbf {A} \wedge \mathbf {A} \right).} Chern–Simons theory was deeply explored in physics, as a toy model for a broad range of geometric phenomena that one might expect to find in a grand unified theory. === Ginzburg–Landau Lagrangian === The Lagrangian density for Ginzburg–Landau theory combines the Lagrangian for the scalar field theory with the Lagrangian for the Yang–Mills action. It may be written as: L ( ψ , A ) = | F | 2 + | D ψ | 2 + 1 4 ( σ − | ψ | 2 ) 2 {\displaystyle {\mathcal {L}}(\psi ,A)=\vert F\vert ^{2}+\vert D\psi \vert ^{2}+{\frac {1}{4}}\left(\sigma -\vert \psi \vert ^{2}\right)^{2}} where ψ {\displaystyle \psi } is a section of a vector bundle with fiber C n {\displaystyle \mathbb {C} ^{n}} . The ψ {\displaystyle \psi } corresponds to the order parameter in a superconductor; equivalently, it corresponds to the Higgs field, after noting that the second term is the famous "Sombrero hat" potential. The field A {\displaystyle A} is the (non-Abelian) gauge field, i.e. the Yang–Mills field and F {\displaystyle F} is its field-strength. The Euler–Lagrange equations for the Ginzburg–Landau functional are the Yang–Mills equations D ⋆ D ψ = 1 2 ( σ − | ψ | 2 ) ψ {\displaystyle D{\star }D\psi ={\frac {1}{2}}\left(\sigma -\vert \psi \vert ^{2}\right)\psi } and D ⋆ F = − Re ⁡ ⟨ D ψ , ψ ⟩ {\displaystyle D{\star }F=-\operatorname {Re} \langle D\psi ,\psi \rangle } where ⋆ {\displaystyle {\star }} is the Hodge star operator, i.e. the fully antisymmetric tensor. These equations are closely related to the Yang–Mills–Higgs equations. Another closely related Lagrangian is found in Seiberg–Witten theory. === Dirac Lagrangian === The Lagrangian density for a Dirac field is: L = ψ ¯ ( i ℏ c ∂ / − m c 2 ) ψ {\displaystyle {\mathcal {L}}={\bar {\psi }}(i\hbar c{\partial }\!\!\!/\ -mc^{2})\psi } where ψ {\displaystyle \psi } is a Dirac spinor, ψ ¯ = ψ † γ 0 {\displaystyle {\bar {\psi }}=\psi ^{\dagger }\gamma ^{0}} is its Dirac adjoint, and ∂ / {\displaystyle {\partial }\!\!\!/} is Feynman slash notation for γ σ ∂ σ {\displaystyle \gamma ^{\sigma }\partial _{\sigma }} . There is no particular need to focus on Dirac spinors in the classical theory. The Weyl spinors provide a more general foundation; they can be constructed directly from the Clifford algebra of spacetime; the construction works in any number of dimensions, and the Dirac spinors appear as a special case. Weyl spinors have the additional advantage that they can be used in a vielbein for the metric on a Riemannian manifold; this enables the concept of a spin structure, which, roughly speaking, is a way of formulating spinors consistently in a curved spacetime. === Quantum electrodynamic Lagrangian === The Lagrangian density for QED combines the Lagrangian for the Dirac field together with the Lagrangian for electrodynamics in a gauge-invariant way. It is: L Q E D = ψ ¯ ( i ℏ c D / − m c 2 ) ψ − 1 4 μ 0 F μ ν F μ ν {\displaystyle {\mathcal {L}}_{\mathrm {QED} }={\bar {\psi }}(i\hbar c{D}\!\!\!\!/\ -mc^{2})\psi -{1 \over 4\mu _{0}}F_{\mu \nu }F^{\mu \nu }} where F μ ν {\displaystyle F^{\mu \nu }} is the electromagnetic tensor, D is the gauge covariant derivative, and D / {\displaystyle {D}\!\!\!\!/} is Feynman notation for γ σ D σ {\displaystyle \gamma ^{\sigma }D_{\sigma }} with D σ = ∂ σ − i e A σ {\displaystyle D_{\sigma }=\partial _{\sigma }-ieA_{\sigma }} where A σ {\displaystyle A_{\sigma }} is the electromagnetic four-potential. Although the word "quantum" appears in the above, this is a historical artifact. The definition of the Dirac field requires no quantization whatsoever, it can be written as a purely classical field of anti-commuting Weyl spinors constructed from first principles from a Clifford algebra. The full gauge-invariant classical formulation is given in Bleecker. === Quantum chromodynamic Lagrangian === The Lagrangian density for quantum chromodynamics combines the Lagrangian for one or more massive Dirac spinors with the Lagrangian for the Yang–Mills action, which describes the dynamics of a gauge field; the combined Lagrangian is gauge invariant. It may be written as: L Q C D = ∑ n ψ ¯ n ( i ℏ c D / − m n c 2 ) ψ n − 1 4 G α μ ν G α μ ν {\displaystyle {\mathcal {L}}_{\mathrm {QCD} }=\sum _{n}{\bar {\psi }}_{n}\left(i\hbar c{D}\!\!\!\!/\ -m_{n}c^{2}\right)\psi _{n}-{1 \over 4}G^{\alpha }{}_{\mu \nu }G_{\alpha }{}^{\mu \nu }} where D is the QCD gauge covariant derivative, n = 1, 2, ...6 counts the quark types, and G α μ ν {\displaystyle G^{\alpha }{}_{\mu \nu }\!} is the gluon field strength tensor. As for the electrodynamics case above, the appearance of the word "quantum" above only acknowledges its historical development. The Lagrangian and its gauge invariance can be formulated and treated in a purely classical fashion. === Einstein gravity === The Lagrange density for general relativity in the presence of matter fields is L GR = L EH + L matter = c 4 16 π G ( R − 2 Λ ) + L matter {\displaystyle {\mathcal {L}}_{\text{GR}}={\mathcal {L}}_{\text{EH}}+{\mathcal {L}}_{\text{matter}}={\frac {c^{4}}{16\pi G}}\left(R-2\Lambda \right)+{\mathcal {L}}_{\text{matter}}} where Λ {\displaystyle \Lambda } is the cosmological constant, R {\displaystyle R} is the curvature scalar, which is the Ricci tensor contracted with the metric tensor, and the Ricci tensor is the Riemann tensor contracted with a Kronecker delta. The integral of L EH {\displaystyle {\mathcal {L}}_{\text{EH}}} is known as the Einstein–Hilbert action. The Riemann tensor is the tidal force tensor, and is constructed out of Christoffel symbols and derivatives of Christoffel symbols, which define the metric connection on spacetime. The gravitational field itself was historically ascribed to the metric tensor; the modern view is that the connection is "more fundamental". This is due to the understanding that one can write connections with non-zero torsion. These alter the metric without altering the geometry one bit. As to the actual "direction in which gravity points" (e.g. on the surface of the Earth, it points down), this comes from the Riemann tensor: it is the thing that describes the "gravitational force field" that moving bodies feel and react to. (This last statement must be qualified: there is no "force field" per se; moving bodies follow geodesics on the manifold described by the connection. They move in a "straight line".) The Lagrangian for general relativity can also be written in a form that makes it manifestly similar to the Yang–Mills equations. This is called the Einstein–Yang–Mills action principle. This is done by noting that most of differential geometry works "just fine" on bundles with an affine connection and arbitrary Lie group. Then, plugging in SO(3,1) for that symmetry group, i.e. for the frame fields, one obtains the equations above. Substituting this Lagrangian into the Euler–Lagrange equation and taking the metric tensor g μ ν {\displaystyle g_{\mu \nu }} as the field, we obtain the Einstein field equations R μ ν − 1 2 R g μ ν + g μ ν Λ = 8 π G c 4 T μ ν . {\displaystyle R_{\mu \nu }-{\frac {1}{2}}Rg_{\mu \nu }+g_{\mu \nu }\Lambda ={\frac {8\pi G}{c^{4}}}T_{\mu \nu }\,.} T μ ν {\displaystyle T_{\mu \nu }} is the energy momentum tensor and is defined by T μ ν ≡ − 2 − g δ ( L m a t t e r − g ) δ g μ ν = − 2 δ L m a t t e r δ g μ ν + g μ ν L m a t t e r . {\displaystyle T_{\mu \nu }\equiv {\frac {-2}{\sqrt {-g}}}{\frac {\delta ({\mathcal {L}}_{\mathrm {matter} }{\sqrt {-g}})}{\delta g^{\mu \nu }}}=-2{\frac {\delta {\mathcal {L}}_{\mathrm {matter} }}{\delta g^{\mu \nu }}}+g_{\mu \nu }{\mathcal {L}}_{\mathrm {matter} }\,.} where g {\displaystyle g} is the determinant of the metric tensor when regarded as a matrix. Generally, in general relativity, the integration measure of the action of Lagrange density is − g d 4 x {\textstyle {\sqrt {-g}}\,d^{4}x} . This makes the integral coordinate independent, as the root of the metric determinant is equivalent to the Jacobian determinant. The minus sign is a consequence of the metric signature (the determinant by itself is negative). This is an example of the volume form, previously discussed, becoming manifest in non-flat spacetime. === Electromagnetism in general relativity === The Lagrange density of electromagnetism in general relativity also contains the Einstein–Hilbert action from above. The pure electromagnetic Lagrangian is precisely a matter Lagrangian L matter {\displaystyle {\mathcal {L}}_{\text{matter}}} . The Lagrangian is L ( x ) = j μ ( x ) A μ ( x ) − 1 4 μ 0 F μ ν ( x ) F ρ σ ( x ) g μ ρ ( x ) g ν σ ( x ) + c 4 16 π G R ( x ) = L Maxwell + L Einstein–Hilbert . {\displaystyle {\begin{aligned}{\mathcal {L}}(x)&=j^{\mu }(x)A_{\mu }(x)-{1 \over 4\mu _{0}}F_{\mu \nu }(x)F_{\rho \sigma }(x)g^{\mu \rho }(x)g^{\nu \sigma }(x)+{\frac {c^{4}}{16\pi G}}R(x)\\&={\mathcal {L}}_{\text{Maxwell}}+{\mathcal {L}}_{\text{Einstein–Hilbert}}.\end{aligned}}} This Lagrangian is obtained by simply replacing the Minkowski metric in the above flat Lagrangian with a more general (possibly curved) metric g μ ν ( x ) {\displaystyle g_{\mu \nu }(x)} . We can generate the Einstein Field Equations in the presence of an EM field using this lagrangian. The energy-momentum tensor is T μ ν ( x ) = 2 − g ( x ) δ δ g μ ν ( x ) S Maxwell = 1 μ 0 ( F λ μ ( x ) F ν λ ( x ) − 1 4 g μ ν ( x ) F ρ σ ( x ) F ρ σ ( x ) ) {\displaystyle T^{\mu \nu }(x)={\frac {2}{\sqrt {-g(x)}}}{\frac {\delta }{\delta g_{\mu \nu }(x)}}{\mathcal {S}}_{\text{Maxwell}}={\frac {1}{\mu _{0}}}\left(F_{{\text{ }}\lambda }^{\mu }(x)F^{\nu \lambda }(x)-{\frac {1}{4}}g^{\mu \nu }(x)F_{\rho \sigma }(x)F^{\rho \sigma }(x)\right)} It can be shown that this energy momentum tensor is traceless, i.e. that T = g μ ν T μ ν = 0 {\displaystyle T=g_{\mu \nu }T^{\mu \nu }=0} If we take the trace of both sides of the Einstein Field Equations, we obtain R = − 8 π G c 4 T {\displaystyle R=-{\frac {8\pi G}{c^{4}}}T} So the tracelessness of the energy momentum tensor implies that the curvature scalar in an electromagnetic field vanishes. The Einstein equations are then R μ ν = 8 π G c 4 1 μ 0 ( F μ λ ( x ) F ν λ ( x ) − 1 4 g μ ν ( x ) F ρ σ ( x ) F ρ σ ( x ) ) {\displaystyle R^{\mu \nu }={\frac {8\pi G}{c^{4}}}{\frac {1}{\mu _{0}}}\left({F^{\mu }}_{\lambda }(x)F^{\nu \lambda }(x)-{\frac {1}{4}}g^{\mu \nu }(x)F_{\rho \sigma }(x)F^{\rho \sigma }(x)\right)} Additionally, Maxwell's equations are D μ F μ ν = − μ 0 j ν {\displaystyle D_{\mu }F^{\mu \nu }=-\mu _{0}j^{\nu }} where D μ {\displaystyle D_{\mu }} is the covariant derivative. For free space, we can set the current tensor equal to zero, j μ = 0 {\displaystyle j^{\mu }=0} . Solving both Einstein and Maxwell's equations around a spherically symmetric mass distribution in free space leads to the Reissner–Nordström charged black hole, with the defining line element (written in natural units and with charge Q): d s 2 = ( 1 − 2 M r + Q 2 r 2 ) d t 2 − ( 1 − 2 M r + Q 2 r 2 ) − 1 d r 2 − r 2 d Ω 2 {\displaystyle \mathrm {d} s^{2}=\left(1-{\frac {2M}{r}}+{\frac {Q^{2}}{r^{2}}}\right)\mathrm {d} t^{2}-\left(1-{\frac {2M}{r}}+{\frac {Q^{2}}{r^{2}}}\right)^{-1}\mathrm {d} r^{2}-r^{2}\mathrm {d} \Omega ^{2}} One possible way of unifying the electromagnetic and gravitational Lagrangians (by using a fifth dimension) is given by Kaluza–Klein theory. Effectively, one constructs an affine bundle, just as for the Yang–Mills equations given earlier, and then considers the action separately on the 4-dimensional and the 1-dimensional parts. Such factorizations, such as the fact that the 7-sphere can be written as a product of the 4-sphere and the 3-sphere, or that the 11-sphere is a product of the 4-sphere and the 7-sphere, accounted for much of the early excitement that a theory of everything had been found. Unfortunately, the 7-sphere proved not large enough to enclose all of the Standard model, dashing these hopes. === Additional examples === The BF model Lagrangian, short for "Background Field", describes a system with trivial dynamics, when written on a flat spacetime manifold. On a topologically non-trivial spacetime, the system will have non-trivial classical solutions, which may be interpreted as solitons or instantons. A variety of extensions exist, forming the foundations for topological field theories. == See also == == Notes == == Citations ==
Wikipedia/Lagrangian_(field_theory)
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization occurs in many physical, chemical, biological, robotic, and cognitive systems. Examples of self-organization include crystallization, thermal convection of fluids, chemical oscillation, animal swarming, neural circuits, and black markets. == Overview == Self-organization is realized in the physics of non-equilibrium processes, and in chemical reactions, where it is often characterized as self-assembly. The concept has proven useful in biology, from the molecular to the ecosystem level. Cited examples of self-organizing behavior also appear in the literature of many other disciplines, both in the natural sciences and in the social sciences (such as economics or anthropology). Self-organization has also been observed in mathematical systems such as cellular automata. Self-organization is an example of the related concept of emergence. Self-organization relies on four basic ingredients: strong dynamical non-linearity, often (though not necessarily) involving positive and negative feedback balance of exploitation and exploration multiple interactions among components availability of energy (to overcome the natural tendency toward entropy, or loss of free energy) == Principles == The cybernetician William Ross Ashby formulated the original principle of self-organization in 1947. It states that any deterministic dynamic system automatically evolves towards a state of equilibrium that can be described in terms of an attractor in a basin of surrounding states. Once there, the further evolution of the system is constrained to remain in the attractor. This constraint implies a form of mutual dependency or coordination between its constituent components or subsystems. In Ashby's terms, each subsystem has adapted to the environment formed by all other subsystems. The cybernetician Heinz von Foerster formulated the principle of "order from noise" in 1960. It notes that self-organization is facilitated by random perturbations ("noise") that let the system explore a variety of states in its state space. This increases the chance that the system will arrive into the basin of a "strong" or "deep" attractor, from which it then quickly enters the attractor itself. The biophysicist Henri Atlan developed this concept by proposing the principle of "complexity from noise" (French: le principe de complexité par le bruit) first in the 1972 book L'organisation biologique et la théorie de l'information and then in the 1979 book Entre le cristal et la fumée. The physicist and chemist Ilya Prigogine formulated a similar principle as "order through fluctuations" or "order out of chaos". It is applied in the method of simulated annealing for problem solving and machine learning. == History == The idea that the dynamics of a system can lead to an increase in its organization has a long history. The ancient atomists such as Democritus and Lucretius believed that a designing intelligence is unnecessary to create order in nature, arguing that given enough time and space and matter, order emerges by itself. The philosopher René Descartes presents self-organization hypothetically in the fifth part of his 1637 Discourse on Method. He elaborated on the idea in his unpublished work The World. Immanuel Kant used the term "self-organizing" in his 1790 Critique of Judgment, where he argued that teleology is a meaningful concept only if there exists such an entity whose parts or "organs" are simultaneously ends and means. Such a system of organs must be able to behave as if it has a mind of its own, that is, it is capable of governing itself. In such a natural product as this every part is thought as owing its presence to the agency of all the remaining parts, and also as existing for the sake of the others and of the whole, that is as an instrument, or organ... The part must be an organ producing the other parts—each, consequently, reciprocally producing the others... Only under these conditions and upon these terms can such a product be an organized and self-organized being, and, as such, be called a physical end. Sadi Carnot (1796–1832) and Rudolf Clausius (1822–1888) discovered the second law of thermodynamics in the 19th century. It states that total entropy, sometimes understood as disorder, will always increase over time in an isolated system. This means that a system cannot spontaneously increase its order without an external relationship that decreases order elsewhere in the system (e.g. through consuming the low-entropy energy of a battery and diffusing high-entropy heat). 18th-century thinkers had sought to understand the "universal laws of form" to explain the observed forms of living organisms. This idea became associated with Lamarckism and fell into disrepute until the early 20th century, when D'Arcy Wentworth Thompson (1860–1948) attempted to revive it. The psychiatrist and engineer W. Ross Ashby introduced the term "self-organizing" to contemporary science in 1947. It was taken up by the cyberneticians Heinz von Foerster, Gordon Pask, Stafford Beer; and von Foerster organized a conference on "The Principles of Self-Organization" at the University of Illinois' Allerton Park in June, 1960 which led to a series of conferences on Self-Organizing Systems. Norbert Wiener took up the idea in the second edition of his Cybernetics: or Control and Communication in the Animal and the Machine (1961). Self-organization was associated with general systems theory in the 1960s, but did not become commonplace in the scientific literature until physicists Hermann Haken et al. and complex systems researchers adopted it in a greater picture from cosmology Erich Jantsch, chemistry with dissipative system, biology and sociology as autopoiesis to system thinking in the following 1980s (Santa Fe Institute) and 1990s (complex adaptive system), until our days with the disruptive emerging technologies profounded by a rhizomatic network theory. Around 2008–2009, a concept of guided self-organization started to take shape. This approach aims to regulate self-organization for specific purposes, so that a dynamical system may reach specific attractors or outcomes. The regulation constrains a self-organizing process within a complex system by restricting local interactions between the system components, rather than following an explicit control mechanism or a global design blueprint. The desired outcomes, such as increases in the resultant internal structure and/or functionality, are achieved by combining task-independent global objectives with task-dependent constraints on local interactions. == By field == === Physics === The many self-organizing phenomena in physics include phase transitions and spontaneous symmetry breaking such as spontaneous magnetization and crystal growth in classical physics, and the laser, superconductivity and Bose–Einstein condensation in quantum physics. Self-organization is found in self-organized criticality in dynamical systems, in tribology, in spin foam systems, and in loop quantum gravity, in plasma, in river basins and deltas, in dendritic solidification (snow flakes), in capillary imbibition and in turbulent structure. === Chemistry === Self-organization in chemistry includes drying-induced self-assembly, molecular self-assembly, reaction–diffusion systems and oscillating reactions, autocatalytic networks, liquid crystals, grid complexes, colloidal crystals, self-assembled monolayers, micelles, microphase separation of block copolymers, and Langmuir–Blodgett films. === Biology === Self-organization in biology can be observed in spontaneous folding of proteins and other biomacromolecules, self-assembly of lipid bilayer membranes, pattern formation and morphogenesis in developmental biology, the coordination of human movement, eusocial behavior in insects (bees, ants, termites) and mammals, and flocking behavior in birds and fish. The mathematical biologist Stuart Kauffman and other structuralists have suggested that self-organization may play roles alongside natural selection in three areas of evolutionary biology, namely population dynamics, molecular evolution, and morphogenesis. However, this does not take into account the essential role of energy in driving biochemical reactions in cells. The systems of reactions in any cell are self-catalyzing, but not simply self-organizing, as they are thermodynamically open systems relying on a continuous input of energy. Self-organization is not an alternative to natural selection, but it constrains what evolution can do and provides mechanisms such as the self-assembly of membranes which evolution then exploits. The evolution of order in living systems and the generation of order in certain non-living systems was proposed to obey a common fundamental principal called “the Darwinian dynamic” that was formulated by first considering how microscopic order is generated in simple non-biological systems that are far from thermodynamic equilibrium. Consideration was then extended to short, replicating RNA molecules assumed to be similar to the earliest forms of life in the RNA world. It was shown that the underlying order-generating processes of self-organization in the non-biological systems and in replicating RNA are basically similar. === Cosmology === In his 1995 conference paper "Cosmology as a problem in critical phenomena" Lee Smolin said that several cosmological objects or phenomena, such as spiral galaxies, galaxy formation processes in general, early structure formation, quantum gravity and the large scale structure of the universe might be the result of or have involved certain degree of self-organization. He argues that self-organized systems are often critical systems, with structure spreading out in space and time over every available scale, as shown for example by Per Bak and his collaborators. Therefore, because the distribution of matter in the universe is more or less scale invariant over many orders of magnitude, ideas and strategies developed in the study of self-organized systems could be helpful in tackling certain unsolved problems in cosmology and astrophysics. === Computer science === Phenomena from mathematics and computer science such as cellular automata, random graphs, and some instances of evolutionary computation and artificial life exhibit features of self-organization. In swarm robotics, self-organization is used to produce emergent behavior. In particular the theory of random graphs has been used as a justification for self-organization as a general principle of complex systems. In the field of multi-agent systems, understanding how to engineer systems that are capable of presenting self-organized behavior is an active research area. Optimization algorithms can be considered self-organizing because they aim to find the optimal solution to a problem. If the solution is considered as a state of the iterative system, the optimal solution is the selected, converged structure of the system. Self-organizing networks include small-world networks self-stabilization and scale-free networks. These emerge from bottom-up interactions, unlike top-down hierarchical networks within organizations, which are not self-organizing. Cloud computing systems have been argued to be inherently self-organizing, but while they have some autonomy, they are not self-managing as they do not have the goal of reducing their own complexity. === Cybernetics === Norbert Wiener regarded the automatic serial identification of a black box and its subsequent reproduction as self-organization in cybernetics. The importance of phase locking or the "attraction of frequencies", as he called it, is discussed in the 2nd edition of his Cybernetics: Or Control and Communication in the Animal and the Machine. K. Eric Drexler sees self-replication as a key step in nano and universal assembly. By contrast, the four concurrently connected galvanometers of W. Ross Ashby's Homeostat hunt, when perturbed, to converge on one of many possible stable states. Ashby used his state counting measure of variety to describe stable states and produced the "Good Regulator" theorem which requires internal models for self-organized endurance and stability (e.g. Nyquist stability criterion). Warren McCulloch proposed "Redundancy of Potential Command" as characteristic of the organization of the brain and human nervous system and the necessary condition for self-organization. Heinz von Foerster proposed Redundancy, R=1 − H/Hmax, where H is entropy. In essence this states that unused potential communication bandwidth is a measure of self-organization. In the 1970s Stafford Beer considered self-organization necessary for autonomy in persisting and living systems. He applied his viable system model to management. It consists of five parts: the monitoring of performance of the survival processes (1), their management by recursive application of regulation (2), homeostatic operational control (3) and development (4) which produce maintenance of identity (5) under environmental perturbation. Focus is prioritized by an alerting "algedonic loop" feedback: a sensitivity to both pain and pleasure produced from under-performance or over-performance relative to a standard capability. In the 1990s Gordon Pask argued that von Foerster's H and Hmax were not independent, but interacted via countably infinite recursive concurrent spin processes which he called concepts. His strict definition of concept "a procedure to bring about a relation" permitted his theorem "Like concepts repel, unlike concepts attract" to state a general spin-based principle of self-organization. His edict, an exclusion principle, "There are No Doppelgangers" means no two concepts can be the same. After sufficient time, all concepts attract and coalesce as pink noise. The theory applies to all organizationally closed or homeostatic processes that produce enduring and coherent products which evolve, learn and adapt. === Sociology === The self-organizing behavior of social animals and the self-organization of simple mathematical structures both suggest that self-organization should be expected in human society. Tell-tale signs of self-organization are usually statistical properties shared with self-organizing physical systems. Examples such as critical mass, herd behavior, groupthink and others, abound in sociology, economics, behavioral finance and anthropology. Spontaneous order can be influenced by arousal. In social theory, the concept of self-referentiality has been introduced as a sociological application of self-organization theory by Niklas Luhmann (1984). For Luhmann the elements of a social system are self-producing communications, i.e. a communication produces further communications and hence a social system can reproduce itself as long as there is dynamic communication. For Luhmann, human beings are sensors in the environment of the system. Luhmann developed an evolutionary theory of society and its subsystems, using functional analyses and systems theory. === Economics === The market economy is sometimes said to be self-organizing. Paul Krugman has written on the role that market self-organization plays in the business cycle in his book The Self Organizing Economy. Friedrich Hayek coined the term catallaxy to describe a "self-organizing system of voluntary co-operation", in regards to the spontaneous order of the free market economy. Neo-classical economists hold that imposing central planning usually makes the self-organized economic system less efficient. On the other end of the spectrum, economists consider that market failures are so significant that self-organization produces bad results and that the state should direct production and pricing. Most economists adopt an intermediate position and recommend a mixture of market economy and command economy characteristics (sometimes called a mixed economy). When applied to economics, the concept of self-organization can quickly become ideologically imbued. === Learning === Enabling others to "learn how to learn" is often taken to mean instructing them how to submit to being taught. Self-organized learning (SOL) denies that "the expert knows best" or that there is ever "the one best method", insisting instead on "the construction of personally significant, relevant and viable meaning" to be tested experientially by the learner. This may be collaborative, and more rewarding personally. It is seen as a lifelong process, not limited to specific learning environments (home, school, university) or under the control of authorities such as parents and professors. It needs to be tested, and intermittently revised, through the personal experience of the learner. It need not be restricted by either consciousness or language. Fritjof Capra argued that it is poorly recognized within psychology and education. It may be related to cybernetics as it involves a negative feedback control loop, or to systems theory. It can be conducted as a learning conversation or dialog between learners or within one person. === Transportation === The self-organizing behavior of drivers in traffic flow determines almost all the spatiotemporal behavior of traffic, such as traffic breakdown at a highway bottleneck, highway capacity, and the emergence of moving traffic jams. These self-organizing effects are explained by Boris Kerner's three-phase traffic theory. === Linguistics === Order appears spontaneously in the evolution of language as individual and population behavior interacts with biological evolution. === Research === Self-organized funding allocation (SOFA) is a method of distributing funding for scientific research. In this system, each researcher is allocated an equal amount of funding, and is required to anonymously allocate a fraction of their funds to the research of others. Proponents of SOFA argue that it would result in similar distribution of funding as the present grant system, but with less overhead. In 2016, a test pilot of SOFA began in the Netherlands. == Criticism == Heinz Pagels, in a 1985 review of Ilya Prigogine and Isabelle Stengers's book Order Out of Chaos in Physics Today, appeals to authority: Most scientists would agree with the critical view expressed in Problems of Biological Physics (Springer Verlag, 1981) by the biophysicist L. A. Blumenfeld, when he wrote: "The meaningful macroscopic ordering of biological structure does not arise due to the increase of certain parameters or a system above their critical values. These structures are built according to program-like complicated architectural structures, the meaningful information created during many billions of years of chemical and biological evolution being used." Life is a consequence of microscopic, not macroscopic, organization. Of course, Blumenfeld does not answer the further question of how those program-like structures emerge in the first place. His explanation leads directly to infinite regress. In short, they [Prigogine and Stengers] maintain that time irreversibility is not derived from a time-independent microworld, but is itself fundamental. The virtue of their idea is that it resolves what they perceive as a "clash of doctrines" about the nature of time in physics. Most physicists would agree that there is neither empirical evidence to support their view, nor is there a mathematical necessity for it. There is no "clash of doctrines." Only Prigogine and a few colleagues hold to these speculations which, in spite of their efforts, continue to live in the twilight zone of scientific credibility. In theology, Thomas Aquinas (1225–1274) in his Summa Theologica assumes a teleological created universe in rejecting the idea that something can be a self-sufficient cause of its own organization: Since nature works for a determinate end under the direction of a higher agent, whatever is done by nature must needs be traced back to God, as to its first cause. So also whatever is done voluntarily must also be traced back to some higher cause other than human reason or will, since these can change or fail; for all things that are changeable and capable of defect must be traced back to an immovable and self-necessary first principle, as was shown in the body of the Article. == See also == == Notes == == References == == Further reading == == External links ==
Wikipedia/Self-organizing_systems
Energy policies are the government's strategies and decisions regarding the production, distribution, and consumption of energy within a specific jurisdiction. Energy is essential for the functioning of modern economies because they require energy for many sectors, such as industry, transport, agriculture, housing. The main components of energy policy include legislation, international treaties, energy subsidies and other public policy techniques. The energy sector emits more greenhouse gas worldwide than any other sector. Therefore, energy policies are closely related to climate policies. These decisions affect how high the greenhouse gas emissions by that country are. == Purposes == Access to energy is critical for basic social needs, such as lighting, heating, cooking, and healthcare. Given the importance of energy, the price of energy has a direct effect on jobs, economic productivity, business competitiveness, and the cost of goods and services. Frequently the dominant issue of energy policy is the risk of supply-demand mismatch (see: energy crisis). Current energy policies also address environmental issues (see: climate change), particularly challenging because of the need to reconcile global objectives and international rules with domestic needs and laws. The "human dimensions" of energy use are of increasing interest to business, utilities, and policymakers. Using the social sciences to gain insights into energy consumer behavior can help policymakers to make better decisions about broad-based climate and energy options. This could facilitate more efficient energy use, renewable-energy commercialization, and carbon-emission reductions. == Approaches == The attributes of energy policy may include legislation, international treaties, incentives to investment, guidelines for energy conservation, taxation and other public policy techniques. Economic and energy modelling can be used by governmental or inter-governmental bodies as an advisory and analysis tool. Energy planning is more detailed than energy policy. === National energy policy === Some governments state an explicit energy policy. Others do not but in any case, each government practices some type of energy policy. A national energy policy comprises a set of measures involving that country's laws, treaties and agency directives. There are a number of elements that are contained in a national energy policy. Some important elements intrinsic to an energy policy include: What is the extent of energy self-sufficiency for this nation Where future energy sources will derive How future energy will be consumed (e.g. among sectors) What are the goals for future energy intensity, ratio of energy consumed to GDP How can the national policy drive province, state and municipal functions What specific mechanisms (e.g. taxes, incentives, manufacturing standards) are in place to implement the total policy Do you want to develop and promote a plan for how to get the world to net zero emissions? What fiscal policies related to energy products and services should be used (taxes, exemptions, subsidies, etc.)? What legislation affecting energy use, such as efficiency standards, emission standards, is needed? === Relationship to other government policies === Energy policy sometimes dominates and sometimes is dominated by other government policies. For example energy policy may dominate, supplying free coal to poor families and schools thus supporting social policy, but thus causing air pollution and so impeding heath policy and environmental policy.: 13  On the other hand energy policy may be dominated by defense policy, for example some counties started building expensive nuclear power plants to supply material for bombs. Or defense policy may be dominated for a while, eventually resulting in stranded assets, such as Nord Stream 2. Energy policy is closely related to climate change policy because totalled worldwide the energy sector emits more greenhouse gas than other sectors. Energy policy decisions are sometimes not taken democratically. === Corporate energy policy === In 2019, some companies “have committed to set climate targets across their operations and value chains aligned with limiting global temperature rise to 1.5°C above pre-industrial levels and reaching net-zero emissions by no later than 2050”. Corporate power purchase agreements can kickstart renewable energy projects, but the energy policies of some countries do not allow or discourage them. == By type of energy == === Nuclear energy === === Renewable energy === == Examples == === China === === India === === Ecuador === === European Union === === Russia === === United Kingdom === === United States === == By country == Energy policies vary by country, see tables below. == See also == Energy balance Energy industry Energy security Energy supply Energy transition Environmental policy Petroleum politics Sustainable energy All pages with titles containing Energy policy of == References == == External links == "Energy Policies of (Country x)" series, International Energy Agency UN-Energy Archived 2011-06-25 at the Wayback Machine - Global energy policy co-ordination Renewable Energy Policy Network (REN21) Information on energy institutions, policies and local energy companies by country, Enerdata Publications
Wikipedia/Energy_policy
The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general and are applicable in other natural sciences. Traditionally, thermodynamics has recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law. A more fundamental statement was later labelled as the zeroth law after the first three laws had been established. The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. The first law of thermodynamics states that, when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy. This also results in the observation that, in an externally isolated system, even with internal changes, the sum of all forms of energy must remain constant, as energy cannot be created or destroyed. The second law of thermodynamics states that in a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems never decreases. A common corollary of the statement is that heat does not spontaneously pass from a colder body to a warmer body. The third law of thermodynamics states that a system's entropy approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses), the entropy of a system at absolute zero is typically close to zero. The first and second laws prohibit two kinds of perpetual motion machines, respectively: the perpetual motion machine of the first kind which produces work with no energy input, and the perpetual motion machine of the second kind which spontaneously converts thermal energy into mechanical work. == History == The history of thermodynamics is fundamentally interwoven with the history of physics and the history of chemistry, and ultimately dates back to theories of heat in antiquity. The laws of thermodynamics are the result of progress made in this field over the nineteenth and early twentieth centuries. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824 in his book Reflections on the Motive Power of Fire. By 1860, as formalized in the works of scientists such as Rudolf Clausius and William Thomson, what are now known as the first and second laws were established. Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated by Walther Nernst over the period 1906–1912. While the numbering of the laws is universal today, various textbooks throughout the 20th century have numbered the laws differently. In some fields, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Gradually, this resolved itself and a zeroth law was later added to allow for a self-consistent definition of temperature. Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard textbooks. == Zeroth law == The zeroth law of thermodynamics provides for the foundation of temperature as an empirical parameter in thermodynamic systems and establishes the transitive relation between the temperatures of multiple bodies in thermal equilibrium. The law may be stated in the following form: If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law". Some statements go further, so as to supply the important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in a real number sequence from colder to hotter. These concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century. The name 'zeroth law' was invented by Ralph H. Fowler in the 1930s, long after the first, second, and third laws were widely recognized. The law allows the definition of temperature in a non-circular way without reference to entropy, its conjugate variable. Such a temperature definition is said to be 'empirical'. == First law == The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes. In general, the conservation law states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. In a closed system (i.e. there is no transfer of matter into or out of the system), the first law states that the change in internal energy of the system (ΔUsystem) is equal to the difference between the heat supplied to the system (Q) and the work (W) done by the system on its surroundings. (Note, an alternate sign convention, not used in this article, is to define W as the work done on the system by its surroundings): Δ U s y s t e m = Q − W . {\displaystyle \Delta U_{\rm {system}}=Q-W.} For processes that include the transfer of matter, a further statement is needed. When two initially isolated systems are combined into a new system, then the total internal energy of the new system, Usystem, will be equal to the sum of the internal energies of the two initial systems, U1 and U2: U s y s t e m = U 1 + U 2 . {\displaystyle U_{\rm {system}}=U_{1}+U_{2}.} The First Law encompasses several principles: Conservation of energy, which says that energy can be neither created nor destroyed, but can only change form. A particular consequence of this is that the total energy of an isolated system does not change. The concept of internal energy and its relationship to temperature. If a system has a definite temperature, then its total energy has three distinguishable components, termed kinetic energy (energy due to the motion of the system as a whole), potential energy (energy resulting from an externally imposed force field), and internal energy. The establishment of the concept of internal energy distinguishes the first law of thermodynamics from the more general law of conservation of energy. E t o t a l = K E s y s t e m + P E s y s t e m + U s y s t e m {\displaystyle E_{\rm {total}}=KE_{\rm {system}}+PE_{\rm {system}}+U_{\rm {system}}} Work is a process of transferring energy to or from a system in ways that can be described by macroscopic mechanical forces acting between the system and its surroundings. The work done by the system can come from its overall kinetic energy, from its overall potential energy, or from its internal energy. For example, when a machine (not a part of the system) lifts a system upwards, some energy is transferred from the machine to the system. The system's energy increases as work is done on the system and in this particular case, the energy increase of the system is manifested as an increase in the system's gravitational potential energy. Work added to the system increases the potential energy of the system. When matter is transferred into a system, the internal energy and potential energy associated with it are transferred into the new combined system. ( u Δ M ) i n = Δ U s y s t e m {\displaystyle \left(u\,\Delta M\right)_{\rm {in}}=\Delta U_{\rm {system}}} where u denotes the internal energy per unit mass of the transferred matter, as measured while in the surroundings; and ΔM denotes the amount of transferred mass. The flow of heat is a form of energy transfer. Heat transfer is the natural process of moving energy to or from a system, other than by work or the transfer of matter. In a diathermal system, the internal energy can only be changed by the transfer of energy as heat: Δ U s y s t e m = Q . {\displaystyle \Delta U_{\rm {system}}=Q.} Combining these principles leads to one traditional statement of the first law of thermodynamics: it is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible. == Second law == The second law of thermodynamics indicates the irreversibility of natural processes, and in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, especially of temperature. It can be formulated in a variety of interesting and important ways. One of the simplest is the Clausius statement, that heat does not spontaneously pass from a colder to a hotter body. It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium with itself but not necessarily with each other, are then allowed to interact, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values. The second law is applicable to a wide variety of processes, both reversible and irreversible. According to the second law, in a reversible heat transfer, an element of heat transferred, δ Q {\displaystyle \delta Q} , is the product of the temperature ( T {\displaystyle T} ), both of the system and of the sources or destination of the heat, with the increment ( d S {\displaystyle dS} ) of the system's conjugate variable, its entropy ( S {\displaystyle S} ): δ Q = T d S . {\displaystyle \delta Q=T\,dS\,.} While reversible processes are a useful and convenient theoretical limiting case, all natural processes are irreversible. A prime example of this irreversibility is the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies, initially of different temperatures, come into direct thermal connection, then heat immediately and spontaneously flows from the hotter body to the colder one. Entropy may also be viewed as a physical measure concerning the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. Such details are often referred to as disorder on a microscopic or molecular scale, and less often as dispersal of energy. For two given macroscopically specified states of a system, there is a mathematically defined quantity called the 'difference of information entropy between them'. This defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from the macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the initial macroscopically specified state from the final macroscopically specified state. Equivalently, in a thermodynamic process, energy spreads. == Third law == The third law of thermodynamics can be stated as: A system's entropy approaches a constant value as its temperature approaches absolute zero. At absolute zero temperature, the system is in the state with the minimum thermal energy, the ground state. The constant value (not necessarily zero) of entropy at this point is called the residual entropy of the system. With the exception of non-crystalline solids (e.g. glass) the residual entropy of a system is typically close to zero. However, it reaches zero only when the system has a unique ground state (i.e., the state with the minimum thermal energy has only one configuration, or microstate). Microstates are used here to describe the probability of a system being in a specific state, as each microstate is assumed to have the same probability of occurring, so macroscopic states with fewer microstates are less probable. In general, entropy is related to the number of possible microstates according to the Boltzmann principle S = k B l n Ω {\displaystyle S=k_{\mathrm {B} }\,\mathrm {ln} \,\Omega } where S is the entropy of the system, kB is the Boltzmann constant, and Ω the number of microstates. At absolute zero there is only 1 microstate possible (Ω = 1 as all the atoms are identical for a pure substance, and as a result all orders are identical as there is only one combination) and ln ⁡ ( 1 ) = 0 {\displaystyle \ln(1)=0} . == Onsager relations == The Onsager reciprocal relations have been considered the fourth law of thermodynamics. They describe the relation between thermodynamic flows and forces in non-equilibrium thermodynamics, under the assumption that thermodynamic variables can be defined locally in a condition of local equilibrium. These relations are derived from statistical mechanics under the principle of microscopic reversibility (in the absence of external magnetic fields). Given a set of extensive parameters Xi (energy, mass, entropy, number of particles and so on) and thermodynamic forces Fi (related to their related intrinsic parameters, such as temperature and pressure), the Onsager theorem states that d J k d F i | F i = 0 = d J i d F k | F k = 0 {\displaystyle {\frac {\mathrm {d} J_{k}}{\mathrm {d} F_{i}}}{\bigg |}_{F_{i}=0}~=~{\frac {\mathrm {d} J_{i}}{\mathrm {d} F_{k}}}{\bigg |}_{F_{k}=0}} where i, k = 1,2,3,... index every parameter and its related force, and J i = d X i d t {\displaystyle J_{i}={\frac {\mathrm {d} X_{i}}{\mathrm {d} t}}} are called the thermodynamic flows. == See also == Chemical thermodynamics Enthalpy Entropy production Ginsberg's theorem (Parody of the laws of thermodynamics) H-theorem Statistical mechanics Table of thermodynamic equations == References == == Further reading == Atkins, Peter (2007). Four Laws That Drive the Universe. OUP Oxford. ISBN 978-0199232369 Goldstein, Martin & Inge F. (1993). The Refrigerator and the Universe. Harvard Univ. Press. ISBN 978-0674753259 Guggenheim, E.A. (1985). Thermodynamics. An Advanced Treatment for Chemists and Physicists, seventh edition. ISBN 0-444-86951-4 Adkins, C. J., (1968) Equilibrium Thermodynamics. McGraw-Hill ISBN 0-07-084057-1 == External links == Media related to Laws of thermodynamics at Wikimedia Commons
Wikipedia/Laws_of_thermodynamics
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0); and an exact form is a differential form, α, that is the exterior derivative of another differential form β, i.e. α = dβ. Thus, an exact form is in the image of d, and a closed form is in the kernel of d (also known as null space). For an exact form α, α = dβ for some differential form β of degree one less than that of α. The form β is called a "potential form" or "primitive" for α. Since the exterior derivative of a closed form is zero, β is not unique, but can be modified by the addition of any closed form of degree one less than that of α. Because d2 = 0, every exact form is necessarily closed. The question of whether every closed form is exact depends on the topology of the domain of interest. On a contractible domain, every closed form is exact by the Poincaré lemma. More general questions of this kind on an arbitrary differentiable manifold are the subject of de Rham cohomology, which allows one to obtain purely topological information using differential methods. == Examples == A simple example of a form that is closed but not exact is the 1-form d θ {\displaystyle d\theta } given by the derivative of argument on the punctured plane R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} . Since θ {\displaystyle \theta } is not actually a function (see the next paragraph) d θ {\displaystyle d\theta } is not an exact form. Still, d θ {\displaystyle d\theta } has vanishing derivative and is therefore closed. Note that the argument θ {\displaystyle \theta } is only defined up to an integer multiple of 2 π {\displaystyle 2\pi } since a single point p {\displaystyle p} can be assigned different arguments r {\displaystyle r} , r + 2 π {\displaystyle r+2\pi } , etc. We can assign arguments in a locally consistent manner around p {\displaystyle p} , but not in a globally consistent manner. This is because if we trace a loop from p {\displaystyle p} counterclockwise around the origin and back to p {\displaystyle p} , the argument increases by 2 π {\displaystyle 2\pi } . Generally, the argument θ {\displaystyle \theta } changes by ∮ S 1 d θ {\displaystyle \oint _{S^{1}}d\theta } over a counter-clockwise oriented loop S 1 {\displaystyle S^{1}} . Even though the argument θ {\displaystyle \theta } is not technically a function, the different local definitions of θ {\displaystyle \theta } at a point p {\displaystyle p} differ from one another by constants. Since the derivative at p {\displaystyle p} only uses local data, and since functions that differ by a constant have the same derivative, the argument has a globally well-defined derivative " d θ {\displaystyle d\theta } ". The upshot is that d θ {\displaystyle d\theta } is a one-form on R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} that is not actually the derivative of any well-defined function θ {\displaystyle \theta } . We say that d θ {\displaystyle d\theta } is not exact. Explicitly, d θ {\displaystyle d\theta } is given as: d θ = − y d x + x d y x 2 + y 2 , {\displaystyle d\theta ={\frac {-y\,dx+x\,dy}{x^{2}+y^{2}}},} which by inspection has derivative zero. Notice that if we restrict the domain to the right half-plane, we can write d θ = d ( tan − 1 ⁡ ( y / x ) ) {\displaystyle d\theta =d\left(\tan ^{-1}(y/x)\right)} , but the angle function θ = tan − 1 ⁡ ( y / x ) {\displaystyle \theta =\tan ^{-1}(y/x)} is neither smooth nor continuous over R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} (as is any choice of angle function). Because d θ {\displaystyle d\theta } has vanishing derivative, we say that it is closed. On the other hand, for the one-form α = − y d x + x d y , {\displaystyle \alpha =-y\,dx+x\,dy,} d α ≠ 0 {\displaystyle d\alpha \neq 0} . Thus α {\displaystyle \alpha } is not even closed, never mind exact. The form d θ {\displaystyle d\theta } generates the de Rham cohomology group H d R 1 ( R 2 ∖ { 0 } ) ≅ R , {\displaystyle H_{dR}^{1}(\mathbb {R} ^{2}\smallsetminus \{0\})\cong \mathbb {R} ,} meaning that any closed form ω {\displaystyle \omega } is the sum of an exact form d f {\displaystyle df} and a multiple of d θ {\displaystyle d\theta } : ω = d f + k d θ {\displaystyle \omega =df+k\ d\theta } , where k = 1 2 π ∮ S 1 ω {\textstyle k={\frac {1}{2\pi }}\oint _{S^{1}}\omega } accounts for a non-trivial contour integral around the origin, which is the only obstruction to a closed form on the punctured plane (locally the derivative of a potential function) being the derivative of a globally defined function. == Examples in low dimensions == Differential forms in R 2 {\displaystyle \mathbb {R} ^{2}} and R 3 {\displaystyle \mathbb {R} ^{3}} were well known in the mathematical physics of the nineteenth century. In the plane, 0-forms are just functions, and 2-forms are functions times the basic area element d x ∧ d y {\displaystyle dx\wedge dy} , so that it is the 1-forms α = f ( x , y ) d x + g ( x , y ) d y {\displaystyle \alpha =f(x,y)\,dx+g(x,y)\,dy} that are of real interest. The formula for the exterior derivative d {\displaystyle d} here is d α = ( g x − f y ) d x ∧ d y {\displaystyle d\alpha =(g_{x}-f_{y})\,dx\wedge dy} where the subscripts denote partial derivatives. Therefore the condition for α {\displaystyle \alpha } to be closed is f y = g x . {\displaystyle f_{y}=g_{x}.} In this case if h ( x , y ) {\displaystyle h(x,y)} is a function then d h = h x d x + h y d y . {\displaystyle dh=h_{x}\,dx+h_{y}\,dy.} The implication from 'exact' to 'closed' is then a consequence of the symmetry of second derivatives, with respect to x {\displaystyle x} and y {\displaystyle y} . The gradient theorem asserts that a 1-form is exact if and only if the line integral of the form depends only on the endpoints of the curve, or equivalently, if the integral around any smooth closed curve is zero. === Vector field analogies === On a Riemannian manifold, or more generally a pseudo-Riemannian manifold, k-forms correspond to k-vector fields (by duality via the metric), so there is a notion of a vector field corresponding to a closed or exact form. In 3 dimensions, an exact vector field (thought of as a 1-form) is called a conservative vector field, meaning that it is the derivative (gradient) of a 0-form (smooth scalar field), called the scalar potential. A closed vector field (thought of as a 1-form) is one whose derivative (curl) vanishes, and is called an irrotational vector field. Thinking of a vector field as a 2-form instead, a closed vector field is one whose derivative (divergence) vanishes, and is called an incompressible flow (sometimes solenoidal vector field). The term incompressible is used because a non-zero divergence corresponds to the presence of sources and sinks in analogy with a fluid. The concepts of conservative and incompressible vector fields generalize to n dimensions, because gradient and divergence generalize to n dimensions; curl is defined only in three dimensions, thus the concept of irrotational vector field does not generalize in this way. == Poincaré lemma == The Poincaré lemma states that if B is an open ball in Rn, any closed p-form ω defined on B is exact, for any integer p with 1 ≤ p ≤ n. More generally, the lemma states that on a contractible open subset of a manifold (e.g., R n {\displaystyle \mathbb {R} ^{n}} ), a closed p-form, p > 0, is exact. == Formulation as cohomology == When the difference of two closed forms is an exact form, they are said to be cohomologous to each other. That is, if ζ and η are closed forms, and one can find some β such that ζ − η = d β {\displaystyle \zeta -\eta =d\beta } then one says that ζ and η are cohomologous to each other. Exact forms are sometimes said to be cohomologous to zero. The set of all forms cohomologous to a given form (and thus to each other) is called a de Rham cohomology class; the general study of such classes is known as cohomology. It makes no real sense to ask whether a 0-form (smooth function) is exact, since d increases degree by 1; but the clues from topology suggest that only the zero function should be called "exact". The cohomology classes are identified with locally constant functions. Using contracting homotopies similar to the one used in the proof of the Poincaré lemma, it can be shown that de Rham cohomology is homotopy-invariant. == Relevance to thermodynamics == Consider a thermodynamic system whose equilibrium states are specified by n {\displaystyle n} thermodynamic variables, x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} . The first law of thermodynamics can be stated as follows: In any process that results in an infinitesimal change of state where the internal energy of the system changes by an amount d U ( x 1 , x 2 , … , x n ) , {\displaystyle dU(x_{1},x_{2},\ldots ,x_{n}),} and an amount of work d W ( x 1 , x 2 , … , x n ) {\displaystyle dW(x_{1},x_{2},\ldots ,x_{n})} is done on the system, one must also supply an amount of heat d U − d W . {\displaystyle dU-dW.} The second law of thermodynamics is an empirical law of nature which says that there is no thermodynamic system for which d U = d W {\displaystyle dU=dW} in every circumstance, or in mathematical terms that, the differential form d U − d W {\displaystyle dU-dW} is not closed. Caratheodory's theorem further states that there exists an integrating denominator T {\displaystyle T} such that d S ≡ d U − d W T {\displaystyle dS\equiv {\frac {dU-dW}{T}}} is a closed 1-form. The integrating denominator T {\displaystyle T} is the temperature, and the state function S ( x 1 , x 2 , … , x n ) {\displaystyle S(x_{1},x_{2},\ldots ,x_{n})} is the equilibrium entropy. == Application in electrodynamics == In electrodynamics, the case of the magnetic field B → ( r ) {\displaystyle {\vec {B}}(\mathbf {r} )} produced by a stationary electrical current is important. There one deals with the vector potential A → ( r ) {\displaystyle {\vec {A}}(\mathbf {r} )} of this field. This case corresponds to k = 2, and the defining region is the full R 3 {\displaystyle \mathbb {R} ^{3}} . The current-density vector is j → {\displaystyle {\vec {j}}} . It corresponds to the current two-form I := j 1 ( x 1 , x 2 , x 3 ) d x 2 ∧ d x 3 + j 2 ( x 1 , x 2 , x 3 ) d x 3 ∧ d x 1 + j 3 ( x 1 , x 2 , x 3 ) d x 1 ∧ d x 2 . {\displaystyle \mathbf {I} :=j_{1}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{2}\wedge {\rm {d}}x_{3}+j_{2}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{3}\wedge {\rm {d}}x_{1}+j_{3}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{1}\wedge {\rm {d}}x_{2}.} For the magnetic field B → {\displaystyle {\vec {B}}} one has analogous results: it corresponds to the induction two-form Φ B := B 1 d x 2 ∧ d x 3 + ⋯ {\displaystyle \Phi _{B}:=B_{1}{\rm {d}}x_{2}\wedge {\rm {d}}x_{3}+\cdots } , and can be derived from the vector potential A → {\displaystyle {\vec {A}}} , or the corresponding one-form A {\displaystyle \mathbf {A} } , B → = curl ⁡ A → = { ∂ A 3 ∂ x 2 − ∂ A 2 ∂ x 3 , ∂ A 1 ∂ x 3 − ∂ A 3 ∂ x 1 , ∂ A 2 ∂ x 1 − ∂ A 1 ∂ x 2 } , or Φ B = d A . {\displaystyle {\vec {B}}=\operatorname {curl} {\vec {A}}=\left\{{\frac {\partial A_{3}}{\partial x_{2}}}-{\frac {\partial A_{2}}{\partial x_{3}}},{\frac {\partial A_{1}}{\partial x_{3}}}-{\frac {\partial A_{3}}{\partial x_{1}}},{\frac {\partial A_{2}}{\partial x_{1}}}-{\frac {\partial A_{1}}{\partial x_{2}}}\right\},{\text{ or }}\Phi _{B}={\rm {d}}\mathbf {A} .} Thereby the vector potential A → {\displaystyle {\vec {A}}} corresponds to the potential one-form A := A 1 d x 1 + A 2 d x 2 + A 3 d x 3 . {\displaystyle \mathbf {A} :=A_{1}\,{\rm {d}}x_{1}+A_{2}\,{\rm {d}}x_{2}+A_{3}\,{\rm {d}}x_{3}.} The closedness of the magnetic-induction two-form corresponds to the property of the magnetic field that it is source-free: div ⁡ B → ≡ 0 {\displaystyle \operatorname {div} {\vec {B}}\equiv 0} , i.e., that there are no magnetic monopoles. In a special gauge, div ⁡ A → = ! 0 {\displaystyle \operatorname {div} {\vec {A}}{~{\stackrel {!}{=}}~}0} , this implies for i = 1, 2, 3 A i ( r → ) = ∫ μ 0 j i ( r → ′ ) d x 1 ′ d x 2 ′ d x 3 ′ 4 π | r → − r → ′ | . {\displaystyle A_{i}({\vec {r}})=\int {\frac {\mu _{0}j_{i}\left({\vec {r}}'\right)\,\,dx_{1}'\,dx_{2}'\,dx_{3}'}{4\pi |{\vec {r}}-{\vec {r}}'|}}\,.} (Here μ 0 {\displaystyle \mu _{0}} is the magnetic constant.) This equation is remarkable, because it corresponds completely to a well-known formula for the electrical field E → {\displaystyle {\vec {E}}} , namely for the electrostatic Coulomb potential φ ( x 1 , x 2 , x 3 ) {\displaystyle \varphi (x_{1},x_{2},x_{3})} of a charge density ρ ( x 1 , x 2 , x 3 ) {\displaystyle \rho (x_{1},x_{2},x_{3})} . At this place one can already guess that E → {\displaystyle {\vec {E}}} and B → , {\displaystyle {\vec {B}},} ρ {\displaystyle \rho } and j → , {\displaystyle {\vec {j}},} φ {\displaystyle \varphi } and A → {\displaystyle {\vec {A}}} can be unified to quantities with six rsp. four nontrivial components, which is the basis of the relativistic invariance of the Maxwell equations. If the condition of stationarity is left, on the left-hand side of the above-mentioned equation one must add, in the equations for A i {\displaystyle A_{i}} , to the three space coordinates, as a fourth variable also the time t, whereas on the right-hand side, in j i ′ {\displaystyle j_{i}'} , the so-called "retarded time", t ′ := t − | r → − r → ′ | c {\displaystyle t':=t-{\frac {|{\vec {r}}-{\vec {r}}'|}{c}}} , must be used, i.e. it is added to the argument of the current-density. Finally, as before, one integrates over the three primed space coordinates. (As usual c is the vacuum velocity of light.) == Notes == == Citations == == References == Chandrasekhar, S. (1939). An Introduction to the Study of Stellar Structure. Dover. Flanders, Harley (1989) [1963]. Differential forms with applications to the physical sciences. New York: Dover Publications. ISBN 978-0-486-66169-8.. Warner, Frank W. (1983), Foundations of differentiable manifolds and Lie groups, Graduate Texts in Mathematics, vol. 94, Springer, ISBN 0-387-90894-3 Napier, Terrence; Ramachandran, Mohan (2011), An introduction to Riemann surfaces, Birkhäuser, ISBN 978-0-8176-4693-6 Singer, I. M.; Thorpe, J. A. (1976), Lecture Notes on Elementary Topology and Geometry, University of Bangalore Press, ISBN 0721114784
Wikipedia/Closed_differential_form
Energy transformation, also known as energy conversion, is the process of changing energy from one form to another. In physics, energy is a quantity that provides the capacity to perform work (e.g. lifting an object) or provides heat. In addition to being converted, according to the law of conservation of energy, energy is transferable to a different location or object or living being, but it cannot be created or destroyed. == Limitations in the conversion of thermal energy == Conversions to thermal energy from other forms of energy may occur with 100% efficiency. Conversion among non-thermal forms of energy may occur with fairly high efficiency, though there is always some energy dissipated thermally due to friction and similar processes. Sometimes the efficiency is close to 100%, such as when potential energy is converted to kinetic energy as an object falls in a vacuum. This also applies to the opposite case; for example, an object in an elliptical orbit around another body converts its kinetic energy (speed) into gravitational potential energy (distance from the other object) as it moves away from its parent body. When it reaches the furthest point, it will reverse the process, accelerating and converting potential energy into kinetic. Since space is a near-vacuum, this process has close to 100% efficiency. Because transformations between non-thermal forms of energy are constrained only by the conservation of energy, they have a theoretical maximum efficiency of 100%. By contrast, transformations from thermal energy to other forms of energy are additionally constrained by the second law of thermodynamics and have a theoretical maximum efficiency strictly less than 100% (see Carnot cycle), and typically much lower. In addition, only a difference in the density of thermal/heat energy (temperature) can be used to perform work. This is because thermal energy represents a particularly disordered form of energy; it is spread out randomly among many available states of a collection of microscopic particles constituting the system (these combinations of position and momentum for each of the particles are said to form a phase space). The measure of this disorder or randomness is entropy, and its defining feature is that the entropy of an isolated system never decreases. One cannot take a high-entropy system (like a hot substance, with a certain amount of thermal energy) and convert it into a low entropy state (like a low-temperature substance, with correspondingly lower energy), without that entropy going somewhere else (like the surrounding air). In other words, there is no way to concentrate energy without spreading out energy somewhere else. Thermal energy in equilibrium at a given temperature already represents the maximal evening-out of energy between all possible states because it is not entirely convertible to a "useful" form, i.e. one that can do more than just affect temperature. The second law of thermodynamics states that the entropy of a closed system can never decrease. For this reason, thermal energy in a system may be converted to other kinds of energy with efficiencies approaching 100% only if the entropie of the universe is increased by other means, to compensate for the decrease in entropy associated with the disappearance of the thermal energy and its entropy content. Otherwise, only a part of that thermal energy may be converted to other kinds of energy (and thus useful work). This is because the remainder of the heat must be reserved to be transferred to a thermal reservoir at a lower temperature. The increase in entropy for this process is greater than the decrease in entropy associated with the transformation of the rest of the heat into other types of energy. In order to make energy transformation more efficient, it is desirable to avoid thermal conversion. For example, the efficiency of nuclear reactors, where the kinetic energy of the nuclei is first converted to thermal energy and then to electrical energy, lies at around 35%. By direct conversion of kinetic energy to electric energy, effected by eliminating the intermediate thermal energy transformation, the efficiency of the energy transformation process can be dramatically improved. == History of energy transformation == Energy transformations in the universe over time are usually characterized by various kinds of energy, which have been available since the Big Bang, later being "released" (that is, transformed to more active types of energy such as kinetic or radiant energy) by a triggering mechanism. === Release of energy from gravitational potential === A direct transformation of energy occurs when hydrogen produced in the Big Bang collects into structures such as planets, in a process during which part of the gravitational potential is to be converted directly into heat. In Jupiter, Saturn, and Neptune, for example, such heat from the continued collapse of the planets' large gas atmospheres continue to drive most of the planets' weather systems. These systems, consisting of atmospheric bands, winds, and powerful storms, are only partly powered by sunlight. However, on Uranus, little of this process occurs. On Earth, a significant portion of the heat output from the interior of the planet, estimated at a third to half of the total, is caused by the slow collapse of planetary materials to a smaller size, generating heat. === Release of energy from radioactive potential === Familiar examples of other such processes transforming energy from the Big Bang include nuclear decay, which releases energy that was originally "stored" in heavy isotopes, such as uranium and thorium. This energy was stored at the time of the nucleosynthesis of these elements. This process uses the gravitational potential energy released from the collapse of Type II supernovae to create these heavy elements before they are incorporated into star systems such as the Solar System and the Earth. The energy locked into uranium is released spontaneously during most types of radioactive decay, and can be suddenly released in nuclear fission bombs. In both cases, a portion of the energy binding the atomic nuclei together is released as heat. === Release of energy from hydrogen fusion potential === In a similar chain of transformations beginning at the dawn of the universe, nuclear fusion of hydrogen in the Sun releases another store of potential energy which was created at the time of the Big Bang. At that time, according to one theory, space expanded and the universe cooled too rapidly for hydrogen to completely fuse into heavier elements. This resulted in hydrogen representing a store of potential energy which can be released by nuclear fusion. Such a fusion process is triggered by heat and pressure generated from the gravitational collapse of hydrogen clouds when they produce stars, and some of the fusion energy is then transformed into starlight. Considering the solar system, starlight, overwhelmingly from the Sun, may again be stored as gravitational potential energy after it strikes the Earth. This occurs in the case of avalanches, or when water evaporates from oceans and is deposited as precipitation high above sea level (where, after being released at a hydroelectric dam, it can be used to drive turbine/generators to produce electricity). Sunlight also drives many weather phenomena on Earth. One example is a hurricane, which occurs when large unstable areas of warm ocean, heated over months, give up some of their thermal energy suddenly to power a few days of violent air movement. Sunlight is also captured by plants as a chemical potential energy via photosynthesis, when carbon dioxide and water are converted into a combustible combination of carbohydrates, lipids, and oxygen. The release of this energy as heat and light may be triggered suddenly by a spark, in a forest fire; or it may be available more slowly for animal or human metabolism when these molecules are ingested, and catabolism is triggered by enzyme action. Through all of these transformation chains, the potential energy stored at the time of the Big Bang is later released by intermediate events, sometimes being stored in several different ways for long periods between releases, as more active energy. All of these events involve the conversion of one kind of energy into others, including heat. == Examples == === Examples of sets of energy conversions in machines === A coal-fired power plant involves these energy transformations: Chemical energy in the coal is converted into thermal energy in the exhaust gases of combustion Thermal energy of the exhaust gases converted into thermal energy of steam through heat exchange Kinetic energy of steam converted to mechanical energy in the turbine Mechanical energy of the turbine is converted to electrical energy by the generator, which is the ultimate output In such a system, the first and fourth steps are highly efficient, but the second and third steps are less efficient. The most efficient gas-fired electrical power stations can achieve 50% conversion efficiency. Oil- and coal-fired stations are less efficient. In a conventional automobile, the following energy transformations occur: Chemical energy in the fuel is converted into kinetic energy of expanding gas via combustion Kinetic energy of expanding gas converted to the linear piston movement Linear piston movement converted to rotary crankshaft movement Rotary crankshaft movement passed into transmission assembly Rotary movement passed out of transmission assembly Rotary movement passed through a differential Rotary movement passed out of differential to drive wheels Rotary movement of drive wheels converted to linear motion of the vehicle === Other energy conversions === There are many different machines and transducers that convert one energy form into another. A short list of examples follows: ATP hydrolysis (chemical energy in adenosine triphosphate → mechanical energy) Battery (electricity) (chemical energy → electrical energy) Electric generator (kinetic energy or mechanical work → electrical energy) Electric heater (electric energy → heat) Fire (chemical energy → heat and light) Friction (kinetic energy → heat) Fuel cell (chemical energy → electrical energy) Geothermal power (heat→ electrical energy) Heat engines, such as the internal combustion engine used in cars, or the steam engine (heat → mechanical energy) Hydroelectric dam (gravitational potential energy → electrical energy) Electric lamp (electrical energy → heat and light) Microphone (sound → electrical energy) Ocean thermal power (heat → electrical energy) Photosynthesis (electromagnetic radiation → chemical energy) Piezoelectrics (strain → electrical energy) Thermoelectric (heat → electrical energy) Wave power (mechanical energy → electrical energy) Windmill (wind energy → electrical energy or mechanical energy) == See also == == References == == Further reading == "Energy—Volume 3: Nuclear energy and energy policies". Applied Energy. 5 (4): 321. October 1979. doi:10.1016/0306-2619(79)90027-8. Energy Transfer and Transformation | Core knowledge science
Wikipedia/Energy_transformation
Bioenergy is a type of renewable energy that is derived from plants and animal waste. The biomass that is used as input materials consists of recently living (but now dead) organisms, mainly plants. Thus, fossil fuels are not regarded as biomass under this definition. Types of biomass commonly used for bioenergy include wood, food crops such as corn, energy crops and waste from forests, yards, or farms. According to IEA, bioenergy is the largest source of renewable energy worldwide, representing nearly 55% of all renewable energy consumption, excluding the traditional use of biomass, and contributing over 6% to the global energy supply. Bioenergy can help with climate change mitigation but in some cases the required biomass production can increase greenhouse gas emissions or lead to local biodiversity loss. The environmental impacts of biomass production can be problematic, depending on how the biomass is produced and harvested. But it still produces CO2; so long as the energy is derived from breaking chemical bonds. The IEA's Net Zero by 2050 scenario calls for traditional bioenergy to be phased out by 2030, with modern bioenergy's share increasing from 6.6% in 2020 to 13.1% in 2030 and 18.7% in 2050. Bioenergy has a significant climate change mitigation potential if implemented correctly.: 637  Most of the recommended pathways to limit global warming include substantial contributions from bioenergy in 2050 (average at 200 EJ).: B 7.4  == Definition and terminology == The IPCC Sixth Assessment Report defines bioenergy as "energy derived from any form of biomass or its metabolic by-products".: 1795  It goes on to define biomass in this context as "organic material excluding the material that is fossilised or embedded in geological formations".: 1795  This means that coal or other fossil fuels is not a form of biomass in this context. The term traditional biomass for bioenergy means "the combustion of wood, charcoal, agricultural residues and/or animal dung for cooking or heating in open fires or in inefficient stoves as is common in low-income countries".: 1796  Since biomass can also be used as a fuel directly (e.g. wood logs), the terms biomass and biofuel have sometimes been used interchangeably. However, the term biomass usually denotes the biological raw material the fuel is made of. The terms biofuel or biogas are generally reserved for liquid or gaseous fuels respectively. == Input materials == Wood and wood residues is the largest biomass energy source today. Wood can be used as a fuel directly or processed into pellet fuel or other forms of fuels. Other plants can also be used as fuel, for instance maize, switchgrass, miscanthus and bamboo. The main waste feedstocks are wood waste, agricultural waste, municipal solid waste, and manufacturing waste. Upgrading raw biomass to higher grade fuels can be achieved by different methods, broadly classified as thermal, chemical, or biochemical: Thermal conversion processes use heat as the dominant mechanism to upgrade biomass into a better and more practical fuel. The basic alternatives are torrefaction, pyrolysis, and gasification, these are separated mainly by the extent to which the chemical reactions involved are allowed to proceed (mainly controlled by the availability of oxygen and conversion temperature). Many chemical conversions are based on established coal-based processes, such as the Fischer-Tropsch synthesis. Like coal, biomass can be converted into multiple commodity chemicals. Biochemical processes have developed in nature to break down the molecules of which biomass is composed, and many of these can be harnessed. In most cases, microorganisms are used to perform the conversion. The processes are called anaerobic digestion, fermentation, and composting. == Applications == === Biomass for heating === === Biofuel for transportation === Based on the source of biomass, biofuels are classified broadly into two major categories, depending if food crops are used or not: First-generation (or "conventional") biofuels are made from food sources grown on arable lands, such as sugarcane and maize. Sugars present in this biomass are fermented to produce bioethanol, an alcohol fuel which serves as an additive to gasoline, or in a fuel cell to produce electricity. Bioethanol is made by fermentation, mostly from carbohydrates produced in sugar or starch crops such as corn, sugarcane, or sweet sorghum. Bioethanol is widely used in the United States and in Brazil. Biodiesel is produced from the oils in for instance rapeseed or sugar beets and is the most common biofuel in Europe. Second-generation biofuels (also called "advanced biofuels") utilize non-food-based biomass sources such as perennial energy crops and agricultural residues/waste. The feedstock used to make the fuels either grow on arable land but are byproducts of the main crop, or they are grown on marginal land. Waste from industry, agriculture, forestry and households can also be used for second-generation biofuels, using e.g. anaerobic digestion to produce biogas, gasification to produce syngas or by direct combustion. Cellulosic biomass, derived from non-food sources, such as trees and grasses, is being developed as a feedstock for ethanol production, and biodiesel can be produced from left-over food products like vegetable oils and animal fats. === Production of liquid fuels === Biomass to liquid Bioconversion of biomass to mixed alcohol fuels == Comparison with other renewable energy types == === Land requirement === The surface power production densities of a crop will determine how much land is required for production. The average lifecycle surface power densities for biomass, wind, hydro and solar power production are 0.30 W/m2, 1 W/m2, 3 W/m2 and 5 W/m2, respectively (power in the form of heat for biomass, and electricity for wind, hydro and solar). Lifecycle surface power density includes land used by all supporting infrastructure, manufacturing, mining/harvesting and decommissioning. Another estimate puts the values at 0.08 W/m2 for biomass, 0.14 W/m2 for hydro, 1.84 W/m2 for wind, and 6.63 W/m2 for solar (median values, with none of the renewable sources exceeding 10 W/m2). == Related technologies == === Bioenergy with carbon capture and storage (BECCS) === Carbon capture and storage technology can be used to capture emissions from bioenergy power plants. This process is known as bioenergy with carbon capture and storage (BECCS) and can result in net carbon dioxide removal from the atmosphere. However, BECCS can also result in net positive emissions depending on how the biomass material is grown, harvested, and transported. Deployment of BECCS at scales described in some climate change mitigation pathways would require converting large amounts of cropland. == Climate and sustainability aspects == == Environmental impacts == Bioenergy can either mitigate (i.e. reduce) or increase greenhouse gas emissions. Local environmental impacts can be problematic. For example, forests are sometimes cleared for the production of sugarcane-derived bioethanol, like in the case of a large-scale project in Indonesia in 2025. Biomass production can create significant social and environmental pressure in the locations where the biomass is produced. The impact is primarily related to the low surface power density of biomass. The low surface power density has the effect that much larger land areas are needed in order to produce the same amount of energy, compared to for instance fossil fuels. Long-distance transport of biomass have been criticised as wasteful and unsustainable, and there have been protests against forest biomass export in Sweden and Canada. == Scale and future trends == In 2020 bioenergy produced 58 EJ (exajoules) of energy, compared to 172 EJ from crude oil, 157 EJ from coal, 138 EJ from natural gas, 29 EJ from nuclear, 16 EJ from hydro and 15 EJ from wind, solar and geothermal combined. Most of the global bioenergy is produced from forest resources.: 3 : 1  Generally, bioenergy expansion fell by 50% in 2020. China and Europe are the only two regions that reported significant expansion in 2020, adding 2 GW and 1.2 GW of bioenergy capacity, respectively. Almost all available sawmill residue is already being utilized for pellet production, so there is no room for expansion. For the bioenergy sector to significantly expand in the future, more of the harvested pulpwood must go to pellet mills. However, the harvest of pulpwood (tree thinnings) removes the possibility for these trees to grow old and therefore maximize their carbon holding capacity.: 19  Compared to pulpwood, sawmill residues have lower net emissions: "Some types of biomass feedstock can be carbon-neutral, at least over a period of a few years, including in particular sawmill residues. These are wastes from other forest operations that imply no additional harvesting, and if otherwise burnt as waste or left to rot would release carbon to the atmosphere in any case.": 68  == By country == == See also == == References == === Sources ===
Wikipedia/Bioenergy
Gravitational energy or gravitational potential energy is the potential energy an object with mass has due to the gravitational potential of its position in a gravitational field. Mathematically, it is the minimum mechanical work that has to be done against the gravitational force to bring a mass from a chosen reference point (often an "infinite distance" from the mass generating the field) to some other point in the field, which is equal to the change in the kinetic energies of the objects as they fall towards each other. Gravitational potential energy increases when two objects are brought further apart and is converted to kinetic energy as they are allowed to fall towards each other. == Formulation == For two pairwise interacting point particles, the gravitational potential energy U {\displaystyle U} is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): U = − W g = − ∫ F → g ⋅ d r → {\displaystyle U=-W_{g}=-\int {\vec {F}}_{g}\cdot d{\vec {r}}} where d r → {\textstyle d{\vec {r}}} is the displacement vector of the mass, F g → {\displaystyle {\vec {F_{g}}}} is gravitational force acting on it and ⋅ {\textstyle \cdot } denotes scalar product. == Newtonian mechanics == In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude & direction of gravitational force experienced by a point mass m {\displaystyle m} , due to the presence of another point mass M {\displaystyle M} at a distance r {\displaystyle r} , is given by Newton's law of gravitation. Taking origin to be at the position of M {\displaystyle M} , F g → = − G M m r 2 r ^ {\displaystyle {\vec {F_{g}}}=-{\frac {GMm}{r^{2}}}{\hat {r}}} To get the total work done by the gravitational force in bringing point mass m {\displaystyle m} from infinity to final distance R {\displaystyle R} (for example, the radius of Earth) from point mass M {\textstyle M} , the force is integrated with respect to displacement: W g = ∫ F → g ⋅ d r → = − ∫ ∞ R G M m r 2 d r = G M m r | ∞ R = G M m R {\displaystyle W_{g}=\int {\vec {F}}_{g}\cdot d{\vec {r}}=-\int _{\infty }^{R}{\frac {GMm}{r^{2}}}dr=\left.{\frac {GMm}{r}}\right|_{\infty }^{R}={\frac {GMm}{R}}} Gravitational potential energy being the minimum (quasi-static) work that needs to be done against gravitational force in this procedure, === Simplified version for Earth's surface === In the common situation where a much smaller mass m {\displaystyle m} is moving near the surface of a much larger object with mass M {\displaystyle M} , the gravitational field is nearly constant and so the expression for gravitational energy can be considerably simplified. The change in potential energy moving from the surface (a distance R {\displaystyle R} from the center) to a height h {\displaystyle h} above the surface is Δ U = G M m R − G M m R + h = G M m R ( 1 − 1 1 + h / R ) {\displaystyle {\begin{aligned}\Delta U&={\frac {GMm}{R}}-{\frac {GMm}{R+h}}\\&={\frac {GMm}{R}}\left(1-{\frac {1}{1+h/R}}\right)\end{aligned}}} If h / R {\displaystyle h/R} is small, as it must be close to the surface where g {\displaystyle g} is constant, then this expression can be simplified using the binomial approximation 1 1 + h / R ≈ 1 − h R {\displaystyle {\frac {1}{1+h/R}}\approx 1-{\frac {h}{R}}} to Δ U ≈ G M m R [ 1 − ( 1 − h R ) ] Δ U ≈ G M m h R 2 Δ U ≈ m ( G M R 2 ) h {\displaystyle {\begin{aligned}\Delta U&\approx {\frac {GMm}{R}}\left[1-\left(1-{\frac {h}{R}}\right)\right]\\\Delta U&\approx {\frac {GMmh}{R^{2}}}\\\Delta U&\approx m\left({\frac {GM}{R^{2}}}\right)h\end{aligned}}} As the gravitational field is g = G M / R 2 {\displaystyle g=GM/R^{2}} , this reduces to Δ U ≈ m g h {\displaystyle \Delta U\approx mgh} Note, this is the change of energy in gaining some height h {\displaystyle h} from the surface. == General relativity == In general relativity gravitational energy is extremely complex, and there is no single agreed upon definition of the concept. It is sometimes modelled via the Landau–Lifshitz pseudotensor that allows retention for the energy–momentum conservation laws of classical mechanics. Addition of the matter stress–energy tensor to the Landau–Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor that has a vanishing 4-divergence in all frames—ensuring the conservation law. Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a tensor. == See also == Gravitational binding energy Gravitational potential Gravitational potential energy storage Positive energy theorem == References ==
Wikipedia/Gravitational_potential_energy
Solar thermal energy (STE) is a form of energy and a technology for harnessing solar energy to generate thermal energy for use in industry, and in the residential and commercial sectors. Solar thermal collectors are classified by the United States Energy Information Administration as low-, medium-, or high-temperature collectors. Low-temperature collectors are generally unglazed and used to heat swimming pools or to heat ventilation air. Medium-temperature collectors are also usually flat plates but are used for heating water or air for residential and commercial use. High-temperature collectors concentrate sunlight using mirrors or lenses and are generally used for fulfilling heat requirements up to 300 °C (600 °F) / 20 bar (300 psi) pressure in industries, and for electric power production. Two categories include Concentrated Solar Thermal (CST) for fulfilling heat requirements in industries, and concentrated solar power (CSP) when the heat collected is used for electric power generation. CST and CSP are not replaceable in terms of application. Unlike photovoltaic cells that convert sunlight directly into electricity, solar thermal systems convert it into heat. They use mirrors or lenses to concentrate sunlight onto a receiver, which in turn heats a water reservoir. The heated water can then be used in homes. The advantage of solar thermal is that the heated water can be stored until it is needed, eliminating the need for a separate energy storage system. Solar thermal power can also be converted to electricity by using the steam generated from the heated water to drive a turbine connected to a generator. However, because generating electricity this way is much more expensive than photovoltaic power plants, there are very few in use today. == History == Augustin Mouchot demonstrated a solar collector with a cooling engine making ice cream at the 1878 Universal Exhibition in Paris. The first installation of solar thermal energy equipment occurred in the Sahara approximately in 1910 by Frank Shuman when a steam engine was run on steam produced by sunlight. Because liquid fuel engines were developed and found more convenient, the Sahara project was abandoned, only to be revisited several decades later. As of 2023, the world's largest thermal solar power plant is in the United Arab Emirates. == Low-temperature heating and cooling == Systems for utilizing low-temperature solar thermal energy include means for heat collection; usually heat storage, either short-term or interseasonal; and distribution within a structure or a district heating network. In some cases a single feature can do more than one of these things (e.g. some kinds of solar collectors also store heat). Some systems are passive, others are active (requiring other external energy to function). Heating is the most obvious application, but solar cooling can be achieved for a building or for district cooling by using a heat-driven absorption or adsorption chiller (heat pump). There is a productive coincidence that the greater the driving heat from insolation, the greater the cooling output. In 1878, Auguste Mouchout pioneered solar cooling by making ice using a solar steam engine attached to a refrigeration device. In the United States, heating, ventilation, and air conditioning (HVAC) systems account for over 25% (4.75 EJ) of the energy used in commercial buildings (50% in northern cities) and nearly half (10.1 EJ) of the energy used in residential buildings. Solar heating, cooling, and ventilation technologies can be used to offset a portion of this energy. The most popular solar heating technology for heating buildings is the building integrated transpired solar air collection system which connects to the building's HVAC equipment. According to Solar Energy Industries Association over 500,000 m2 (5,000,000 square feet) of these panels are in operation in North America as of 2015. In Europe, since the mid-1990s about 125 large solar-thermal district heating plants have been constructed, each with over 500 m2 (5400 ft2) of solar collectors. The largest are about 10,000 m2 (2.5 acres), with capacities of 7 MW-thermal and solar heat costs around 4 Eurocents/kWh without subsidies. 40 of them have nominal capacities of 1 MW-thermal or more. The Solar District Heating program (SDH) has participation from 14 European Nations and the European Commission, and is working toward technical and market development, and holds annual conferences. === Low-temperature collectors === Glazed solar collectors are designed primarily for space heating. They recirculate building air through a solar air panel where the air is heated and then directed back into the building. These solar space heating systems require at least two penetrations into the building and only perform when the air in the solar collector is warmer than the building room temperature. Most glazed collectors are used in the residential sector. Unglazed solar collectors are primarily used to pre-heat make-up ventilation air in commercial, industrial and institutional buildings with a high ventilation load. They turn building walls or sections of walls into low cost, high performance, unglazed solar collectors. Also called, "transpired solar panels" or "solar wall", they employ a painted perforated metal solar heat absorber that also serves as the exterior wall surface of the building. Heat transfer to the air takes place on the surface of the absorber, through the metal absorber and behind the absorber. The boundary layer of solar heated air is drawn into a nearby perforation before the heat can escape by convection to the outside air. The heated air is then drawn from behind the absorber plate into the building's ventilation system. A Trombe wall is a passive solar heating and ventilation system consisting of an air channel sandwiched between a window and a sun-facing thermal mass. During the ventilation cycle, sunlight stores heat in the thermal mass and warms the air channel causing circulation through vents at the top and bottom of the wall. During the heating cycle the Trombe wall radiates stored heat. Solar roof ponds for solar heating and cooling were developed by Harold Hay in the 1960s. A basic system consists of a roof-mounted water bladder with a movable insulating cover. This system can control heat exchange between interior and exterior environments by covering and uncovering the bladder between night and day. When heating is a concern the bladder is uncovered during the day allowing sunlight to warm the water bladder and store heat for evening use. When cooling is a concern the covered bladder draws heat from the building's interior during the day and is uncovered at night to radiate heat to the cooler atmosphere. The Skytherm house in Atascadero, California uses a prototype roof pond for heating and cooling. Solar space heating with solar air heat collectors is more popular in the USA and Canada than heating with solar liquid collectors since most buildings already have a ventilation system for heating and cooling. The two main types of solar air panels are glazed and unglazed. Of the 21,000,000 square feet (2,000,000 m2) of solar thermal collectors produced in the United States in 2007, 16,000,000 square feet (1,500,000 m2) were of the low-temperature variety. Low-temperature collectors are generally installed to heat swimming pools, although they can also be used for space heating. Collectors can use air or water as the medium to transfer the heat to their destination. The sun's free energy can also be used to heat water to fulfil domestic hot water demands, such as the hot water that comes out of taps. Solar thermal water heating systems can provide approximately 50% of a property's annual hot water demand (depending on the size of the property, its location etc) which in turn can help homeowners make savings on their energy bills. == Heat storage for space heating == A collection of mature technologies called seasonal thermal energy storage (STES) is capable of storing heat for months at a time, so solar heat collected primarily in Summer can be used for all-year heating. Solar-supplied STES technology has been advanced primarily in Denmark, Germany, and Canada, and applications include individual buildings and district heating networks. Drake Landing Solar Community in Alberta, Canada has a small district system and in 2012 achieved a world record of providing 97% of the community's all-year space heating needs from the sun. STES thermal storage mediums include deep aquifers; native rock surrounding clusters of small-diameter, heat exchanger equipped boreholes; large, shallow, lined pits that are filled with gravel and top-insulated; and large, insulated and buried surface water tanks. Centralized district heating round the clock is also feasible with concentrated solar thermal (CST) storage plant. Interseasonal storage. Solar heat (or heat from other sources) can be effectively stored between opposing seasons in aquifers, underground geological strata, large specially constructed pits, and large tanks that are insulated and covered with earth. Short-term storage. Thermal mass materials store solar energy during the day and release this energy during cooler periods. Common thermal mass materials include stone, concrete, and water. The proportion and placement of thermal mass should consider several factors such as climate, daylighting, and shading conditions. When properly incorporated, thermal mass can passively maintain comfortable temperatures while reducing energy consumption. === Solar-driven cooling === Worldwide, by 2011 there were about 750 cooling systems with solar-driven heat pumps, and annual market growth was 40 to 70% over the prior seven years. It is a niche market because the economics are challenging, with the annual number of cooling hours a limiting factor. Respectively, the annual cooling time is roughly 1000 hours in the Mediterranean, 2500 hours in Southeast Asia, and only 50 to 200 hours in Central Europe. However, system construction costs dropped about 50% between 2007 and 2011. The International Energy Agency (IEA) Solar Heating and Cooling program (IEA-SHC) task groups working on further development of the technologies involved. === Solar-heat-driven ventilation === A solar chimney (or thermal chimney) is a passive solar ventilation system composed of a hollow thermal mass connecting the interior and exterior of a building. As the chimney warms, the air inside is heated causing an updraft that pulls air through the building. These systems have been in use since Roman times and remain common in the Middle East. === Process heat === Solar process heating systems are designed to provide large quantities of hot water or space heating for nonresidential buildings. Evaporation ponds are shallow ponds that concentrate dissolved solids through evaporation. The use of evaporation ponds to obtain salt from sea water is one of the oldest applications of solar energy. Modern uses include concentrating brine solutions used in leach mining and removing dissolved solids from waste streams. Altogether, evaporation ponds represent one of the largest commercial applications of solar energy in use today. Unglazed transpired collectors are perforated sun-facing walls used for preheating ventilation air. Transpired collectors can also be roof mounted for year-round use and can raise the incoming air temperature up to 22 °C (72 °F) and deliver outlet temperatures of 45–60 °C (110–140 °F). The short payback period of transpired collectors (3 to 12 years) make them a more cost-effective alternative to glazed collection systems. As of 2015, over 4000 systems with a combined collector area of 500,000 m2 (100 acres) had been installed worldwide. Representatives include an 860 m2 (9,300 ft2) collector in Costa Rica used for drying coffee beans and a 1300 m2 (14,000 ft2) collector in Coimbatore, India used for drying marigolds. A food processing facility in Modesto, California uses parabolic troughs to produce steam used in the manufacturing process. The 5,000 m2 collector area is expected to provide 15 TJ per year. == Medium-temperature collectors == These collectors could be used to produce approximately 50% and more of the hot water needed for residential and commercial use in the United States. In the United States, a typical system costs $4000–$6000 retail ($1400 to $2200 wholesale for the materials) and 30% of the system qualifies for a federal tax credit + additional state credit exists in about half of the states. Labor for a simple open loop system in southern climates can take 3–5 hours for the installation and 4–6 hours in Northern areas. Northern system require more collector area and more complex plumbing to protect the collector from freezing. With this incentive, the payback time for a typical household is four to nine years, depending on the state. Similar subsidies exist in parts of Europe. A crew of one solar plumber and two assistants with minimal training can install a system per day. Thermosiphon installation have negligible maintenance costs (costs rise if antifreeze and mains power are used for circulation) and in the US reduces a household's operating costs by $6 per person per month. Solar water heating can reduce CO2 emissions of a family of four by 1 ton/year (if replacing natural gas) or 3 ton/year (if replacing electricity). Medium-temperature installations can use any of several designs: common designs are pressurized glycol, drain back, batch systems and newer low pressure freeze tolerant systems using polymer pipes containing water with photovoltaic pumping. European and International standards are being reviewed to accommodate innovations in design and operation of medium temperature collectors. Operational innovations include "permanently wetted collector" operation. This innovation reduces or even eliminates the occurrence of no-flow high temperature stresses called stagnation which would otherwise reduce the life expectancy of collectors. === Solar drying === Solar thermal energy can be useful for drying wood for construction and wood fuels such as wood chips for combustion. Solar is also used for food products such as fruits, grains, and fish. Crop drying by solar means is environmentally friendly as well as cost effective while improving the quality. The less money it takes to make a product, the less it can be sold for, pleasing both the buyers and the sellers. Technologies in solar drying include ultra low cost pumped transpired plate air collectors based on black fabrics. Solar thermal energy is helpful in the process of drying products such as wood chips and other forms of biomass by raising the temperature while allowing air to pass through and get rid of the moisture. === Cooking === Solar cookers use sunlight for cooking, drying and pasteurization. Solar cooking offsets fuel costs, reduces demand for fuel or firewood, and improves air quality by reducing or removing a source of smoke. The simplest type of solar cooker is the box cooker first built by Horace de Saussure in 1767. A basic box cooker consists of an insulated container with a transparent lid. These cookers can be used effectively with partially overcast skies and will typically reach temperatures of 50–100 °C (100–200 °F). Concentrating solar cookers use reflectors to concentrate solar energy onto a cooking container. The most common reflector geometries are flat plate, disc and parabolic trough type. These designs cook faster and at higher temperatures (up to 350 °C; 660 °F) but require direct light to function properly. The Solar Kitchen in Auroville, India uses a unique concentrating technology known as the solar bowl. Contrary to conventional tracking reflector/fixed receiver systems, the solar bowl uses a fixed spherical reflector with a receiver which tracks the focus of light as the Sun moves across the sky. The solar bowl's receiver reaches temperature of 150 °C (300 °F) that is used to produce steam that helps cook 2,000 daily meals. Many other solar kitchens in India use another unique concentrating technology known as the Scheffler reflector. This technology was first developed by Wolfgang Scheffler in 1986. A Scheffler reflector is a parabolic dish that uses single axis tracking to follow the Sun's daily course. These reflectors have a flexible reflective surface that is able to change its curvature to adjust to seasonal variations in the incident angle of sunlight. Scheffler reflectors have the advantage of having a fixed focal point which improves the ease of cooking and are able to reach temperatures of 450-650 °C (850 °F to 1200 °F). Built in 1999 by the Brahma Kumaris, the world's largest Scheffler reflector system in Abu Road, Rajasthan India is capable of cooking up to 35,000 meals a day. By early 2008, over 2000 large cookers of the Scheffler design had been built worldwide. === Distillation === Solar stills can be used to make drinking water in areas where clean water is not common. Solar distillation is necessary in these situations to provide people with purified water. Solar energy heats up the water in the still. The water then evaporates and condenses on the bottom of the covering glass. === Surgical autoclave steriliser === Dr Lin Zhao of MIT published a peer-reviewed academic journal in Joule detailing their design for a solar autoclave for the sterilisation of surgical instruments without electricity. A prototype, which incorporates inexpensive aerogel was successfully demonstrated at a hospital in Mumbai in conjunction with IIT Bombay, Indian Institute of Technology. == High-temperature collectors == Where temperatures below about 95 °C (200 °F) are sufficient, as for space heating, flat-plate collectors of the nonconcentrating type are generally used. Because of the relatively high heat losses through the glazing, flat plate collectors will not reach temperatures much above 200 °C (400 °F) even when the heat transfer fluid is stagnant. Such temperatures are too low for efficient conversion to electricity. The efficiency of heat engines increases with the temperature of the heat source. To achieve this in solar thermal energy plants, solar radiation is concentrated by mirrors or lenses to obtain higher temperatures – a technique called Concentrated Solar Power (CSP). The practical effect of high efficiencies is to reduce the plant's collector size and total land use per unit power generated, reducing the environmental impacts of a power plant as well as its expense. As the temperature increases, different forms of conversion become practical. Up to 600 °C (1100 °F), steam turbines, standard technology, have an efficiency up to 41%. Above 600 °C (1100 °F), gas turbines can be more efficient. Higher temperatures are problematic because different materials and techniques are needed. One proposal for very high temperatures is to use liquid fluoride salts operating between 700 °C (1300 °F) to 800 °C (1500 °F), using multi-stage turbine systems to achieve 50% or more thermal efficiencies. The higher operating temperatures permit the plant to use higher-temperature dry heat exchangers for its thermal exhaust, reducing the plant's water use – critical in the deserts where large solar plants are practical. High temperatures also make heat storage more efficient, because more watt-hours are stored per unit of fluid. Commercial concentrating solar thermal power (CSP) plants were first developed in the 1980s. The world's largest solar thermal power plants are now the 370 MW Ivanpah Solar Power Facility, commissioned in 2014, and the 354 MW SEGS CSP installation, both located in the Mojave Desert of California, where several other solar projects have been realized as well. The principal advantage of CSP is the ability to efficiently add thermal storage, allowing the dispatching of electricity over up to a 24-hour period. Since peak electricity demand typically occurs between about 4 and 8 pm, many CSP power plants use 3 to 5 hours of thermal storage. With current technology, storage of heat is much cheaper and more efficient than storage of electricity. In this way, the CSP plant can produce electricity day and night. If the CSP site has predictable solar radiation, then the CSP plant becomes a reliable power plant. Reliability can further be improved by installing a back-up combustion system. The back-up system can use most of the CSP plant, which decreases the cost of the back-up system. With reliability, unused desert, no pollution, and no fuel costs, the obstacles for large deployment for CSP are cost, aesthetics, land use and similar factors for the necessary connecting high tension lines. Although only a small percentage of the desert is necessary to meet global electricity demand, still a large area must be covered with mirrors or lenses to obtain a significant amount of energy. An important way to decrease cost is the use of a simple design. When considering land use impacts associated with the exploration and extraction through to transportation and conversion of fossil fuels, which are used for most of our electrical power, utility-scale solar power compares as one of the most land-efficient energy resources available: The federal government has dedicated nearly 2,000 times more acreage to oil and gas leases than to solar development. In 2010 the Bureau of Land Management approved nine large-scale solar projects, with a total generating capacity of 3,682 megawatts, representing approximately 40,000 acres. In contrast, in 2010, the Bureau of Land Management processed more than 5,200 applications gas and oil leases, and issued 1,308 leases, for a total of 3.2 million acres. Currently, 38.2 million acres of onshore public lands and an additional 36.9 million acres of offshore exploration in the Gulf of Mexico are under lease for oil and gas development, exploration and production. === System designs === During the day the sun has different positions. For low concentration systems (and low temperatures) tracking can be avoided (or limited to a few positions per year) if nonimaging optics are used. For higher concentrations, however, if the mirrors or lenses do not move, then the focus of the mirrors or lenses changes. A tracking system that follows the position of the sun is required. The tracking system increases the cost and complexity. With this in mind, different designs can be distinguished in how they concentrate the light and track the position of the sun. ==== Parabolic trough designs ==== Parabolic trough power plants use a curved, mirrored trough which reflects the direct solar radiation onto a glass tube containing a fluid (also called a receiver, absorber or collector) running the length of the trough, positioned at the focal point of the reflectors. The trough is parabolic along one axis and linear in the orthogonal axis. For change of the daily position of the sun perpendicular to the receiver, the trough tilts east to west so that the direct radiation remains focused on the receiver. However, seasonal changes in the angle of sunlight parallel to the trough does not require adjustment of the mirrors, since the light is simply concentrated elsewhere on the receiver. Thus the trough design does not require tracking on a second axis. The receiver may be enclosed in a glass vacuum chamber. The vacuum significantly reduces convective heat loss. A fluid (also called heat transfer fluid) passes through the receiver and becomes very hot. Common fluids are synthetic oil, molten salt and pressurized steam. The fluid containing the heat is transported to a heat engine where about a third of the heat is converted to electricity. Full-scale parabolic trough systems consist of many such troughs laid out in parallel over a large area of land. Since 1985 a solar thermal system using this principle has been in full operation in California in the United States. It is called the Solar Energy Generating Systems (SEGS) system. Other CSP designs lack this kind of long experience and therefore it can currently be said that the parabolic trough design is the most thoroughly proven CSP technology. The SEGS is a collection of nine plants with a total capacity of 354 MW and has been the world's largest solar power plant, both thermal and non-thermal, for many years. A newer plant is Nevada Solar One plant with a capacity of 64 MW. The 150 MW Andasol solar power stations are in Spain with each site having a capacity of 50 MW. Note however, that those plants have heat storage which requires a larger field of solar collectors relative to the size of the steam turbine-generator to store heat and send heat to the steam turbine at the same time. Heat storage enables better utilization of the steam turbine. With day and some nighttime operation of the steam-turbine Andasol 1 at 50 MW peak capacity produces more energy than Nevada Solar One at 64 MW peak capacity, due to the former plant's thermal energy storage system and larger solar field. The 280 MW Solana Generating Station came online in Arizona in 2013 with 6 hours of power storage. Hassi R'Mel integrated solar combined cycle power station in Algeria and Martin Next Generation Solar Energy Center both use parabolic troughs in a combined cycle with natural gas. ==== Enclosed trough ==== The enclosed trough architecture encapsulates the solar thermal system within a greenhouse-like glasshouse. The glasshouse creates a protected environment to withstand the elements that can negatively impact reliability and efficiency of the solar thermal system. Lightweight curved solar-reflecting mirrors are suspended within the glasshouse structure. A single-axis tracking system positions the mirrors to track the sun and focus its light onto a network of stationary steel pipes, also suspended from the glasshouse structure. Steam is generated directly, using oil field-quality water, as water flows from the inlet throughout the length of the pipes, without heat exchangers or intermediate working fluids. The steam produced is then fed directly to the field's existing steam distribution network, where the steam is continuously injected deep into the oil reservoir. Sheltering the mirrors from the wind allows them to achieve higher temperature rates and prevents dust from building up as a result from exposure to humidity. GlassPoint Solar, the company that created the Enclosed Trough design, states its technology can produce heat for EOR for about $5 per million British thermal units in sunny regions, compared to between $10 and $12 for other conventional solar thermal technologies. GlassPoint's enclosed trough system has been utilized at the Miraah facility in Oman, and a new project has recently been announced for the company to bring its enclosed trough technology to the South Belridge Oil Field, near Bakersfield, California. ==== Power tower designs ==== Power towers (also known as 'central tower' power plants or 'heliostat' power plants) capture and focus the sun's thermal energy with thousands of tracking mirrors (called heliostats) in roughly a two square mile field. A tower resides in the center of the heliostat field. The heliostats focus concentrated sunlight on a receiver which sits on top of the tower. Within the receiver the concentrated sunlight heats molten salt to over 1,000 °F (538 °C). The heated molten salt then flows into a thermal storage tank where it is stored, maintaining 98% thermal efficiency, and eventually pumped to a steam generator. The steam drives a standard turbine to generate electricity. This process, also known as the "Rankine cycle" is similar to a standard coal-fired power plant, except it is fueled by solar energy. The advantage of this design above the parabolic trough design is the higher temperature. Thermal energy at higher temperatures can be converted to electricity more efficiently and can be more cheaply stored for later use. Furthermore, there is less need to flatten the ground area. In principle a power tower can be built on the side of a hill. Mirrors can be flat and plumbing is concentrated in the tower. The disadvantage is that each mirror must have its own dual-axis control, while in the parabolic trough design single axis tracking can be shared for a large array of mirrors. A cost/performance comparison between power tower and parabolic trough concentrators was made by the NREL which estimated that by 2020 electricity could be produced from power towers for 5.47 ¢/kWh and for 6.21 ¢/kWh from parabolic troughs. The capacity factor for power towers was estimated to be 72.9% and 56.2% for parabolic troughs. There is some hope that the development of cheap, durable, mass producible heliostat power plant components could bring this cost down. The first commercial tower power plant was PS10 in Spain with a capacity of 11 MW, completed in 2007. Since then a number of plants have been proposed, several have been built in a number of countries (Spain, Germany, U.S., Turkey, China, India) but several proposed plants were cancelled as photovoltaic solar prices plummeted. A solar power tower went online in South Africa in 2016. Ivanpah Solar Power Facility in California generates 392 MW of electricity from three towers, making it the largest solar power tower plant when it came online in late 2013. ==== Dish designs ==== A dish Stirling system uses a large, reflective, parabolic dish (similar in shape to a satellite television dish). It focuses all the sunlight that strikes the dish up onto a single point above the dish, where a receiver captures the heat and transforms it into a useful form. Typically the dish is coupled with a Stirling engine in a Dish-Stirling System, but also sometimes a steam engine is used. These create rotational kinetic energy that can be converted to electricity using an electric generator. In 2005 Southern California Edison announced an agreement to purchase solar powered Stirling engines from Stirling Energy Systems over a twenty-year period and in quantities (20,000 units) sufficient to generate 500 megawatts of electricity. In January 2010, Stirling Energy Systems and Tessera Solar commissioned the first demonstration 1.5-megawatt power plant ("Maricopa Solar") using Stirling technology in Peoria, Arizona. At the beginning of 2011 Stirling Energy's development arm, Tessera Solar, sold off its two large projects, the 709 MW Imperial project and the 850 MW Calico project to AES Solar and K.Road, respectively. In 2012 the Maricopa plant was bought and dismantled by United Sun Systems. United Sun Systems released a new generation system, based on a V-shaped Stirling engine and a peak production of 33 kW. The new CSP-Stirling technology brings down LCOE to USD 0.02 in utility scale. According to its developer, Rispasso Energy, a Swedish firm, in 2015 its Dish Sterling system being tested in the Kalahari Desert in South Africa showed 34% efficiency. ==== Fresnel technologies ==== A linear Fresnel reflector power plant uses a series of long, narrow, shallow-curvature (or even flat) mirrors to focus light onto one or more linear receivers positioned above the mirrors. On top of the receiver a small parabolic mirror can be attached for further focusing the light. These systems aim to offer lower overall costs by sharing a receiver between several mirrors (as compared with trough and dish concepts), while still using the simple line-focus geometry with one axis for tracking. This is similar to the trough design (and different from central towers and dishes with dual-axis). The receiver is stationary and so fluid couplings are not required (as in troughs and dishes). The mirrors also do not need to support the receiver, so they are structurally simpler. When suitable aiming strategies are used (mirrors aimed at different receivers at different times of day), this can allow a denser packing of mirrors on available land area. Rival single axis tracking technologies include the relatively new linear Fresnel reflector (LFR) and compact-LFR (CLFR) technologies. The LFR differs from that of the parabolic trough in that the absorber is fixed in space above the mirror field. Also, the reflector is composed of many low row segments, which focus collectively on an elevated long tower receiver running parallel to the reflector rotational axis. Prototypes of Fresnel lens concentrators have been produced for the collection of thermal energy by International Automated Systems. No full-scale thermal systems using Fresnel lenses are known to be in operation, although products incorporating Fresnel lenses in conjunction with photovoltaic cells are already available. ==== MicroCSP ==== MicroCSP is used for community-sized power plants (1 MW to 50 MW), for industrial, agricultural and manufacturing 'process heat' applications, and when large amounts of hot water are needed, such as resort swimming pools, water parks, large laundry facilities, sterilization, distillation and other such uses. == Heat collection and exchange == Heat in a solar thermal system is guided by five basic principles: heat gain; heat transfer; heat storage; heat transport; and heat insulation. Here, heat is the measure of the amount of thermal energy an object contains and is determined by the temperature, mass and specific heat of the object. Solar thermal power plants use heat exchangers that are designed for constant working conditions, to provide heat exchange. Copper heat exchangers are important in solar thermal heating and cooling systems because of copper's high thermal conductivity, resistance to atmospheric and water corrosion, sealing and joining by soldering, and mechanical strength. Copper is used both in receivers and in primary circuits (pipes and heat exchangers for water tanks) of solar thermal water systems. Heat gain is the heat accumulated from the sun in the system. Solar thermal heat is trapped using the greenhouse effect; the greenhouse effect in this case is the ability of a reflective surface to transmit short wave radiation and reflect long wave radiation. Heat and infrared radiation (IR) are produced when short wave radiation light hits the absorber plate, which is then trapped inside the collector. Fluid, usually water, in the absorber tubes collect the trapped heat and transfer it to a heat storage vault. Heat is transferred either by conduction or convection. When water is heated, kinetic energy is transferred by conduction to water molecules throughout the medium. These molecules spread their thermal energy by conduction and occupy more space than the cold slow moving molecules above them. The distribution of energy from the rising hot water to the sinking cold water contributes to the convection process. Heat is transferred from the absorber plates of the collector in the fluid by conduction. The collector fluid is circulated through the carrier pipes to the heat transfer vault. Inside the vault, heat is transferred throughout the medium through convection. Heat storage enables solar thermal plants to produce electricity during hours without sunlight. Heat is transferred to a thermal storage medium in an insulated reservoir during hours with sunlight, and is withdrawn for power generation during hours lacking sunlight. Thermal storage mediums will be discussed in a heat storage section. Rate of heat transfer is related to the conductive and convection medium as well as the temperature differences. Bodies with large temperature differences transfer heat faster than bodies with lower temperature differences. Heat transport refers to the activity in which heat from a solar collector is transported to the heat storage vault. Heat insulation is vital in both heat transport tubing as well as the storage vault. It prevents heat loss, which in turn relates to energy loss, or decrease in the efficiency of the system. == Heat storage for electric base loads == Heat storage allows a solar thermal plant to produce electricity at night and on overcast days. This allows the use of solar power for baseload generation as well as peak power generation, with the potential of displacing both coal- and natural gas-fired power plants. Additionally, the utilization of the generator is higher which reduces cost. Even short term storage can help by smoothing out the "duck curve" of rapid change in generation requirements at sunset when a grid includes large amounts of solar capacity. Heat is transferred to a thermal storage medium in an insulated reservoir during the day, and withdrawn for power generation at night. Thermal storage media include pressurized steam, concrete, a variety of phase change materials, and molten salts such as calcium, sodium and potassium nitrate. === Steam accumulator === The PS10 solar power tower stores heat in tanks as pressurized steam at 50 bar (700 psi) and 285 °C (545 °F). The steam condenses and flashes back to steam, when pressure is lowered. Storage is for one hour. It is suggested that longer storage is possible, but that has not been proven in an existing power plant. === Molten salt storage === Molten salt is used to transport heat in solar power tower systems because it is liquid at atmospheric pressure, provides a low-cost medium to store thermal energy, its operating temperatures are compatible with today's steam turbines, and it is non-flammable and nontoxic. Molten salt is also used in the chemical and metals industries to transport heat. The first commercial molten salt mixture was a common form of saltpeter, 60% sodium nitrate and 40% potassium nitrate. Saltpeter melts at 220 °C (430 °F) and is kept liquid at 290 °C (550 °F) in an insulated storage tank. Calcium nitrate can reduce the melting point to 131 °C (268 °F), permitting more energy to be extracted before the salt freezes. There are now several technical calcium nitrate grades stable at more than 500 °C (1000 °F). This solar power system can generate power in cloudy weather or at night using the heat in the tank of hot salt. The tanks are insulated, able to store heat for a week. Tanks that power a 100-megawatt turbine for four hours would be about 9 m (30 ft) tall and 24 m (80 ft) in diameter. The Andasol power plant in Spain is the first commercial solar thermal power plant using molten salt for heat storage and nighttime generation. It came on line March 2009. On July 4, 2011, a company in Spain celebrated an historic moment for the solar industry: Torresol's 19.9 MW concentrating solar power plant became the first ever to generate uninterrupted electricity for 24 hours straight, using a molten salt heat storage. In January 2019 Shouhang Energy Saving Dunhuang 100MW molten salt tower solar energy photothermal power station project was connected to grid and started operating. Its configuration includes an 11-hour molten salt heat storage system and can generate power consecutively for 24 hours. === Phase-change materials for storage === Phase Change Material (PCMs) offer an alternative solution in energy storage. Using a similar heat transfer infrastructure, PCMs have the potential of providing a more efficient means of storage. PCMs can be either organic or inorganic materials. Advantages of organic PCMs include no corrosives, low or no undercooling, and chemical and thermal stability. Disadvantages include low phase-change enthalpy, low thermal conductivity, and flammability. Inorganics are advantageous with greater phase-change enthalpy, but exhibit disadvantages with undercooling, corrosion, phase separation, and lack of thermal stability. The greater phase-change enthalpy in inorganic PCMs make hydrate salts a strong candidate in the solar energy storage field. == Use of water == A design which requires water for condensation or cooling may conflict with location of solar thermal plants in desert areas with good solar radiation but limited water resources. The conflict is illustrated by plans of Solar Millennium, a German company, to build a plant in the Amargosa Valley of Nevada which would require 20% of the water available in the area. Some other projected plants by the same and other companies in the Mojave Desert of California may also be affected by difficulty in obtaining adequate and appropriate water rights. California water law currently prohibits use of potable water for cooling. Other designs require less water. The Ivanpah Solar Power Facility in south-eastern California conserves scarce desert water by using air-cooling to convert the steam back into water. Compared to conventional wet-cooling, this results in a 90% reduction in water usage at the cost of some loss of efficiency. The water is then returned to the boiler in a closed process which is environmentally friendly. == Electrical conversion efficiency == Of all of these technologies the solar dish/Stirling engine has the highest energy efficiency. A single solar dish-Stirling engine installed at Sandia National Laboratories National Solar Thermal Test Facility (NSTTF) produces as much as 25 kW of electricity, with a conversion efficiency of 31.25%. Solar parabolic trough plants have been built with efficiencies of about 20%. Fresnel reflectors have a slightly lower efficiency (but this is compensated by the denser packing). The gross conversion efficiencies (taking into account that the solar dishes or troughs occupy only a fraction of the total area of the power plant) are determined by net generating capacity over the solar energy that falls on the total area of the solar plant. The 500-megawatt (MW) SCE/SES plant would extract about 2.75% of the radiation (1 kW/m2; see Solar power § Energy from the Sun for a discussion) that falls on its 4,500 acres (18.2 km2). For the 50 MW AndaSol Power Plant that is being built in Spain (total area 1.95 km2; 3⁄4 sq. mi.) gross conversion efficiency comes out at 2.6%. Efficiency does not directly relate to cost: total cost includes the cost of construction and maintenance. == Standards == EN 12975 (efficiency test) == See also == == References == == External links == It's solar power's time to shine MSN Money World's Largest Solar Thermal in Saudi Arabia Onsite Renewable Technologies at United States Environmental Protection Agency website Assessment of the World Bank/GEF Strategy for the Market Development of Concentrating Solar Thermal Power Solar thermal energy calculator Concentrating Solar Power An overview of the technology by Gerry Wolff, coordinator of TREC-UK NREL Concentrating Solar Power Program Site Comprehensive review of parabolic trough technology and markets Nevada Gets First U.S. Solar Thermal Plant Solar thermal and concentrated solar power barometer – 2013 Pdf Solar Water Heating TechScope Market Readiness Assessment Report – UNEP Guide for Solar Heating and Cooling Awareness-Raising Campaigns – UNEP Guidelines for Standardization and Quality Assurance for Solar Thermal – UNEP Guidelines for Solar Water Heating and Cooling Policy and Framework Conditions – UNEP Solar Water Heating, a Strategic Planning Guide for Cities in Developing Countries – UNEP
Wikipedia/Solar_thermal_energy
In physics, potential energy is the energy of an object or system due to the body's position relative to other objects, or the configuration of its particles. The energy is equal to the work done against any restoring forces, such as gravity or those in a spring. The term potential energy was introduced by the 19th-century Scottish engineer and physicist William Rankine, although it has links to the ancient Greek philosopher Aristotle's concept of potentiality. Common types of potential energy include gravitational potential energy, the elastic potential energy of a deformed spring, and the electric potential energy of an electric charge and an electric field. The unit for energy in the International System of Units (SI) is the joule (symbol J). Potential energy is associated with forces that act on a body in a way that the total work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, whose total work is path independent, are called conservative forces. If the force acting on a body varies over space, then one has a force field; such a field is described by vectors at every point in space, which is, in turn, called a vector field. A conservative vector field can be simply expressed as the gradient of a certain scalar function, called a scalar potential. The potential energy is related to, and can be obtained from, this potential function. == Overview == There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces. The work done by a conservative force is W = − Δ U , {\displaystyle W=-\Delta U,} where Δ U {\displaystyle \Delta U} is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy. Common notations for potential energy are PE, U, V, and Ep. Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, which is said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing the stretch of the spring or causing a body to fall. Consider a ball whose mass is m dropped from height h. The acceleration g of free fall is approximately constant, so the weight force of the ball mg is constant. The product of force and displacement gives the work done, which is equal to the gravitational potential energy, thus U g = m g h . {\displaystyle U_{\text{g}}=mgh.} The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position. == History == From around 1840 scientists sought to define and understand energy and work. The term "potential energy" was coined by William Rankine a Scottish engineer and physicist in 1853 as part of a specific effort to develop terminology. He chose the term as part of the pair "actual" vs "potential" going back to work by Aristotle. In his 1867 discussion of the same topic Rankine describes potential energy as 'energy of configuration' in contrast to actual energy as 'energy of activity'. Also in 1867, William Thomson introduced "kinetic energy" as the opposite of "potential energy", asserting that all actual energy took the form of ⁠1/2⁠mv2. Once this hypothesis became widely accepted, the term "actual energy" gradually faded. == Work and potential energy == Potential energy is closely linked with forces. If the work done by a force on a body that moves from A to B does not depend on the path between these points (if the work is done by a conservative force), then the work of this force measured from A assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path, then the work done by the force is evaluated from the start to the end of the trajectory of the point of application. This means that there is a function U(x), called a "potential", that can be evaluated at the two points xA and xB to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is W = ∫ C F ⋅ d x = U ( x A ) − U ( x B ) {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {x} =U(\mathbf {x} _{\text{A}})-U(\mathbf {x} _{\text{B}})} where C is the trajectory taken from A to B. Because the work done is independent of the path taken, then this expression is true for any trajectory, C, from A to B. The function U(x) is called the potential energy associated with the applied force. Examples of forces that have potential energies are gravity and spring forces. === Derivable from a potential === In this section the relationship between work and potential energy is presented in more detail. The line integral that defines work along curve C takes a special form if the force F is related to a scalar field U′(x) so that F = ∇ U ′ = ( ∂ U ′ ∂ x , ∂ U ′ ∂ y , ∂ U ′ ∂ z ) . {\displaystyle \mathbf {F} ={\nabla U'}=\left({\frac {\partial U'}{\partial x}},{\frac {\partial U'}{\partial y}},{\frac {\partial U'}{\partial z}}\right).} This means that the units of U′ must be this case, work along the curve is given by W = ∫ C F ⋅ d x = ∫ C ∇ U ′ ⋅ d x , {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {x} =\int _{C}\nabla U'\cdot d\mathbf {x} ,} which can be evaluated using the gradient theorem to obtain W = U ′ ( x B ) − U ′ ( x A ) . {\displaystyle W=U'(\mathbf {x} _{\text{B}})-U'(\mathbf {x} _{\text{A}}).} This shows that when forces are derivable from a scalar field, the work of those forces along a curve C is computed by evaluating the scalar field at the start point A and the end point B of the curve. This means the work integral does not depend on the path between A and B and is said to be independent of the path. Potential energy U = −U′(x) is traditionally defined as the negative of this scalar field so that work by the force field decreases potential energy, that is W = U ( x A ) − U ( x B ) . {\displaystyle W=U(\mathbf {x} _{\text{A}})-U(\mathbf {x} _{\text{B}}).} In this case, the application of the del operator to the work function yields, ∇ W = − ∇ U = − ( ∂ U ∂ x , ∂ U ∂ y , ∂ U ∂ z ) = F , {\displaystyle {\nabla W}=-{\nabla U}=-\left({\frac {\partial U}{\partial x}},{\frac {\partial U}{\partial y}},{\frac {\partial U}{\partial z}}\right)=\mathbf {F} ,} and the force F is said to be "derivable from a potential". This also necessarily implies that F must be a conservative vector field. The potential U defines a force F at every point x in space, so the set of forces is called a force field. === Computing potential energy === Given a force field F(x), evaluation of the work integral using the gradient theorem can be used to find the scalar function associated with potential energy. This is done by introducing a parameterized curve γ(t) = r(t) from γ(a) = A to γ(b) = B, and computing, ∫ γ ∇ Φ ( r ) ⋅ d r = ∫ a b ∇ Φ ( r ( t ) ) ⋅ r ′ ( t ) d t , = ∫ a b d d t Φ ( r ( t ) ) d t = Φ ( r ( b ) ) − Φ ( r ( a ) ) = Φ ( x B ) − Φ ( x A ) . {\displaystyle {\begin{aligned}\int _{\gamma }\nabla \Phi (\mathbf {r} )\cdot d\mathbf {r} &=\int _{a}^{b}\nabla \Phi (\mathbf {r} (t))\cdot \mathbf {r} '(t)dt,\\&=\int _{a}^{b}{\frac {d}{dt}}\Phi (\mathbf {r} (t))dt=\Phi (\mathbf {r} (b))-\Phi (\mathbf {r} (a))=\Phi \left(\mathbf {x} _{B}\right)-\Phi \left(\mathbf {x} _{A}\right).\end{aligned}}} For the force field F, let v = dr/dt, then the gradient theorem yields, ∫ γ F ⋅ d r = ∫ a b F ⋅ v d t , = − ∫ a b d d t U ( r ( t ) ) d t = U ( x A ) − U ( x B ) . {\displaystyle {\begin{aligned}\int _{\gamma }\mathbf {F} \cdot d\mathbf {r} &=\int _{a}^{b}\mathbf {F} \cdot \mathbf {v} \,dt,\\&=-\int _{a}^{b}{\frac {d}{dt}}U(\mathbf {r} (t))\,dt=U(\mathbf {x} _{A})-U(\mathbf {x} _{B}).\end{aligned}}} The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity v of the point of application, that is P ( t ) = − ∇ U ⋅ v = F ⋅ v . {\displaystyle P(t)=-{\nabla U}\cdot \mathbf {v} =\mathbf {F} \cdot \mathbf {v} .} Examples of work that can be computed from potential functions are gravity and spring forces. == Potential energy for near-Earth gravity == For small height changes, gravitational potential energy can be computed using U g = m g h , {\displaystyle U_{\text{g}}=mgh,} where m is the mass in kilograms, g is the local gravitational field (9.8 metres per second squared on Earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F = (0, 0, Fz) on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r(t) = (x(t), y(t), z(t)), such as the track of a roller coaster is calculated using its velocity, v = (vx, vy, vz), to obtain W = ∫ t 1 t 2 F ⋅ v d t = ∫ t 1 t 2 F z v z d t = F z Δ z . {\displaystyle W=\int _{t_{1}}^{t_{2}}{\boldsymbol {F}}\cdot {\boldsymbol {v}}\,dt=\int _{t_{1}}^{t_{2}}F_{\text{z}}v_{\text{z}}\,dt=F_{\text{z}}\Delta z.} where the integral of the vertical component of velocity is the vertical distance. The work of gravity depends only on the vertical movement of the curve r(t). == Potential energy for a linear spring == A horizontal spring exerts a force F = (−kx, 0, 0) that is proportional to its deformation in the axial or x-direction. The work of this spring on a body moving along the space curve s(t) = (x(t), y(t), z(t)), is calculated using its velocity, v = (vx, vy, vz), to obtain W = ∫ 0 t F ⋅ v d t = − ∫ 0 t k x v x d t = − ∫ 0 t k x d x d t d t = ∫ x ( t 0 ) x ( t ) k x d x = 1 2 k x 2 {\displaystyle W=\int _{0}^{t}\mathbf {F} \cdot \mathbf {v} \,dt=-\int _{0}^{t}kxv_{\text{x}}\,dt=-\int _{0}^{t}kx{\frac {dx}{dt}}dt=\int _{x(t_{0})}^{x(t)}kx\,dx={\frac {1}{2}}kx^{2}} For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x-velocity, xvx, is x2/2. The function U ( x ) = 1 2 k x 2 , {\displaystyle U(x)={\frac {1}{2}}kx^{2},} is called the potential energy of a linear spring. Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology). It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. If the stretch is released, the energy is transformed into kinetic energy. == Potential energy for gravitational forces between two bodies == The gravitational potential function, also known as gravitational potential energy, is: U = − G M m r , {\displaystyle U=-{\frac {GMm}{r}},} The negative sign follows the convention that work is gained from a loss of potential energy. === Derivation === The gravitational force between two bodies of mass M and m separated by a distance r is given by Newton's law of universal gravitation F = − G M m r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {GMm}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from M to m and G is the gravitational constant. Let the mass m move at the velocity v then the work of gravity on this mass as it moves from position r(t1) to r(t2) is given by W = − ∫ r ( t 1 ) r ( t 2 ) G M m r 3 r ⋅ d r = − ∫ t 1 t 2 G M m r 3 r ⋅ v d t . {\displaystyle W=-\int _{\mathbf {r} (t_{1})}^{\mathbf {r} (t_{2})}{\frac {GMm}{r^{3}}}\mathbf {r} \cdot d\mathbf {r} =-\int _{t_{1}}^{t_{2}}{\frac {GMm}{r^{3}}}\mathbf {r} \cdot \mathbf {v} \,dt.} The position and velocity of the mass m are given by r = r e r , v = r ˙ e r + r θ ˙ e t , {\displaystyle \mathbf {r} =r\mathbf {e} _{r},\qquad \mathbf {v} ={\dot {r}}\mathbf {e} _{\text{r}}+r{\dot {\theta }}\mathbf {e} _{\text{t}},} where er and et are the radial and tangential unit vectors directed relative to the vector from M to m. Use this to simplify the formula for work of gravity to, W = − ∫ t 1 t 2 G m M r 3 ( r e r ) ⋅ ( r ˙ e r + r θ ˙ e t ) d t = − ∫ t 1 t 2 G m M r 3 r r ˙ d t = G M m r ( t 2 ) − G M m r ( t 1 ) . {\displaystyle W=-\int _{t_{1}}^{t_{2}}{\frac {GmM}{r^{3}}}(r\mathbf {e} _{\text{r}})\cdot ({\dot {r}}\mathbf {e} _{\text{r}}+r{\dot {\theta }}\mathbf {e} _{\text{t}})\,dt=-\int _{t_{1}}^{t_{2}}{\frac {GmM}{r^{3}}}r{\dot {r}}dt={\frac {GMm}{r(t_{2})}}-{\frac {GMm}{r(t_{1})}}.} This calculation uses the fact that d d t r − 1 = − r − 2 r ˙ = − r ˙ r 2 . {\displaystyle {\frac {d}{dt}}r^{-1}=-r^{-2}{\dot {r}}=-{\frac {\dot {r}}{r^{2}}}.} == Potential energy for electrostatic forces between two bodies == The electrostatic force exerted by a charge Q on another charge q separated by a distance r is given by Coulomb's law F = 1 4 π ε 0 Q q r 2 r ^ , {\displaystyle \mathbf {F} ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from Q to q and ε0 is the vacuum permittivity. The work W required to move q from A to any point B in the electrostatic force field is given by the potential function U ( r ) = 1 4 π ε 0 Q q r . {\displaystyle U(r)={\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r}}.} == Reference level == The potential energy is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state; it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used; therefore it can be chosen based on convenience. Typically the potential energy of a system depends on the relative positions of its components only, so the reference state can also be expressed in terms of relative positions. == Gravitational potential energy == Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. Consider a book placed on top of a table. As the book is raised from the floor to the table, some external force works against the gravitational force. If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force. Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy. When the book hits the floor this kinetic energy is converted into heat, deformation, and sound by the impact. The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because the Moon's gravity is weaker. "Height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail. === Local approximation === The strength of a gravitational field varies with location. However, when the change of distance is small in relation to the distances from the center of the source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant g = 9.8 m/s2 (standard gravity). In this case, a simple expression for gravitational potential energy can be derived using the W = Fd equation for work, and the equation W F = − Δ U F . {\displaystyle W_{\text{F}}=-\Delta U_{\text{F}}.} The amount of gravitational potential energy held by an elevated object is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward multiplied with the vertical distance it is moved (remember W = Fd). The upward force required while moving at a constant velocity is equal to the weight, mg, of an object, so the work done in lifting it through a height h is the product mgh. Thus, when accounting only for mass, gravity, and altitude, the equation is: U = m g h {\displaystyle U=mgh} where U is the potential energy of the object relative to its being on the Earth's surface, m is the mass of the object, g is the acceleration due to gravity, and h is the altitude of the object. Hence, the potential difference is Δ U = m g Δ h . {\displaystyle \Delta U=mg\Delta h.} === General formula === However, over large variations in distance, the approximation that g is constant is no longer valid, and we have to use calculus and the general mathematical definition of work to determine gravitational potential energy. For the computation of the potential energy, we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to the distance r between the two bodies. Using that definition, the gravitational potential energy of a system of masses m1 and M2 at a distance r using the Newtonian constant of gravitation G is U = − G m 1 M 2 r + K , {\displaystyle U=-G{\frac {m_{1}M_{2}}{r}}+K,} where K is an arbitrary constant dependent on the choice of datum from which potential is measured. Choosing the convention that K = 0 (i.e. in relation to a point at infinity) makes calculations simpler, albeit at the cost of making U negative; for why this is physically reasonable, see below. Given this formula for U, the total potential energy of a system of n bodies is found by summing, for all n ( n − 1 ) 2 {\textstyle {\frac {n(n-1)}{2}}} pairs of two bodies, the potential energy of the system of those two bodies. Considering the system of bodies as the combined set of small particles the bodies consist of, and applying the previous on the particle level we get the negative gravitational binding energy. This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of the system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity. U = − m ( G M 1 r 1 + G M 2 r 2 ) {\displaystyle U=-m\left(G{\frac {M_{1}}{r_{1}}}+G{\frac {M_{2}}{r_{2}}}\right)} therefore, U = − m ∑ G M r , {\displaystyle U=-m\sum G{\frac {M}{r}},} === Negative gravitational energy === As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and the choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite r over another, there seem to be only two reasonable choices for the distance at which U becomes zero: r = 0 {\displaystyle r=0} and r = ∞ {\displaystyle r=\infty } . The choice of U = 0 {\displaystyle U=0} at infinity may seem peculiar, and the consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative. The singularity at r = 0 {\displaystyle r=0} in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with U = 0 {\displaystyle U=0} for ⁠ r = 0 {\displaystyle r=0} ⁠, would result in potential energy being positive, but infinitely large for all nonzero values of r, and would make calculations involving sums or differences of potential energies beyond what is possible with the real number system. Since physicists abhor infinities in their calculations, and r is always non-zero in practice, the choice of U = 0 {\displaystyle U=0} at infinity is by far the more preferable choice, even if the idea of negative energy in a gravity well appears to be peculiar at first. The negative value for gravitational energy also has deeper implications that make it seem more reasonable in cosmological calculations where the total energy of the universe can meaningfully be considered; see inflation theory for more on this. === Uses === Gravitational potential energy has a number of practical uses, notably the generation of pumped-storage hydroelectricity. For example, in Dinorwig, Wales, there are two lakes, one at a higher elevation than the other. At times when surplus electricity is not required (and so is comparatively cheap), water is pumped up to the higher lake, thus converting the electrical energy (running the pump) to gravitational potential energy. At times of peak demand for electricity, the water flows back down through electrical generator turbines, converting the potential energy into kinetic energy and then back into electricity. The process is not completely efficient and some of the original energy from the surplus electricity is in fact lost to friction. Gravitational potential energy is also used to power clocks in which falling weights operate the mechanism. It is also used by counterweights for lifting up an elevator, crane, or sash window. Roller coasters are an entertaining way to utilize potential energy – chains are used to move a car up an incline (building up gravitational potential energy), to then have that energy converted into kinetic energy as it falls. Another practical use is utilizing gravitational potential energy to descend (perhaps coast) downhill in transportation such as the descent of an automobile, truck, railroad train, bicycle, airplane, or fluid in a pipeline. In some cases the kinetic energy obtained from the potential energy of descent may be used to start ascending the next grade such as what happens when a road is undulating and has frequent dips. The commercialization of stored energy (in the form of rail cars raised to higher elevations) that is then converted to electrical energy when needed by an electrical grid, is being undertaken in the United States in a system called Advanced Rail Energy Storage (ARES). == Chemical potential energy == Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. As an example, when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy through the process known as photosynthesis, and electrical energy can be converted to chemical energy through electrochemical reactions. The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc. == Electric potential energy == An object can have potential energy by virtue of its electric charge and several forces related to their presence. There are two main types of this kind of potential energy: electrostatic potential energy, electrodynamic potential energy (also sometimes called magnetic potential energy). === Electrostatic potential energy === Electrostatic potential energy between two bodies in space is obtained from the force exerted by a charge Q on another charge q, which is given by F e = − 1 4 π ε 0 Q q r 2 r ^ , {\displaystyle \mathbf {F} _{e}=-{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {r}} ,} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from Q to q and ε0 is the vacuum permittivity. If the electric charge of an object can be assumed to be at rest, then it has potential energy due to its position relative to other charged objects. The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, adjusted for non-electrical forces on the object. This energy will generally be non-zero if there is another electrically charged object nearby. The work W required to move q from A to any point B in the electrostatic force field is given by Δ U A B ( r ) = − ∫ A B F e ⋅ d r {\displaystyle \Delta U_{AB}({\mathbf {r} })=-\int _{A}^{B}\mathbf {F_{e}} \cdot d\mathbf {r} } typically given in J for Joules. A related quantity called electric potential (commonly denoted with a V for voltage) is equal to the electric potential energy per unit charge. === Magnetic potential energy === The energy of a magnetic moment μ {\displaystyle {\boldsymbol {\mu }}} in an externally produced magnetic B-field B has potential energy U = − μ ⋅ B . {\displaystyle U=-{\boldsymbol {\mu }}\cdot \mathbf {B} .} The magnetization M in a field is U = − 1 2 ∫ M ⋅ B d V , {\displaystyle U=-{\frac {1}{2}}\int \mathbf {M} \cdot \mathbf {B} \,dV,} where the integral can be over all space or, equivalently, where M is nonzero. Magnetic potential energy is the form of energy related not only to the distance between magnetic materials, but also to the orientation, or alignment, of those materials within the field. For example, the needle of a compass has the lowest magnetic potential energy when it is aligned with the north and south poles of the Earth's magnetic field. If the needle is moved by an outside force, torque is exerted on the magnetic dipole of the needle by the Earth's magnetic field, causing it to move back into alignment. The magnetic potential energy of the needle is highest when its field is in the same direction as the Earth's magnetic field. Two magnets will have potential energy in relation to each other and the distance between them, but this also depends on their orientation. If the opposite poles are held apart, the potential energy will be higher the further they are apart and lower the closer they are. Conversely, like poles will have the highest potential energy when forced together, and the lowest when they spring apart. == Nuclear potential energy == Nuclear potential energy is the potential energy of the particles inside an atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Their rest mass provides the potential energy for certain kinds of radioactive decay, such as beta decay. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them can have less mass than if they were individually free, in which case this mass difference can be liberated as heat and radiation in nuclear reactions. The process of hydrogen fusion occurring in the Sun is an example of this form of energy release – 600 million tonnes of hydrogen nuclei are fused into helium nuclei, with a loss of about 4 million tonnes of mass per second. This energy, now in the form of kinetic energy and gamma rays, keeps the solar core hot even as electromagnetic radiation carries electromagnetic energy into space. == Forces and potential energy == Potential energy is closely linked with forces. If the work done by a force on a body that moves from A to B does not depend on the path between these points, then the work of this force measured from A assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. For example, gravity is a conservative force. The associated potential is the gravitational potential, often denoted by ϕ {\displaystyle \phi } or V {\displaystyle V} , corresponding to the energy per unit mass as a function of position. The gravitational potential energy of two particles of mass M and m separated by a distance r is U = − G M m r . {\displaystyle U=-{\frac {GMm}{r}}.} The gravitational potential (specific energy) of the two bodies is ϕ = − ( G M r + G m r ) = − G ( M + m ) r = − G M m μ r = U μ {\displaystyle \phi =-\left({\frac {GM}{r}}+{\frac {Gm}{r}}\right)=-{\frac {G(M+m)}{r}}=-{\frac {GMm}{\mu r}}={\frac {U}{\mu }}} where μ {\displaystyle \mu } is the reduced mass. The work done against gravity by moving an infinitesimal mass from point A with U = a {\displaystyle U=a} to point B with U = b {\displaystyle U=b} is ( b − a ) {\displaystyle (b-a)} and the work done going back the other way is ( a − b ) {\displaystyle (a-b)} so that the total work done in moving from A to B and returning to A is U A → B → A = ( b − a ) + ( a − b ) = 0. {\displaystyle U_{A\to B\to A}=(b-a)+(a-b)=0.} If the potential is redefined at A to be a + c {\displaystyle a+c} and the potential at B to be b + c {\displaystyle b+c} , where c {\displaystyle c} is a constant (i.e. c {\displaystyle c} can be any number, positive or negative, but it must be the same at A as it is at B) then the work done going from A to B is U A → B = ( b + c ) − ( a + c ) = b − a {\displaystyle U_{A\to B}=(b+c)-(a+c)=b-a} as before. In practical terms, this means that one can set the zero of U {\displaystyle U} and ϕ {\displaystyle \phi } anywhere one likes. One may set it to be zero at the surface of the Earth, or may find it more convenient to set zero at infinity (as in the expressions given earlier in this section). A conservative force can be expressed in the language of differential geometry as a closed form. As Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is also an exact form, and can be expressed as the gradient of a scalar field. This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field. == Notes == == References == Serway, Raymond A.; Jewett, John W. (2010). Physics for Scientists and Engineers (8th ed.). Brooks/Cole cengage. ISBN 978-1-4390-4844-3. Tipler, Paul (2004). Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.). W. H. Freeman. ISBN 0-7167-0809-4. == External links == What is potential energy?
Wikipedia/Magnetic_potential_energy
Energy democracy is a concept developed within the environmental justice movement that pairs the renewable energy transition with efforts to democratize the production and management of energy resources— including the social ownership of energy infrastructure, decentralization of energy systems, and expansion of public participation in energy-related policymaking. Energy democracy calls for greater participation in transitions and is being used in literature to describe an overall ongoing democratic transition. Energy democracy and climate justice are increasingly associated. Rather than view decarbonization as a purely technological challenge, energy democracy identifies the renewable energy transition as an opportunity to redistribute political and economic power toward egalitarian ends. Energy democracy has been endorsed by community organizations, think tanks, labor unions, and NGOs as a framework for decarbonization. Energy Democracy began in western Europe between 2000 and 2010 and has become a worldwide practice and point of reference except Asia. The concept is also associated with a number of campaigns in Europe and North America calling for the municipalization of energy companies and democratization of their governance structures. In the United States, the term “energy democracy” has become more widespread as calls for it greatly increased in the 2010s. The American branch of energy democracy builds on the foundation of a 2017 “Energy Democracy Symposium” in Utah. The number of publications on energy democracy peaked in the US in 2018, which can be correlated to a growing social demand. == Principles == The exact definition of energy democracy is contested and the term is used to refer to a diverse set of proposals, practices, and ideas. However, advocates most often define energy democracy as embodying progressive principles they believe should guide contemporary energy policy and governance— namely social ownership, public participation, decentralization, and source information. === Social ownership === Advocates of energy democracy support a transition toward social ownership of energy companies and infrastructure, arguing that existing privately-owned utilities are poorly-suited to undertake rapid decarbonization and address concerns of environmental justice. The call for social ownership encompasses both expansions of public ownership (i.e. municipalization and nationalization) and the promotion of forms of collective ownership (e.g. energy cooperatives). === Public participation === Energy democracy calls for expanding public participation in the renewable energy transition and the broader functionings of the energy sector. In doing so, advocates argue that energy policy and decision-making will better incorporate local knowledge and the environmental justice concerns of local communities. Various mechanisms for public participation have been suggested, including the creation of democratically-elected energy oversight boards and the incorporation of public deliberation into the policymaking process. Globally, end user communities of community renewable energy projects are expressing a desire for increased participation and ownership, while engineers and project managers outside of a community tend to want to preserve the status quo. The need for a democratic transition in energy ownership arises from this discrepancy, as end users—"energy citizens"—of energy transitions are often underrepresented. === Decentralization === Solar panels, wind turbines, and other renewable energy technologies allow for energy generation to be physically decentralized; advocates of energy democracy believe this energy decentralization could be a tool for empowering local communities and deconcentrating wealth and power. By building and managing energy infrastructure at the community-scale (e.g. community wind and solar farms), communities avoid having to outsource energy generation to privately-owned utilities with regional monopolies. Additionally, advocates argue that decentralization can change community-wide relationships with energy consumption by turning community members into prosumers with a direct stake in questions of production. == Campaigns == In 2012, a global coalition of trade unionists founded Trade Unions for Energy Democracy to organize workers in support of climate action and a just transition to renewable energy. As of 2021, the network claims a membership of 89 trade union bodies in 26 countries. In 2021, the New York Energy Democracy Alliance joined other state advocacy organizations in forming the Public Power NY Coalition. The coalition is currently advocating for the passage of the New York Utility Democracy Act (S.B. S7243), which would municipalize the New York's private utility companies and create democratically-elected utility boards to oversee their operations. == See also == Community solar farm Community wind energy Economic democracy RAPS Soft energy path Wadebridge Renewable Energy Network a solar farm entity in Aus/ NZ; who create and facilitate co-op owned community renewable energy farms. https://energydemocracy.net/ == References ==
Wikipedia/Energy_democracy
Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means. The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, E = mc2, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed. The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles (nuclear fission products). These nuclear binding energies and forces are on the order of one million times greater than the electron binding energies of light atoms like hydrogen. == Introduction == === Nuclear energy === An absorption or release of nuclear energy occurs in nuclear reactions or radioactive decay; those that absorb energy are called endothermic reactions and those that release energy are exothermic reactions. Energy is consumed or released because of differences in the nuclear binding energy between the incoming and outgoing products of the nuclear transmutation. The best-known classes of exothermic nuclear transmutations are nuclear fission and nuclear fusion. Nuclear energy may be released by fission, when heavy atomic nuclei (like uranium and plutonium) are broken apart into lighter nuclei. The energy from fission is used to generate electric power in hundreds of locations worldwide. Nuclear energy is also released during fusion, when light nuclei like hydrogen are combined to form heavier nuclei such as helium. The Sun and other stars use nuclear fusion to generate thermal energy which is later radiated from the surface, a type of stellar nucleosynthesis. In any exothermic nuclear process, nuclear mass might ultimately be converted to thermal energy, emitted as heat. In order to quantify the energy released or absorbed in any nuclear transmutation, one must know the nuclear binding energies of the nuclear components involved in the transmutation. === The nuclear force === Electrons and nuclei are kept together by electrostatic attraction (negative attracts positive). Furthermore, electrons are sometimes shared by neighboring atoms or transferred to them (by processes of quantum physics); this link between atoms is referred to as a chemical bond and is responsible for the formation of all chemical compounds. The electric force does not hold nuclei together, because all protons carry a positive charge and repel each other. If two protons were touching, their repulsion force would be almost 40 newtons. Because each of the neutrons carries total charge zero, a proton could electrically attract a neutron if the proton could induce the neutron to become electrically polarized. However, having the neutron between two protons (so their mutual repulsion decreases to 10 N) would attract the neutron only for an electric quadrupole (− + + −) arrangement. Higher multipoles, needed to satisfy more protons, cause weaker attraction, and quickly become implausible. After the proton and neutron magnetic moments were measured and verified, it was apparent that their magnetic forces might be 20 or 30 newtons, attractive if properly oriented. A pair of protons would do 10−13 joules of work to each other as they approach – that is, they would need to release energy of 0.5 MeV in order to stick together. On the other hand, once a pair of nucleons magnetically stick, their external fields are greatly reduced, so it is difficult for many nucleons to accumulate much magnetic energy. Therefore, another force, called the nuclear force (or residual strong force) holds the nucleons of nuclei together. This force is a residuum of the strong interaction, which binds quarks into nucleons at an even smaller level of distance. The fact that nuclei do not clump together (fuse) under normal conditions suggests that the nuclear force must be weaker than the electric repulsion at larger distances, but stronger at close range. Therefore, it has short-range characteristics. An analogy to the nuclear force is the force between two small magnets: magnets are very difficult to separate when stuck together, but once pulled a short distance apart, the force between them drops almost to zero. Unlike gravity or electrical forces, the nuclear force is effective only at very short distances. At greater distances, the electrostatic force dominates: the protons repel each other because they are positively charged, and like charges repel. For that reason, the protons forming the nuclei of ordinary hydrogen—for instance, in a balloon filled with hydrogen—do not combine to form helium (a process that also would require some protons to combine with electrons and become neutrons). They cannot get close enough for the nuclear force, which attracts them to each other, to become important. Only under conditions of extreme pressure and temperature (for example, within the core of a star), can such a process take place. === Physics of nuclei === There are around 94 naturally occurring elements on Earth. The atoms of each element have a nucleus containing a specific number of protons (always the same number for a given element), and some number of neutrons, which is often roughly a similar number. Two atoms of the same element having different numbers of neutrons are known as isotopes of the element. Different isotopes may have different properties – for example one might be stable and another might be unstable, and gradually undergo radioactive decay to become another element. The hydrogen nucleus contains just one proton. Its isotope deuterium, or heavy hydrogen, contains a proton and a neutron. The most common isotope of helium contains two protons and two neutrons, and those of carbon, nitrogen and oxygen – six, seven and eight of each particle, respectively. However, a helium nucleus weighs less than the sum of the weights of the two heavy hydrogen nuclei which combine to make it. The same is true for carbon, nitrogen and oxygen. For example, the carbon nucleus is slightly lighter than three helium nuclei, which can combine to make a carbon nucleus. This difference is known as the mass defect. ==== Mass defect ==== Mass defect (also called "mass deficit") is the difference between the mass of an object and the sum of the masses of its constituent particles. Discovered by Albert Einstein in 1905, it can be explained using his formula E = mc2, which describes the equivalence of energy and mass. The decrease in mass is equal to the energy emitted in the reaction of an atom's creation divided by c2. By this formula, adding energy also increases mass (both weight and inertia), whereas removing energy decreases mass. For example, a helium atom containing four nucleons has a mass about 0.8% less than the total mass of four hydrogen atoms (each containing one nucleon). The helium nucleus has four nucleons bound together, and the binding energy which holds them together is, in effect, the missing 0.8% of mass. For lighter elements, the energy that can be released by assembling them from lighter elements decreases, and energy can be released when they fuse. This is true for nuclei lighter than iron/nickel. For heavier nuclei, more energy is needed to bind them, and that energy may be released by breaking them up into fragments (known as nuclear fission). Nuclear power is generated at present by breaking up uranium nuclei in nuclear power reactors, and capturing the released energy as heat, which is converted to electricity. As a rule, very light elements can fuse comparatively easily, and very heavy elements can break up via fission very easily; elements in the middle are more stable and it is difficult to make them undergo either fusion or fission in an environment such as a laboratory. The reason the trend reverses after iron is the growing positive charge of the nuclei, which tends to force nuclei to break up. It is resisted by the strong nuclear interaction, which holds nucleons together. The electric force may be weaker than the strong nuclear force, but the strong force has a much more limited range: in an iron nucleus, each proton repels the other 25 protons, while the nuclear force only binds close neighbors. So for larger nuclei, the electrostatic forces tend to dominate and the nucleus will tend over time to break up. As nuclei grow bigger still, this disruptive effect becomes steadily more significant. By the time polonium is reached (84 protons), nuclei can no longer accommodate their large positive charge, but emit their excess protons quite rapidly in the process of alpha radioactivity—the emission of helium nuclei, each containing two protons and two neutrons. (Helium nuclei are an especially stable combination.) Because of this process, nuclei with more than 94 protons are not found naturally on Earth (see periodic table). The isotopes beyond uranium (atomic number 92) with the longest half-lives are plutonium-244 (80 million years) and curium-247 (16 million years). ==== Nuclear reactions in the Sun ==== The nuclear fusion process works as follows: five billion years ago, the new Sun formed when gravity pulled together a vast cloud of hydrogen and dust, from which the Earth and other planets also arose. The gravitational pull released energy and heated the early Sun, much in the way Helmholtz proposed. Thermal energy appears as the motion of atoms and molecules: the higher the temperature of a collection of particles, the greater is their velocity and the more violent are their collisions. When the temperature at the center of the newly formed Sun became great enough for collisions between hydrogen nuclei to overcome their electric repulsion, and bring them into the short range of the attractive nuclear force, nuclei began to stick together. When this began to happen, protons combined into deuterium and then helium, with some protons changing in the process to neutrons (plus positrons, positive electrons, which combine with electrons and annihilate into gamma-ray photons). This released nuclear energy now keeps up the high temperature of the Sun's core, and the heat also keeps the gas pressure high, keeping the Sun at its present size, and stopping gravity from compressing it any more. There is now a stable balance between gravity and pressure. Different nuclear reactions may predominate at different stages of the Sun's existence, including the proton–proton reaction and the carbon–nitrogen cycle—which involves heavier nuclei, but whose final product is still the combination of protons to form helium. A branch of physics, the study of controlled nuclear fusion, has tried since the 1950s to derive useful power from nuclear fusion reactions that combine small nuclei into bigger ones, typically to heat boilers, whose steam could turn turbines and produce electricity. No earthly laboratory can match one feature of the solar powerhouse: the great mass of the Sun, whose weight keeps the hot plasma compressed and confines the nuclear furnace to the Sun's core. Instead, physicists use strong magnetic fields to confine the plasma, and for fuel they use heavy forms of hydrogen, which burn more easily. Magnetic traps can be rather unstable, and any plasma hot enough and dense enough to undergo nuclear fusion tends to slip out of them after a short time. Even with ingenious tricks, the confinement in most cases lasts only a small fraction of a second. ==== Combining nuclei ==== Small nuclei that are larger than hydrogen can combine into bigger ones and release energy, but in combining such nuclei, the amount of energy released is much smaller compared to hydrogen fusion. The reason is that while the overall process releases energy from letting the nuclear attraction do its work, energy must first be injected to force together positively charged protons, which also repel each other with their electric charge. For elements that weigh more than iron (a nucleus with 26 protons), the fusion process no longer releases energy. In even heavier nuclei energy is consumed, not released, by combining similarly sized nuclei. With such large nuclei, overcoming the electric repulsion (which affects all protons in the nucleus) requires more energy than is released by the nuclear attraction (which is effective mainly between close neighbors). Conversely, energy could actually be released by breaking apart nuclei heavier than iron. With the nuclei of elements heavier than lead, the electric repulsion is so strong that some of them spontaneously eject positive fragments, usually nuclei of helium that form stable alpha particles. This spontaneous break-up is one of the forms of radioactivity exhibited by some nuclei. Nuclei heavier than lead (except for bismuth, thorium, and uranium) spontaneously break up too quickly to appear in nature as primordial elements, though they can be produced artificially or as intermediates in the decay chains of heavier elements. Generally, the heavier the nuclei are, the faster they spontaneously decay. Iron nuclei are the most stable nuclei (in particular iron-56), and the best sources of energy are therefore nuclei whose weights are as far removed from iron as possible. One can combine the lightest ones—nuclei of hydrogen (protons)—to form nuclei of helium, and that is how the Sun generates its energy. Alternatively, one can break up the heaviest ones—nuclei of uranium or plutonium—into smaller fragments, and that is what nuclear reactors do. === Nuclear binding energy === An example that illustrates nuclear binding energy is the nucleus of 12C (carbon-12), which contains 6 protons and 6 neutrons. The protons are all positively charged and repel each other, but the nuclear force overcomes the repulsion and causes them to stick together. The nuclear force is a close-range force (it is strongly attractive at a distance of 1.0 fm and becomes extremely small beyond a distance of 2.5 fm), and virtually no effect of this force is observed outside the nucleus. The nuclear force also pulls neutrons together, or neutrons and protons. The energy of the nucleus is negative with regard to the energy of the particles pulled apart to infinite distance (just like the gravitational energy of planets of the Solar System), because energy must be utilized to split a nucleus into its individual protons and neutrons. Mass spectrometers have measured the masses of nuclei, which are always less than the sum of the masses of protons and neutrons that form them, and the difference—by the formula E = mc2—gives the binding energy of the nucleus. ==== Nuclear fusion ==== The binding energy of helium is the energy source of the Sun and of most stars. The sun is composed of 74 percent hydrogen (measured by mass), an element having a nucleus consisting of a single proton. Energy is released in the Sun when 4 protons combine into a helium nucleus, a process in which two of them are also converted to neutrons. The conversion of protons to neutrons is the result of another nuclear force, known as the weak (nuclear) force. The weak force, like the strong force, has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons into the most energetically stable configuration. For nuclei containing less than 40 particles, these numbers are usually about equal. Protons and neutrons are closely related and are collectively known as nucleons. As the number of particles increases toward a maximum of about 209, the number of neutrons to maintain stability begins to outstrip the number of protons, until the ratio of neutrons to protons is about three to two. The protons of hydrogen combine to helium only if they have enough velocity to overcome each other's mutual repulsion sufficiently to get within range of the strong nuclear attraction. This means that fusion only occurs within a very hot gas. Hydrogen hot enough for combining to helium requires an enormous pressure to keep it confined, but suitable conditions exist in the central regions of the Sun, where such pressure is provided by the enormous weight of the layers above the core, pressed inwards by the Sun's strong gravity. The process of combining protons to form helium is an example of nuclear fusion. Producing helium from normal hydrogen would be practically impossible on earth because of the difficulty in creating deuterium. Research is being undertaken on developing a process using deuterium and tritium. The Earth's oceans contain a large amount of deuterium that could be used and tritium can be made in the reactor itself from lithium, and furthermore the helium product does not harm the environment, so some consider nuclear fusion a good alternative to supply our energy needs. Experiments to carry out this form of fusion have so far only partially succeeded. Sufficiently hot deuterium and tritium must be confined. One technique is to use very strong magnetic fields, because charged particles (like those trapped in the Earth's radiation belt) are guided by magnetic field lines. ==== The binding energy maximum and ways to approach it by decay ==== In the main isotopes of light elements, such as carbon, nitrogen and oxygen, the most stable combination of neutrons and of protons occurs when the numbers are equal (this continues to element 20, calcium). However, in heavier nuclei, the disruptive energy of protons increases, since they are confined to a tiny volume and repel each other. The energy of the strong force holding the nucleus together also increases, but at a slower rate, as if inside the nucleus, only nucleons close to each other are tightly bound, not ones more widely separated. The net binding energy of a nucleus is that of the nuclear attraction, minus the disruptive energy of the electric force. As nuclei get heavier than helium, their net binding energy per nucleon (deduced from the difference in mass between the nucleus and the sum of masses of component nucleons) grows more and more slowly, reaching its peak at iron. As nucleons are added, the total nuclear binding energy always increases—but the total disruptive energy of electric forces (positive protons repelling other protons) also increases, and past iron, the second increase outweighs the first. Iron-56 (56Fe) is the most efficiently bound nucleus meaning that it has the least average mass per nucleon. However, nickel-62 is the most tightly bound nucleus in terms of binding energy per nucleon. (Nickel-62's higher binding energy does not translate to a larger mean mass loss than 56Fe, because 62Ni has a slightly higher ratio of neutrons/protons than does iron-56, and the presence of the heavier neutrons increases nickel-62's average mass per nucleon). To reduce the disruptive energy, the weak interaction allows the number of neutrons to exceed that of protons—for instance, the main isotope of iron has 26 protons and 30 neutrons. Isotopes also exist where the number of neutrons differs from the most stable number for that number of nucleons. If changing one proton into a neutron or one neutron into a proton increases the stability (lowering the mass), then this will happen through beta decay, meaning the nuclide will be radioactive. The two methods for this conversion are mediated by the weak force, and involve types of beta decay. In the simplest beta decay, neutrons are converted to protons by emitting a negative electron and an antineutrino. This is always possible outside a nucleus because neutrons are more massive than protons by an equivalent of about 2.5 electrons. In the opposite process, which only happens within a nucleus, and not to free particles, a proton may become a neutron by ejecting a positron and an electron neutrino. This is permitted if enough energy is available between parent and daughter nuclides to do this (the required energy difference is equal to 1.022 MeV, which is the mass of 2 electrons). If the mass difference between parent and daughter is less than this, a proton-rich nucleus may still convert protons to neutrons by the process of electron capture, in which a proton simply electron captures one of the atom's K orbital electrons, emits a neutrino, and becomes a neutron. Among the heaviest nuclei, starting with tellurium nuclei (element 52) containing 104 or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus may be ejected, usually as alpha particles, which consist of two protons and two neutrons (alpha particles are fast helium nuclei). (Beryllium-8 also decays, very quickly, into two alpha particles.) This type of decay becomes more and more probable as elements rise in atomic weight past 104. The curve of binding energy is a graph that plots the binding energy per nucleon against atomic mass. This curve has its main peak at iron and nickel and then slowly decreases again, and also a narrow isolated peak at helium, which is more stable than other low-mass nuclides. The heaviest nuclei in more than trace quantities in nature, uranium 238U, are unstable, but having a half-life of 4.5 billion years, close to the age of the Earth, they are still relatively abundant; they (and other nuclei heavier than helium) have formed in stellar evolution events like supernova explosions preceding the formation of the Solar System. The most common isotope of thorium, 232Th, also undergoes alpha particle emission, and its half-life (time over which half a number of atoms decays) is even longer, by several times. In each of these, radioactive decay produces daughter isotopes that are also unstable, starting a chain of decays that ends in some stable isotope of lead. == Calculation of nuclear binding energy == Calculation can be employed to determine the nuclear binding energy of nuclei. The calculation involves determining the nuclear mass defect, converting it into energy, and expressing the result as energy per mole of atoms, or as energy per nucleon. === Conversion of nuclear mass defect into energy === Nuclear mass defect is defined as the difference between the nuclear mass, and the sum of the masses of the constituent nucleons and electrons. It is given by Δ m = Z m H + ( A − Z ) m n − M = Z m H + N m n − M {\displaystyle \Delta m=Zm_{H}+(A-Z)m_{n}-M=Zm_{H}+Nm_{n}-M} where: Z is the proton number (atomic number). A is the nucleon number (mass number). mH is the mass of hydrogen. mn is the mass of neutron. M is the nuclear mass. N is the neutron number. The nuclear mass defect is usually converted into nuclear binding energy, which is the minimum energy required to disassemble the nucleus into its constituent nucleons. This conversion is done with the mass-energy equivalence: E = ∆mc2. However it must be expressed as energy per mole of atoms or as energy per nucleon. == Fission and fusion == Nuclear energy is released by the splitting (fission) or merging (fusion) of the nuclei of atom(s). The conversion of nuclear mass–energy to a form of energy, which can remove some mass when the energy is removed, is consistent with the mass–energy equivalence formula: ΔE = Δm c2, where ΔE = energy release, Δm = mass defect, and c = the speed of light in vacuum. Nuclear energy was first discovered by French physicist Henri Becquerel in 1896, when he found that photographic plates stored in the dark near uranium were blackened like X-ray plates (X-rays had recently been discovered in 1895). Nickel-62 has the highest binding energy per nucleon of any isotope. If an atom of lower average binding energy per nucleon is changed into two atoms of higher average binding energy per nucleon, energy is emitted. (The average here is the weighted average.) Also, if two atoms of lower average binding energy fuse into an atom of higher average binding energy, energy is emitted. The chart shows that fusion, or combining, of hydrogen nuclei to form heavier atoms releases energy, as does fission of uranium, the breaking up of a larger nucleus into smaller parts. Nuclear energy is released by three exoenergetic (or exothermic) processes: Radioactive decay, where a neutron or proton in the radioactive nucleus decays spontaneously by emitting either particles, electromagnetic radiation (gamma rays), or both. Note that for radioactive decay, it is not strictly necessary for the binding energy to increase. What is strictly necessary is that the mass decrease. If a neutron turns into a proton and the energy of the decay is less than 0.782343 MeV, the difference between the masses of the neutron and proton multiplied by the speed of light squared, (such as rubidium-87 decaying to strontium-87), the average binding energy per nucleon will actually decrease. Fusion, two atomic nuclei fuse together to form a heavier nucleus Fission, the breaking of a heavy nucleus into two (or more rarely three) lighter nuclei, and some neutrons The energy-producing nuclear interaction of light elements requires some clarification. Frequently, all light element energy-producing nuclear interactions are classified as fusion, however by the given definition above fusion requires that the products include a nucleus that is heavier than the reactants. Light elements can undergo energy-producing nuclear interactions by fusion or fission. All energy-producing nuclear interactions between two hydrogen isotopes and between hydrogen and helium-3 are fusion, as the product of these interactions include a heavier nucleus. However, the energy-producing nuclear interaction of a neutron with lithium–6 produces Hydrogen-3 and Helium-4, each a lighter nucleus. By the definition above, this nuclear interaction is fission, not fusion. When fission is caused by a neutron, as in this case, it is called induced fission. == Binding energy for atoms == The binding energy of an atom (including its electrons) is not exactly the same as the binding energy of the atom's nucleus. The measured mass deficits of isotopes are always listed as mass deficits of the neutral atoms of that isotope, and mostly in MeV/c2. As a consequence, the listed mass deficits are not a measure of the stability or binding energy of isolated nuclei, but for the whole atoms. There is a very practical reason for this, namely that it is very hard to totally ionize heavy elements, i.e. strip them of all of their electrons. This practice is useful for other reasons, too: stripping all the electrons from a heavy unstable nucleus (thus producing a bare nucleus) changes the lifetime of the nucleus, or the nucleus of a stable neutral atom can likewise become unstable after stripping, indicating that the nucleus cannot be treated independently. Examples of this have been shown in bound-state β decay experiments performed at the GSI heavy ion accelerator. This is also evident from phenomena like electron capture. Theoretically, in orbital models of heavy atoms, the electron orbits partially inside the nucleus (it does not orbit in a strict sense, but has a non-vanishing probability of being located inside the nucleus). A nuclear decay happens to the nucleus, meaning that properties ascribed to the nucleus change in the event. In the field of physics the concept of "mass deficit" as a measure for "binding energy" means "mass deficit of the neutral atom" (not just the nucleus) and is a measure for stability of the whole atom. == Nuclear binding energy curve == In the periodic table of elements, the series of light elements from hydrogen up to sodium is observed to exhibit generally increasing binding energy per nucleon as the atomic mass increases. This increase is generated by increasing forces per nucleon in the nucleus, as each additional nucleon is attracted by other nearby nucleons, and thus more tightly bound to the whole. Helium-4 and oxygen-16 are particularly stable exceptions to the trend (see figure on the right). This is because they are doubly magic, meaning their protons and neutrons both fill their respective nuclear shells. The region of increasing binding energy is followed by a region of relative stability (saturation) in the sequence from about mass 30 through about mass 90. In this region, the nucleus has become large enough that nuclear forces no longer completely extend efficiently across its width. Attractive nuclear forces in this region, as atomic mass increases, are nearly balanced by repellent electromagnetic forces between protons, as the atomic number increases. Finally, in the heavier elements, there is a gradual decrease in binding energy per nucleon as atomic number increases. In this region of nuclear size, electromagnetic repulsive forces are beginning to overcome the strong nuclear force attraction. At the peak of binding energy, nickel-62 is the most tightly bound nucleus (per nucleon), followed by iron-58 and iron-56. This is the approximate basic reason why iron and nickel are very common metals in planetary cores, since they are produced profusely as end products in supernovae and in the final stages of silicon burning in stars. However, it is not binding energy per defined nucleon (as defined above), which controls exactly which nuclei are made, because within stars, neutrons and protons can inter-convert to release even more energy per generic nucleon. In fact, it has been argued that photodisintegration of 62Ni to form 56Fe may be energetically possible in an extremely hot star core, due to this beta decay conversion of neutrons to protons. This favors the creation of 56Fe, the nuclide with the lowest mass per nucleon. However, at high temperatures not all matter will be in the lowest energy state. This energetic maximum should also hold for ambient conditions, say T = 298 K and p = 1 atm, for neutral condensed matter consisting of 56Fe atoms—however, in these conditions nuclei of atoms are inhibited from fusing into the most stable and low energy state of matter. Elements with high binding energy per nucleon, like iron and nickel, cannot undergo fission, but they can theoretically undergo fusion with hydrogen, deuterium, helium, and carbon, for instance: 62Ni + 12C → 74Se Q = 5.467 MeV It is generally believed that iron-56 is more common than nickel isotopes in the universe for mechanistic reasons, because its unstable progenitor nickel-56 is copiously made by staged build-up of 14 helium nuclei inside supernovas, where it has no time to decay to iron before being released into the interstellar medium in a matter of a few minutes, as the supernova explodes. However, nickel-56 then decays to cobalt-56 within a few weeks, then this radioisotope finally decays to iron-56 with a half life of about 77.3 days. The radioactive decay-powered light curve of such a process has been observed to happen in type II supernovae, such as SN 1987A. In a star, there are no good ways to create nickel-62 by alpha-addition processes, or else there would presumably be more of this highly stable nuclide in the universe. === Binding energy and nuclide masses === The fact that the maximum binding energy is found in medium-sized nuclei is a consequence of the trade-off in the effects of two opposing forces that have different range characteristics. The attractive nuclear force (strong nuclear force), which binds protons and neutrons equally to each other, has a limited range due to a rapid exponential decrease in this force with distance. However, the repelling electromagnetic force, which acts between protons to force nuclei apart, falls off with distance much more slowly (as the inverse square of distance). For nuclei larger than about four nucleons in diameter, the additional repelling force of additional protons more than offsets any binding energy that results between further added nucleons as a result of additional strong force interactions. Such nuclei become increasingly less tightly bound as their size increases, though most of them are still stable. Finally, nuclei containing more than 209 nucleons (larger than about 6 nucleons in diameter) are all too large to be stable, and are subject to spontaneous decay to smaller nuclei. Nuclear fusion produces energy by combining the very lightest elements into more tightly bound elements (such as hydrogen into helium), and nuclear fission produces energy by splitting the heaviest elements (such as uranium and plutonium) into more tightly bound elements (such as barium and krypton). The nuclear fission of a few light elements (such as Lithium) occurs because Helium-4 is a product and a more tightly bound element than slightly heavier elements. Both processes produce energy as the sum of the masses of the products is less than the sum of the masses of the reacting nuclei. As seen above in the example of deuterium, nuclear binding energies are large enough that they may be easily measured as fractional mass deficits, according to the equivalence of mass and energy. The atomic binding energy is simply the amount of energy (and mass) released, when a collection of free nucleons are joined to form a nucleus. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the masses of the number of free neutrons and protons that make up the nucleus. Once this mass difference, called the mass defect or mass deficiency, is known, Einstein's mass–energy equivalence formula E = mc2 can be used to compute the binding energy of any nucleus. Early nuclear physicists used to refer to computing this value as a "packing fraction" calculation. For example, the dalton (1 Da) is defined as 1/12 of the mass of a 12C atom—but the atomic mass of a 1H atom (which is a proton plus electron) is 1.007825 Da, so each nucleon in 12C has lost, on average, about 0.8% of its mass in the form of binding energy. === Semiempirical formula for nuclear binding energy === For a nucleus with A nucleons, including Z protons and N neutrons, a semi-empirical formula for the binding energy (EB) per nucleon is: E B A ⋅ MeV = a − b A 1 / 3 − c Z 2 A 4 / 3 − d ( N − Z ) 2 A 2 ± e A 7 / 4 {\displaystyle {\frac {E_{\text{B}}}{A\cdot {\text{MeV}}}}=a-{\frac {b}{A^{1/3}}}-{\frac {cZ^{2}}{A^{4/3}}}-{\frac {d\left(N-Z\right)^{2}}{A^{2}}}\pm {\frac {e}{A^{7/4}}}} where the coefficients are given by: a = 14.0 {\displaystyle a=14.0} ; b = 13.0 {\displaystyle b=13.0} ; c = 0.585 {\displaystyle c=0.585} ; d = 19.3 {\displaystyle d=19.3} ; e = 33 {\displaystyle e=33} . The first term a {\displaystyle a} is called the saturation contribution and ensures that the binding energy per nucleon is the same for all nuclei to a first approximation. The term − b / A 1 / 3 {\displaystyle -b/A^{1/3}} is a surface tension effect and is proportional to the number of nucleons that are situated on the nuclear surface; it is largest for light nuclei. The term − c Z 2 / A 4 / 3 {\displaystyle -cZ^{2}/A^{4/3}} is the Coulomb electrostatic repulsion; this becomes more important as Z {\displaystyle Z} increases. The symmetry correction term − d ( N − Z ) 2 / A 2 {\displaystyle -d(N-Z)^{2}/A^{2}} takes into account the fact that in the absence of other effects the most stable arrangement has equal numbers of protons and neutrons; this is because the n–p interaction in a nucleus is stronger than either the n−n or p−p interaction. The pairing term ± e / A 7 / 4 {\displaystyle \pm e/A^{7/4}} is purely empirical; it is + for even–even nuclei and − for odd–odd nuclei. When A is odd, the pairing term is identically zero. == Example values deduced from experimentally measured atom nuclide masses == The following table lists some binding energies and mass defect values. Notice also that we use 1 Da = 931.494028(23) MeV/c2. To calculate the binding energy we use the formula Z (mp + me) + N mn − mnuclide where Z denotes the number of protons in the nuclides and N their number of neutrons. We take mp = 938.2720813(58) MeV/c2, me = 0.5109989461(30) MeV/c2 and mn = 939.5654133(58) MeV/c2. The letter A denotes the sum of Z and N (number of nucleons in the nuclide). If we assume the reference nucleon has the mass of a neutron (so that all "total" binding energies calculated are maximal) we could define the total binding energy as the difference from the mass of the nucleus, and the mass of a collection of A free neutrons. In other words, it would be (Z + N) mn − mnuclide. The "total binding energy per nucleon" would be this value divided by A. 56Fe has the lowest nucleon-specific mass of the four nuclides listed in this table, but this does not imply it is the strongest bound atom per hadron, unless the choice of beginning hadrons is completely free. Iron releases the largest energy if any 56 nucleons are allowed to build a nuclide—changing one to another if necessary. The highest binding energy per hadron, with the hadrons starting as the same number of protons Z and total nucleons A as in the bound nucleus, is 62Ni. Thus, the true absolute value of the total binding energy of a nucleus depends on what we are allowed to construct the nucleus out of. If all nuclei of mass number A were to be allowed to be constructed of A neutrons, then 56Fe would release the most energy per nucleon, since it has a larger fraction of protons than 62Ni. However, if nuclei are required to be constructed of only the same number of protons and neutrons that they contain, then nickel-62 is the most tightly bound nucleus, per nucleon. In the table above it can be seen that the decay of a neutron, as well as the transformation of tritium into helium-3, releases energy; hence, it manifests a stronger bound new state when measured against the mass of an equal number of neutrons (and also a lighter state per number of total hadrons). Such reactions are not driven by changes in binding energies as calculated from previously fixed N and Z numbers of neutrons and protons, but rather in decreases in the total mass of the nuclide/per nucleon, with the reaction. (Note that the Binding Energy given above for hydrogen-1 is the atomic binding energy, not the nuclear binding energy which would be zero.) == See also == Gravitational binding energy Bond-dissociation energy (binding energy between the atoms in a chemical bond) Electron binding energy (energy required to free an electron from its atomic orbital or from a solid) Atomic binding energy (energy required to disassemble an atom into free electrons and a nucleus) Quantum chromodynamics binding energy (addresses the mass and kinetic energy of the parts that bind the various quarks together inside a hadron) == References == == External links == Media related to Nuclear binding energy at Wikimedia Commons
Wikipedia/Nuclear_binding_energy
The potential magnetic energy of a magnet or magnetic moment m {\displaystyle \mathbf {m} } in a magnetic field B {\displaystyle \mathbf {B} } is defined as the mechanical work of the magnetic force on the re-alignment of the vector of the magnetic dipole moment and is equal to: E p,m = − m ⋅ B {\displaystyle E_{\text{p,m}}=-\mathbf {m} \cdot \mathbf {B} } The mechanical work takes the form of a torque N {\displaystyle {\boldsymbol {N}}} : N = m × B = − r × ∇ E p,m {\displaystyle \mathbf {N} =\mathbf {m} \times \mathbf {B} =-\mathbf {r} \times \mathbf {\nabla } E_{\text{p,m}}} which will act to "realign" the magnetic dipole with the magnetic field. In an electronic circuit the energy stored in an inductor (of inductance L {\displaystyle L} ) when a current I {\displaystyle I} flows through it is given by: E p,m = 1 2 L I 2 . {\displaystyle E_{\text{p,m}}={\frac {1}{2}}LI^{2}.} This expression forms the basis for superconducting magnetic energy storage. It can be derived from a time average of the product of current and voltage across an inductor. Energy is also stored in a magnetic field itself. The energy per unit volume u {\displaystyle u} in a region of free space with vacuum permeability μ 0 {\displaystyle \mu _{0}} containing magnetic field B {\displaystyle \mathbf {B} } is: u = 1 2 B 2 μ 0 {\displaystyle u={\frac {1}{2}}{\frac {B^{2}}{\mu _{0}}}} More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates B {\displaystyle \mathbf {B} } and the magnetization H {\displaystyle \mathbf {H} } (for example H = B / μ {\displaystyle \mathbf {H} =\mathbf {B} /\mu } where μ {\displaystyle \mu } is the magnetic permeability of the material), then it can be shown that the magnetic field stores an energy of E = 1 2 ∫ H ⋅ B d V {\displaystyle E={\frac {1}{2}}\int \mathbf {H} \cdot \mathbf {B} \,\mathrm {d} V} where the integral is evaluated over the entire region where the magnetic field exists. For a magnetostatic system of currents in free space, the stored energy can be found by imagining the process of linearly turning on the currents and their generated magnetic field, arriving at a total energy of: E = 1 2 ∫ J ⋅ A d V {\displaystyle E={\frac {1}{2}}\int \mathbf {J} \cdot \mathbf {A} \,\mathrm {d} V} where J {\displaystyle \mathbf {J} } is the current density field and A {\displaystyle \mathbf {A} } is the magnetic vector potential. This is analogous to the electrostatic energy expression 1 2 ∫ ρ ϕ d V {\textstyle {\frac {1}{2}}\int \rho \phi \,\mathrm {d} V} ; note that neither of these static expressions apply in the case of time-varying charge or current distributions. == References == == External links == Magnetic Energy, Richard Fitzpatrick Professor of Physics The University of Texas at Austin.
Wikipedia/Magnetic_energy
Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. (Note however, the work done by a stretched rubber band is not an example of elastic energy. It is an example of entropic elasticity.) The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity. U = 1 2 k Δ x 2 {\displaystyle U={\frac {1}{2}}k\,\Delta x^{2}} The essence of elasticity is reversibility. Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape. However, all materials have limits to the degree of distortion they can endure without breaking or irreversibly altering their internal structure. Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. Beyond the elastic limit, a material is no longer storing all of the energy from mechanical work performed on it in the form of elastic energy. Elastic energy of or within a substance is static energy of configuration. It corresponds to energy stored principally by changing the interatomic distances between nuclei. Thermal energy is the randomized distribution of kinetic energy within the material, resulting in statistical fluctuations of the material about the equilibrium configuration. There is some interaction, however. For example, for some solid objects, twisting, bending, and other distortions may generate thermal energy, causing the material's temperature to rise. Thermal energy in solids is often carried by internal elastic waves, called phonons. Elastic waves that are large on the scale of an isolated object usually produce macroscopic vibrations . Although elasticity is most commonly associated with the mechanics of solid bodies or materials, even the early literature on classical thermodynamics defines and uses "elasticity of a fluid" in ways compatible with the broad definition provided in the Introduction above.: 107 et seq.  Solids include complex crystalline materials with sometimes complicated behavior. By contrast, the behavior of compressible fluids, and especially gases, demonstrates the essence of elastic energy with negligible complication. The simple thermodynamic formula: d U = − P d V , {\displaystyle dU=-P\,dV\ ,} where dU is an infinitesimal change in recoverable internal energy U, P is the uniform pressure (a force per unit area) applied to the material sample of interest, and dV is the infinitesimal change in volume that corresponds to the change in internal energy. The minus sign appears because dV is negative under compression by a positive applied pressure which also increases the internal energy. Upon reversal, the work that is done by a system is the negative of the change in its internal energy corresponding to the positive dV of an increasing volume. The system loses stored internal energy when doing work on its surroundings. Pressure is stress and volumetric change corresponds to changing the relative spacing of points within the material. The stress-strain-internal energy relationship of the foregoing formula is repeated in formulations for elastic energy of solid materials with complicated crystalline structure. == Elastic potential energy in mechanical systems == Components of mechanical systems store elastic potential energy if they are deformed when forces are applied to the system. Energy is transferred to an object by work when an external force displaces or deforms the object. The quantity of energy transferred is the vector dot product of the force and the displacement of the object. As forces are applied to the system they are distributed internally to its component parts. While some of the energy transferred can end up stored as the kinetic energy of acquired velocity, the deformation of component objects results in stored elastic energy. A prototypical elastic component is a coiled spring. The linear elastic performance of a spring is parametrized by a constant of proportionality, called the spring constant. This constant is usually denoted as k (see also Hooke's law) and depends on the geometry, cross-sectional area, undeformed length and nature of the material from which the coil is fashioned. Within a certain range of deformation, k remains constant and is defined as the negative ratio of displacement to the magnitude of the restoring force produced by the spring at that displacement. k = − F r L − L o {\displaystyle k=-{\frac {F_{r}}{L-L_{o}}}} The deformed length, L, can be larger or smaller than Lo, the undeformed length, so to keep k positive, Fr must be given as a vector component of the restoring force whose sign is negative for L>Lo and positive for L< Lo. If the displacement is abbreviated as L − L o = x , {\displaystyle L-L_{o}=x,} then Hooke's law can be written in the usual form F r = − k x . {\displaystyle F_{r}=-k\,x.} Energy absorbed and held in the spring can be derived using Hooke's law to compute the restoring force as a measure of the applied force. This requires the assumption, sufficiently correct in most circumstances, that at a given moment, the magnitude of applied force. For each infinitesimal displacement dx, the applied force is simply k x and the product of these is the infinitesimal transfer of energy into the spring dU. The total elastic energy placed into the spring from zero displacement to final length L is thus the integral U = ∫ 0 L − L o k x d x = 1 2 k ( L − L o ) 2 {\displaystyle U=\int _{0}^{L-L_{o}}k\,x\,dx={\tfrac {1}{2}}k(L-L_{o})^{2}} For a material of Young's modulus, Y (same as modulus of elasticity λ), cross sectional area, A0, initial length, l0, which is stretched by a length, Δ l {\displaystyle \Delta l} : U e = ∫ Y A 0 Δ l l 0 d ( Δ l ) = Y A 0 Δ l 2 2 l 0 {\displaystyle U_{e}=\int {\frac {YA_{0}\Delta l}{l_{0}}}\,d\left(\Delta l\right)={\frac {YA_{0}{\Delta l}^{2}}{2l_{0}}}} where Ue is the elastic potential energy. The elastic potential energy per unit volume is given by: U e A 0 l 0 = Y Δ l 2 2 l 0 2 = 1 2 Y ε 2 {\displaystyle {\frac {U_{e}}{A_{0}l_{0}}}={\frac {Y{\Delta l}^{2}}{2l_{0}^{2}}}={\frac {1}{2}}Y{\varepsilon }^{2}} where ε = Δ l l 0 {\displaystyle \varepsilon ={\frac {\Delta l}{l_{0}}}} is the strain in the material. In the general case, elastic energy is given by the free energy per unit of volume f as a function of the strain tensor components εij f ( ε i j ) = 1 2 λ ε i i 2 + μ ε i j 2 {\displaystyle f(\varepsilon _{ij})={\frac {1}{2}}\lambda \varepsilon _{ii}^{2}+\mu \varepsilon _{ij}^{2}} where λ and μ are the Lamé elastic coefficients and we use Einstein summation convention. Noting the thermodynamic connection between stress tensor components and strain tensor components, σ i j = ( ∂ f ∂ ε i j ) T , {\displaystyle \sigma _{ij}=\left({\frac {\partial f}{\partial \varepsilon _{ij}}}\right)_{T},} where the subscript T denotes that temperature is held constant, then we find that if Hooke's law is valid, we can write the elastic energy density as f = 1 2 ε i j σ i j . {\displaystyle f={\frac {1}{2}}\varepsilon _{ij}\sigma _{ij}.} == Continuum systems == Matter in bulk can be distorted in many different ways: stretching, shearing, bending, twisting, etc. Each kind of distortion contributes to the elastic energy of a deformed material. In orthogonal coordinates, the elastic energy per unit volume due to strain is thus a sum of contributions: U = 1 2 C i j k l ε i j ε k l , {\displaystyle U={\frac {1}{2}}C_{ijkl}\varepsilon _{ij}\varepsilon _{kl},} where C i j k l {\displaystyle C_{ijkl}} is a 4th rank tensor, called the elastic tensor or stiffness tensor which is a generalization of the elastic moduli of mechanical systems, and ε i j {\displaystyle \varepsilon _{ij}} is the strain tensor (Einstein summation notation has been used to imply summation over repeated indices). The values of C i j k l {\displaystyle C_{ijkl}} depend upon the crystal structure of the material: in the general case, due to symmetric nature of σ {\displaystyle \sigma } and ε {\displaystyle \varepsilon } , the elastic tensor consists of 21 independent elastic coefficients. This number can be further reduced by the symmetry of the material: 9 for an orthorhombic crystal, 5 for an hexagonal structure, and 3 for a cubic symmetry. Finally, for an isotropic material, there are only two independent parameters, with C i j k l = λ δ i j δ k l + μ ( δ i k δ j l + δ i l δ j k ) {\displaystyle C_{ijkl}=\lambda \delta _{ij}\delta _{kl}+\mu \left(\delta _{ik}\delta _{jl}+\delta _{il}\delta _{jk}\right)} , where λ {\displaystyle \lambda } and μ {\displaystyle \mu } are the Lamé constants, and δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. The strain tensor itself can be defined to reflect distortion in any way that results in invariance under total rotation, but the most common definition with regard to which elastic tensors are usually expressed defines strain as the symmetric part of the gradient of displacement with all nonlinear terms suppressed: ε i j = 1 2 ( ∂ i u j + ∂ j u i ) {\displaystyle \varepsilon _{ij}={\frac {1}{2}}\left(\partial _{i}u_{j}+\partial _{j}u_{i}\right)} where u i {\displaystyle u_{i}} is the displacement at a point in the i {\displaystyle i} -th direction and ∂ j {\displaystyle \partial _{j}} is the partial derivative in the j {\displaystyle j} -th direction. Note that: ε j j = ∂ j u j {\displaystyle \varepsilon _{jj}=\partial _{j}u_{j}} where no summation is intended. Although full Einstein notation sums over raised and lowered pairs of indices, the values of elastic and strain tensor components are usually expressed with all indices lowered. Thus beware (as here) that in some contexts a repeated index does not imply a sum overvalues of that index ( j {\displaystyle j} in this case), but merely a single component of a tensor. == See also == Clockwork Elasto-capillarity Rubber elasticity == References == == Sources == Eshelby, J.D (November 1975). "The elastic energy-momentum tensor". Journal of Elasticity. 5 (3–4): 321–335. doi:10.1007/BF00126994. S2CID 121320629.
Wikipedia/Elastic_potential_energy
In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field F {\displaystyle \mathbf {F} } , where F ( r ) {\displaystyle \mathbf {F} (\mathbf {r} )} is the force that a particle would feel if it were at the position r {\displaystyle \mathbf {r} } . == Examples == Gravity is the force of attraction between two objects. A gravitational force field models this influence that a massive body (or more generally, any quantity of energy) extends into the space around itself. In Newtonian gravity, a particle of mass M creates a gravitational field g = − G M r 2 r ^ {\displaystyle \mathbf {g} ={\frac {-GM}{r^{2}}}{\hat {\mathbf {r} }}} , where the radial unit vector r ^ {\displaystyle {\hat {\mathbf {r} }}} points away from the particle. The gravitational force experienced by a particle of light mass m, close to the surface of Earth is given by F = m g {\displaystyle \mathbf {F} =m\mathbf {g} } , where g is Earth's gravity. An electric field E {\displaystyle \mathbf {E} } exerts a force on a point charge q, given by F = q E {\displaystyle \mathbf {F} =q\mathbf {E} } . In a magnetic field B {\displaystyle \mathbf {B} } , a point charge moving through it experiences a force perpendicular to its own velocity and to the direction of the field, following the relation: F = q v × B {\displaystyle \mathbf {F} =q\mathbf {v} \times \mathbf {B} } . == Work == Work is dependent on the displacement as well as the force acting on an object. As a particle moves through a force field along a path C, the work done by the force is a line integral: W = ∫ C F ⋅ d r {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} } This value is independent of the velocity/momentum that the particle travels along the path. === Conservative force field === For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points. Therefore, the work for an object travelling in a closed path is zero, since its starting and ending points are the same: ∮ C F ⋅ d r = 0 {\displaystyle \oint _{C}\mathbf {F} \cdot d\mathbf {r} =0} If the field is conservative, the work done can be more easily evaluated by realizing that a conservative vector field can be written as the gradient of some scalar potential function: F = − ∇ ϕ {\displaystyle \mathbf {F} =-\nabla \phi } The work done is then simply the difference in the value of this potential in the starting and end points of the path. If these points are given by x = a and x = b, respectively: W = ϕ ( b ) − ϕ ( a ) {\displaystyle W=\phi (b)-\phi (a)} == See also == Classical mechanics Field line Force Mechanical work == References == == External links == Conservative and non-conservative force-fields, Classical Mechanics, University of Texas at Austin
Wikipedia/Force_field_(physics)
Energy engineering is a multidisciplinary field of engineering that focuses on optimizing energy systems, developing renewable energy technologies, and improving energy efficiency to meet the world's growing demand for energy in a sustainable manner. It encompasses areas such as energy harvesting and storage, energy conversion, energy materials, energy systems, energy efficiency, energy services, facility management, plant engineering, energy modelling, environmental compliance, As one of the most recent engineering disciplines to emerge, energy engineering plays a critical role in addressing global challenges like climate change, carbon reduction, and the transition from fossil fuels to renewable energy sources and sustainable energy. Energy engineering is one of the most recent engineering disciplines to emerge. Energy engineering combines knowledge from the fields of physics, math, and chemistry with economic and environmental engineering practices. Energy engineers apply their skills to increase efficiency and further develop renewable sources of energy. The main job of energy engineers is to find the most efficient and sustainable ways to operate buildings and manufacturing processes. Energy engineers audit the use of energy in those processes and suggest ways to improve the systems. This means suggesting advanced lighting, better insulation, more efficient heating and cooling properties of buildings. Although an energy engineer is concerned about obtaining and using energy in the most environmentally friendly ways, their field is not limited to strictly renewable energy like hydro, solar, biomass, or geothermal. Energy engineers are also employed by the fields of oil and natural gas extraction. == Purpose == The primary purpose of energy engineering is to optimize the production and use of energy resources while minimizing energy waste and reducing environmental impact. This discipline is vital for designing systems that consume less energy, meet carbon reduction targets, and improve the energy efficiency of processes in industrial, commercial, and residential sectors. Often applied to building design, heavy consideration is given to HVAC, lighting, refrigeration, to both reduce energy loads and increase efficiency of current systems. Energy engineering is increasingly seen as a major step forward in meeting carbon reduction targets. Since buildings and houses consume over 40% of the United States energy, the services an energy engineer performs are in demand. == History == Human civilizations have long relied on the conversion of energy for various purposes, from the use of fire to the development of water wheels, windmills, and, eventually, electricity generation. The formalization of energy engineering began during the industrial revolution and accelerated in the mid-20th century with advancements in electrical power systems, nuclear energy, and renewable energy technologies. The oil crisis of 1973 highlighted the need for increased energy efficiency and energy independence, leading to the establishment of new government programs and industry standards. In addition, the energy crisis of 1979 brought to light the need to get more work out of less energy. The United States government passed several laws to promote increased energy efficiency, such as United States public law 94-413, the Federal Clean Car Incentive Program. == Power engineering == Power engineering, often viewed as a subset of electrical engineering, focuses on the generation, transmission, distribution, and utilization of electrical power. This subfield covers critical infrastructure such as power plants, electric grids, and energy storage systems, ensuring the efficient and reliable delivery of energy across various sectors. Emerging technologies in power engineering include the development of smart grids, microgrids, and advanced energy storage systems like lithium-ion batteries and hydrogen fuel cells, which are central to the future of renewable energy integration. == Leadership in Energy and Environmental Design == Leadership in Energy and Environmental Design (LEED) is a program created by the United States Green Building Council (USGBC) in March 2000. LEED is a program that encourages green building and promotes sustainability in the construction of buildings and the efficiency of the utilities in the buildings. In 2012 the United States Green Building Council asked the independent firm Booz Allen Hamilton to conduct a study on the effectiveness of LEED program. "This study confirmed that green buildings generate substantial energy savings. From 2000–2008, green construction and renovation generated $1.3 billion in energy savings. Of that $1.3 billion, LEED-certified buildings accounted for $281 million." The study also found the summation of all green construction supported 2.4 million jobs. == Energy efficiency == Energy efficiency is seen two ways. The first view is that more work is done from the same amount of energy used. The other perception is that the same amount of work is accomplished with less energy used in the system. Some ways to get more work out of less energy is to "Reduce, Reuse, and Recycle" the materials used in daily life. The advancement of technology has led to other uses of waste. Technology such as waste-to-energy facilities which convert solid wastes through the process of gasification or pyrolysis to liquid fuels to be burned. The Environmental Protection Agency stated that the United States produced 250 million tons of municipal waste in 2010. Of that 250 million tons roughly 54% gets thrown in land fills, 33% is recycled, and 13% goes to energy recovery plants. In European countries who pay more for fuel, such as Denmark where the price of gas neared $2.6 per litre ($10/US gal) in 2010, have more fully developed waste-to energy facilities. In 2010 Denmark sent 7% of waste to landfills, 69% was recycled, and 24% was sent to waste-to-energy facilities. There are several other developed Western European countries that also have taken energy engineering into consideration. Germany's "Energiewende", a policy which set the goal by 2050 to meet 80% of electrical needs from renewable energy sources. == Statistics == As of 2023, the median annual salary for energy engineers in the U.S. ranges from $75,000 to $95,000, depending on experience and location. Energy engineers with expertise in renewable energy and energy storage tend to receive higher salaries due to the growing demand for sustainable solutions. The gender distribution in the field remains prominent, with around 80% male engineers, though efforts to increase diversity are underway through scholarships and mentorship programs. The job market for energy engineers is expected to grow rapidly over the next decade, driven by the shift towards clean energy and sustainable solutions to modern climate issues. == Education == To become an energy engineer, a bachelor's degree in energy engineering or related fields such as mechanical, electrical, or environmental engineering is typically required. Many universities now offer specialized energy engineering programs with a focus on renewable energy, energy storage, and grid management. Advanced certifications like the Certified Energy Manager (CEM) credential, offered by the Association of Energy Engineers, and graduate programs in sustainable energy systems further improve career plans. Also, several universities across the world have established departments or centers offering energy engineering degrees, to better prepare future engineers for their career. One of those programs is the IEP PEM Certification which is offered at Virginia Tech University. == Emerging Technologies == Emerging technologies in energy engineering are reshaping the way energy is produced, stored, and consumed. Innovations such as next-generation solar panels, modern wind turbine innovations, energy storage systems (such as flow batteries and hydrogen fuel cells), and smart grid technologies are paving the way for a more sustainable energy future. These technologies are critical in reducing reliance on fossil fuels and ensuring the stability of renewable energy systems. Other advances include artificial intelligence and machine learning applications for optimizing energy use in real-time, and carbon capture and storage (CCS) systems to mitigate emissions from existing power plants. == Energy Engineering in Policy and Society == Energy engineers play a key role in shaping energy policies and regulations worldwide. Their expertise is essential in setting standards for energy efficiency, renewable energy integration, and reducing carbon footprints. Global initiatives like the Paris Agreement and the European Green Deal are influencing energy engineering practices, pushing the field toward more sustainable and equitable energy solutions. Additionally, energy engineers are increasingly involved in public and private sector collaborations, working with governments and corporations to design and implement large-scale energy infrastructure projects which would have both societal and political impacts. == Notes == == References == "Energy engineer – Job description". Graduate Prospects Ltd. December 2011. Retrieved 2013-06-11. Baake, Rainer; Morgan, Jennifer (May 15, 2013). "U.S. Energy Policy Should Take a Lesson From Germany's Energiewende". Bloomberg. Retrieved 2013-06-13. Battles, Stephanie J.; Burns, Eugene M. (October 17, 1999). "United States Energy Usage and Efficiency: Measuring Changes Over Time". Energy Information Administration. Retrieved 2013-06-11. "Energy Engineering". Berkeley Engineering. University of California. Retrieved 2013-06-13. Berman, Brad (June 14, 2011). "History of Hybrid Vehicles". HybridCars.com. Retrieved 2013-06-13. "What is Energy Engineering?". science-engineering.net. BigChoice Group Ltd. Archived from the original on 2012-10-21. Retrieved 2013-06-13. Booz Allen Hamilton (January 1, 2012). "Green Jobs Study". U.S. Green Building Council. Retrieved 2013-06-11. Crawford, Mark (2013). "Turning Trash into Treasure". Mechanical Engineering. 135 (May 2013). ASME: 42–47. doi:10.1115/1.2013-MAY-3. Retrieved 2013-06-12. "Energy Engineer Salary". PayScale. June 12, 2013. Retrieved 2013-06-13. "Energy Engineer - Key Facts & Information". Science Buddies. Retrieved 2013-06-11. Thompson, Derek (May 3, 2011). "Gas Prices Around the World: Cheaper Than Water and $10 a Gallon". The Atlantic. Retrieved 2013-06-13. == External links == Association of Energy Engineers World Energy Engineering Congress Penn State Energy Engineering Energy Managers Association
Wikipedia/Energy_engineering
The energy efficiency in transport is the useful travelled distance, of passengers, goods or any type of load; divided by the total energy put into the transport propulsion means. The energy input might be rendered in several different types depending on the type of propulsion, and normally such energy is presented in liquid fuels, electrical energy or food energy. The energy efficiency is also occasionally known as energy intensity. The inverse of the energy efficiency in transport is the energy consumption in transport. Energy efficiency in transport is often described in terms of fuel consumption, fuel consumption being the reciprocal of fuel economy. Nonetheless, fuel consumption is linked with a means of propulsion which uses liquid fuels, whilst energy efficiency is applicable to any sort of propulsion. To avoid said confusion, and to be able to compare the energy efficiency in any type of vehicle, experts tend to measure the energy in the International System of Units, i.e., joules. Therefore, in the International System of Units, the energy efficiency in transport is measured in terms of metre per joule, or m/J, while the energy consumption in transport is measured in terms of joules per metre, or J/m. The more efficient the vehicle, the more metres it covers with one joule (more efficiency), or the fewer joules it uses to travel over one metre (less consumption). The energy efficiency in transport largely varies by means of transport. Different types of transport range from some hundred kilojoules per kilometre (kJ/km) for a bicycle to tens of megajoules per kilometre (MJ/km) for a helicopter. Via type of fuel used and rate of fuel consumption, energy efficiency is also often related to operating cost ($/km) and environmental emissions (e.g. CO2/km). == Units of measurement == In the International System of Units, the energy efficiency in transport is measured in terms of metre per joule, or m/J. Nonetheless, several conversions are applicable, depending on the unit of distance and on the unit of energy. For liquid fuels, normally the quantity of energy input is measured in terms of the liquid's volume, such as litres or gallons. For propulsion which runs on electricity, normally kWh is used, while for any type of human-propelled vehicle, the energy input is measured in terms of Calories. It is typical to convert between different types of energy and units. For passenger transport, the energy efficiency is normally measured in terms of passengers times distance per unit of energy, in the SI, passengers metres per joule (pax.m/J); while for cargo transport the energy efficiency is normally measured in terms of the mass of transported cargo times distance per unit of energy, in the SI, kilograms metres per joule (kg.m/J). Volumetric efficiency with respect to vehicle capacity may also be reported, such as passenger-mile per gallon (PMPG), obtained by multiplying the miles per gallon of fuel by either the passenger capacity or the average occupancy. The occupancy of personal vehicles is typically lower than capacity by a considerable degree and thus the values computed based on capacity and on occupancy will often be quite different. === Typical conversions into SI unit === === Liquid fuels === Energy efficiency is expressed in terms of fuel economy: distance per vehicle per unit fuel volume; e.g., km/L or miles per gallon (US or imperial). distance per vehicle per unit fuel mass; e.g., km/kg. distance per vehicle per unit energy; e.g., miles per gallon equivalent (mpg-e). Energy consumption (reciprocal efficiency) is expressed terms of fuel consumption: volume of fuel (or total energy) consumed per unit distance per vehicle; e.g. l/100 km or MJ/100 km. volume of fuel (or total energy) consumed per unit distance per passenger; e.g., l/(100 passenger·km). volume of fuel (or total energy) consumed per unit distance per unit mass of cargo transported; e.g., l/100 kg·km or MJ/t·km. === Electricity === Electricity consumption: electrical energy used per vehicle per unit distance; e.g., kWh/100 km. Producing electricity from fuel requires much more primary energy than the amount of electricity produced. === Food energy === Energy consumption: calories burnt by the body's metabolism per kilometre; e.g., Cal/km. calories burnt by the body's metabolism per mile; e.g., Cal/miles. == Land Passenger Transport == === Table Overview === In the following table the energy efficiency and energy consumption for different types of passenger land vehicles and modes of transport, as well as standard occupancy rates, are presented. The sources for these figures are in the correspondent section for each vehicle, in the following article. The conversions amongst different types of units, are well known in the art. For the conversion amongst units of energy in the following table, 1 litre of petrol amounts to 34.2 MJ, 1 kWh amounts to 3.6 MJ and 1 kilocalorie amounts to 4184 J. For the car occupation ratio, the value of 1.2 passengers per automobile was considered. Nonetheless, in Europe this value slightly increases to 1.4. The sources for conversions amongst units of measurements appear only of the first row. == Land transport means == === Walking === A 68 kg (150 lb) person walking at 4 km/h (2.5 mph) requires approximately 210 kilocalories (880 kJ) of food energy per hour, which is equivalent to 4.55 km/MJ. 1 US gal (3.8 L) of petrol contains about 114,000 British thermal units (120 MJ) of energy, so this is approximately equivalent to 360 miles per US gallon (0.65 L/100 km). === Velomobile === Velomobiles (enclosed recumbent bicycles) have the highest energy efficiency of any known mode of personal transport because of their small frontal area and aerodynamic shape. At a speed of 50 km/h (31 mph), the velomobile manufacturer WAW claims that only 0.5 kWh (1.8 MJ) of energy per 100 km is needed to transport the passenger (= 18 J/m). This is around 1⁄5 (20%) of what is needed to power a standard upright bicycle without aerodynamic cladding at same speed, and 1⁄50 (2%) of that which is consumed by an average fossil fuel or electric car (the velomobile efficiency corresponds to 4700 miles per US gallon, 2000 km/L, or 0.05 L/100 km). Real energy from food used by human is 4–5 times more. Unfortunately their energy efficiency advantage over bicycles becomes smaller with decreasing speed and disappears at around 10 km/h where power needed for velomobiles and triathlon bikes are almost the same. === Bicycle === A standard lightweight, moderate-speed bicycle is one of the most energy-efficient forms of transport. Compared with walking, a 64 kg (140 lb) cyclist riding at 16 km/h (10 mph) requires about half the food energy per unit distance: 27 kcal/km, 3.1 kWh (11 MJ) per 100 km, or 43 kcal/mi. This converts to about 732 mpg‑US (0.321 L/100 km; 879 mpg‑imp). This means that a bicycle will use between 10 and 25 times less energy per distance travelled than a personal car, depending on fuel source and size of the car. This figure does depend on the speed and mass of the rider: greater speeds give higher air drag and heavier riders consume more energy per unit distance. In addition, because bicycles are very lightweight (usually between 7–15 kg) this means they consume very low amounts of materials and energy to manufacture. In comparison to an automobile weighing 1500 kg or more, a bicycle typically requires 100–200 times less energy to produce than an automobile. In addition, bicycles require less space both to park and to operate and they damage road surfaces less, adding an infrastructural factor of efficiency. === Motorised bicycle === A motorised bicycle allows human power and the assistance of a 49 cm3 (3.0 cu in) engine, giving a range of 160 to 200 mpg‑US (1.5–1.2 L/100 km; 190–240 mpg‑imp). Electric pedal-assisted bikes run on as little as 1.0 kWh (3.6 MJ) per 100 km, while maintaining speeds in excess of 30 km/h (19 mph). These best-case figures rely on a human doing 70% of the work, with around 3.6 MJ (1.0 kWh) per 100 km coming from the motor. This makes an electric bicycle one of the most efficient possible motorised vehicles, behind only a motorised velomobile and an electric unicycle (EUC). === Electric kick scooter === Electric kick scooters, such as those used by scooter-sharing systems like Bird or Lime, typically have a maximum range of under 30 km (19 mi) and are commonly limited to a maximum speed of 25 km/h (15.5 mph). Intended to fit into a last mile niche and be ridden in bike lanes, they require little skill from the rider. Because of their light weight and small motors, they are extremely energy-efficient with a typical energy efficiency of 1.1 kWh (4.0 MJ) per 100 km (1904 MPGe 810 km/L 0.124 L/100 km), even more efficient than bicycles and walking. However, as they must be recharged frequently, they are often collected overnight with motor vehicles, somewhat negating this efficiency. The lifecycle of electric scooters is also notably shorter than that of bicycles, often reaching only a single digit number of years. === Electric Unicycle === An electric unicycle (EUC) cross electric skateboard variant called the Onewheel Pint can carry a 50 kg person 21.5 km at an average speed of 20 km/h. The battery holds 148Wh. Without taking energy lost to heat in the charging stage into account, this equates to an efficiency of 6.88Wh/km or 0.688kWh/100 km. Additionally, with regenerative braking as a standard design feature, hilly terrain would have less impact on an EUC compared to a vehicle with friction brakes such as a push bike. This combined with the single wheel ground interaction may make the EUC the most efficient known vehicle at low speeds (below 25 km/h), with the velomobile overtaking the position as most efficient at higher speeds due to superior aerodynamics. === Automobiles === Automobiles are generally inefficient when compared to other modes of transport, due to the relatively high weight of the vehicle compared to its occupants. On a percentage basis, if there is one occupant in an automobile, only about 0.5% of the total energy used is used to move the person in the car, while the remaining 99.5% (about 200 times more) is used to move the car itself. An important driver of energy consumption of cars per passenger is the occupancy rate of the vehicle. Although the consumption per unit distance per vehicle increases with increasing number of passengers, this increase is slight compared to the reduction in consumption per unit distance per passenger. This means that higher occupancy yields higher energy efficiency per passenger. Automobile occupancy varies across regions. For example, the estimated average occupancy rate is about 1.3 passengers per car in the San Francisco Bay Area, while the 2006 UK estimated average is 1.58. Due to the efficiency of electric motors, electric cars are much more efficient than their internal combustion engine counterparts, consuming on the order of 38 megajoules (38 000 kJ) per 100 km in comparison to 142 megajoules per 100 km for combustion powered cars. However, depending on the way the electricity is generated, the actual primary energy use may be higher. Driving practices and vehicles can be modified to improve their energy efficiency by about 15%. ==== Common efficiency measures ==== Automobile fuel efficiency is most commonly expressed in terms of the volume of fuel consumed per one hundred kilometres (l/100 km), but in some countries (including the United States, the United Kingdom and India) it is more commonly expressed in terms of the distance per volume fuel consumed (km/L or miles per gallon). This is complicated by the different energy content of fuels such as petrol and diesel. The Oak Ridge National Laboratory (ORNL) states that the energy content of unleaded petrol is 115,000 British thermal unit (BTU) per US gallon (32 MJ/L) compared to 130,500 BTU per US gallon (36.4 MJ/L) for diesel. ==== Life-cycle energy use ==== Automobiles have significant energy use in their life cycle, not directly attributable to the running of the vehicle. An important consideration is the energy costs of producing the energy form used by the automobile. Bio-fuels, electricity and hydrogen, for instance, have significant energy inputs in their production. Hydrogen production efficiency are 50–70% when produced from natural gas, and 10–15% from electricity. The efficiency of hydrogen production, as well as the energy required to store and transport hydrogen, must to be combined with the vehicle efficiency to yield net efficiency. Because of this, hydrogen automobiles are one of the least efficient means of passenger transport, generally around 50 times as much energy must be put into the production of hydrogen compared to how much is used to move the car. Another important factor is the energy needed to build and maintain roads is an important consideration, as is the energy returned on energy invested (EROEI). Between these two factors, roughly 20% must be added to the energy of the fuel consumed, to accurately account for the total energy used. Finally, vehicle energy efficiency calculations would be misleading without factoring the energy cost of producing the vehicle itself. This initial energy cost can of course be depreciated over the life of the vehicle to calculate an average energy efficiency over its effective life span. In other words, vehicles that take a lot of energy to produce and are used for relatively short periods will require a great deal more energy over their effective lifespan than those that do not, and are therefore much less energy efficient than they may otherwise seem. Hybrid and electric cars use less energy in their operation than comparable petroleum-fuelled cars but more energy is used to manufacture them, so the overall difference would be less than immediately apparent. Compare, for example, walking, which requires no special equipment at all, and an automobile, produced in and shipped from another country, and made from parts manufactured around the world from raw materials and minerals mined and processed elsewhere again, and used for a limited number of years. According to the French energy and environment agency ADEME, an average motor car has an embodied energy content of 20,800 kWh and an average electric vehicle amounts to 34,700 kWh. The electric car requires nearly twice as much energy to produce, primarily due to the large amount of mining and purification necessary for the rare earth metals and other materials used in lithium-ion batteries and in the electric drive motors. This represents a significant portion of the energy used over the life of the car (in some cases nearly as much as energy that is used through the fuel that is consumed, effectively doubling the car's per-distance energy consumption), and cannot be ignored when comparing automobiles to other transport modes. As these are average numbers for French automobiles and they are likely to be significantly larger in more auto-centric countries like the United States and Canada, where much larger and heavier cars are more common. The usage of private vehicles can be significantly decreased and can help to promote sustainable urban growth if more appealing non-motorized transportation options are developed, as well as more comfortable public transportation environments. ==== Example consumption figures ==== Solar cars are electric vehicles that use little or no externally supplied energy other than from sunlight, charging the batteries from built-in solar panels, and typically use less than 3 kWh per 100 miles (67 kJ/km or 1.86 kWh/100 km). Most of these cars are race cars designed for competition and not for passenger or utility use. However several companies are designing solar cars for public use. As of December 2021, none have yet been released. The four passenger GEM NEV uses 169 Wh/mi (199 mpg‑e; 10.5 kW⋅h/100 km), which equates to 2.6 kWh/100 km per person when fully occupied, albeit at only 24 mph (39 km/h). The General Motors EV1 was rated in a test with a charging efficiency of 373 Wh-AC/mile or 23 kWh/100 km approximately equivalent to 2.6 L/100 km (110 mpg‑imp; 90 mpg‑US) for petroleum-fuelled vehicles. Chevrolet Volt in full electric mode uses 36 kilowatt-hours per 100 miles (810 kJ/km; 94 mpg‑e), meaning it may approach or exceed the energy efficiency of walking if the car is fully occupied with 4 or more passengers, although the relative emissions produced may not follow the same trends if analysing environmental impacts. The Daihatsu Charade 993cc turbo diesel (1987–1993) won the most fuel efficient vehicle award for going round the United Kingdom consuming an average of 2.82 L/100 km (100 mpg‑imp). It was surpassed only recently by the VW Lupo 3 L which consumes about 2.77 L/100 km (102 mpg‑imp). Both cars are rare to find on the popular market. The Daihatsu had major problems with rust and structural safety which contributes to its rarity and the quite short production run. The Volkswagen Polo 1.4 TDI Bluemotion and the SEAT Ibiza 1.4 TDI Ecomotion, both rated at 3.8 L/100 km (74 mpg‑imp; 62 mpg‑US) (combined) were the most fuel efficient petroleum-fuelled cars on sale in the UK as of 22 March 2008. Honda Insight – achieves 60 mpg‑US (3.9 L/100 km; 72 mpg‑imp) under real-world conditions. Honda Civic Hybrid regularly averages around 45 mpg‑US (5.2 L/100 km; 54 mpg‑imp). 2012 Cadillac CTS-V Wagon 6.2 L Supercharged, 14 mpg‑US (17 L/100 km; 17 mpg‑imp) 2012 Bugatti Veyron, 10 mpg‑US (24 L/100 km; 12 mpg‑imp) 2018 Honda Civic: 36 mpg‑US (6.5 L/100 km; 43 mpg‑imp) 2017 Mitsubishi Mirage: 39 mpg‑US (6.0 L/100 km; 47 mpg‑imp) 2017 Hyundai Ioniq hybrid: 55 mpg‑US (4.3 L/100 km; 66 mpg‑imp) 2017 Toyota Prius: 56 mpg‑US (4.2 L/100 km; 67 mpg‑imp) (Eco trim) 2018 Nissan Leaf: 30 kWh (110 MJ)/100 mi (671 kJ/km) or 112 MPGe 2017 Hyundai Ioniq EV: 25 kWh (90 MJ)/100 mi (560 kJ/km) or 136 MPGe 2020 Tesla model 3: 24 kWh (86.4 MJ)/100 mi (540 kJ/km) or 141 MPGe === Trains === Trains are in general one of the most efficient means of transport for freight and passengers. Advantages of trains include low friction of steel wheels on steel rails, as well as an intrinsic high occupancy rate. Train lines are typically used to serve urban or inter-urban transit applications where their capacity utilization is maximized. Efficiency varies significantly with passenger loads, and losses incurred in electricity generation and supply (for electrified systems), and, importantly, end-to-end delivery, where stations are not the originating final destinations of a journey. While electric motors used in most passenger trains are more efficient than internal combustion engines, power generation in thermal power plants is limited to (at best) Carnot efficiency and there are transmission losses on the way from the power plant to the train. Switzerland, which has electrified virtually its entire railway network (heritage railways like the Dampfbahn Furka-Bergstrecke being notable exceptions), derives much of the electricity used by trains from hydropower, including pumped hydro storage. While the mechanical efficiency of the turbines involved is comparatively high, pumped hydro involves energy losses and is only cost effective as it can consume energy during times of excess production (leading to low or even negative spot prices) and release the energy again during high-demand times. with some sources claiming up to 87%. Actual consumption depends on gradients, maximum speeds, and loading and stopping patterns. Data produced for the European MEET project (Methodologies for Estimating Air Pollutant Emissions) illustrate the different consumption patterns over several track sections. The results show the consumption for a German ICE high-speed train varied from around 19 to 33 kW⋅h/km (68–119 MJ/km; 31–53 kW⋅h/mi). The Siemens Velaro D type ICE trains seat 460 (16 of which in the restaurant car) in their 200-meter length edition of which two can be coupled together. Per Deutsche Bahn calculations, the energy used per 100 seat-km is the equivalent of 0.33 litres (12 imp fl oz) of gasoline (0.33 litres per 100 kilometres (860 mpg‑imp; 710 mpg‑US)). The data also reflects the weight of the train per passenger. For example, TGV double-deck Duplex trains use lightweight materials, which keep axle loads down and reduce damage to track and also save energy. The TGV mostly runs on French nuclear fission power plants which are again limited – as all thermal power plants – to Carnot efficiency. Due to nuclear reprocessing being standard operating procedure, a higher share of the energy contained in the original Uranium is used in France than in e.g. the United States with its once thru fuel cycle. The specific energy consumption of the trains worldwide amounts to about 150 kJ/pkm (kilojoule per passenger kilometre) and 150 kJ/tkm (kilojoule per tonne kilometre) (ca. 4.2 kWh/100 pkm and 4.2 kWh/100 tkm) in terms of final energy. Passenger transportation by rail systems requires less energy than by car or plane (one seventh of the energy needed to move a person by car in an urban context,). This is the reason why, although accounting for 9% of world passenger transportation activity (expressed in pkm) in 2015, rail passenger services represented only 1% of final energy demand in passenger transportation. ==== Freight ==== Energy consumption estimates for rail freight vary widely, and many are provided by interested parties. Some are tabulated below. ==== Passenger ==== ==== Braking losses ==== Having to accelerate and decelerate a heavy train load of people at every stop is inefficient. Modern electric trains therefore use regenerative braking to return current into the catenary while they brake. The International Union of Railways has stated that full stop service commuter trains reduce emissions by 8-14% by employing regenerative braking, and very dense suburban network trains by ~30%. High-speed electric trains like the N700 Series Shinkansen (the Bullet Train) employ regenerative braking, but due to the high speed, UIC estimates regenerative braking to only reduce emissions by 4.5%. === Buses === In 2024, the average occupancy for buses in Great Britain was stated to be 11.9 passengers per vehicle. The fleet of 244 40-foot (12 m) 1982 New Flyer trolley buses in local service with BC Transit in Vancouver, Canada, in 1994/95 used 35,454,170 kWh for 12,966,285 vehicle km, or 9.84 MJ/vehicle km. Exact ridership on trolleybuses is not known, but with all 34 seats filled this equates to 0.32 MJ/passenger km. It is quite common to see people standing on Vancouver trolleybuses. This is a service with many stops per kilometre; part of the reason for the efficiency is the use of regenerative braking. A commuter service in Santa Barbara, California, USA, found average diesel bus efficiency of 6.0 mpg‑US (39 L/100 km; 7.2 mpg‑imp) (using MCI 102DL3 buses). With all 55 seats filled this equates to 330 passenger mpg; with 70% filled, 231 passenger mpg. In 2011 the fleet of 752 buses in the city of Lisbon had an average speed of 14.4 km/h and an average occupancy of 20.1 passengers per vehicle. Battery electric buses combine the electric motive power of a trolleybus, the drawbacks of battery manufacture, weight and lifespan with the routing flexibility of a bus with any onboard power. Major manufacturers include BYD and Proterra. === Other === NASA's Crawler-Transporter was used to haul the Saturn V and Space Shuttle rockets from storage to the launch pad. It uses diesel and has one of the highest fuel consumption rates on record, 150 US gallons per mile (350 L/km; 120 imp gal/mi). == Air transport means == === Aircraft === A principal determinant of energy consumption in aircraft is drag, which must be in the opposite direction of motion to the craft. Drag is proportional to the lift required for flight, which is equal to the weight of the aircraft. As induced drag increases with weight, mass reduction, with improvements in engine efficiency and reductions in aerodynamic drag, has been a principal source of efficiency gains in aircraft, with a rule-of-thumb being that a 1% weight reduction corresponds to around a 0.75% reduction in fuel consumption. Flight altitude affects engine efficiency. Jet-engine efficiency increases at altitude up to the tropopause, the temperature minimum of the atmosphere; at lower temperatures, the Carnot efficiency is higher. Jet engine efficiency is also increased at high speeds, but above about Mach 0.85 the airframe aerodynamic losses increase faster. Compressibility effects: beginning at transonic speeds of around Mach 0.85, shockwaves form increasing drag. For supersonic flight, it is difficult to achieve a lift to drag ratio greater than 5, and fuel consumption is increased in proportion. However, the faster speed inherent to supersonic flight means that the higher fuel burn is counterbalanced by a shorter flight duration. Passenger airplanes averaged 4.8 L/100 km per passenger (1.4 MJ/passenger-km) (49 passenger-miles per gallon) in 1998. On average 20% of seats are left unoccupied. Jet aircraft efficiencies are improving: Between 1960 and 2000 there was a 55% overall fuel efficiency gain (if one were to exclude the inefficient and limited fleet of the DH Comet 4 and to consider the Boeing 707 as the base case). Most of the improvements in efficiency were gained in the first decade when jet craft first came into widespread commercial use. Compared to advanced piston engine airliners of the 1950s, current jet airliners are only marginally more efficient per passenger-mile. Between 1971 and 1998 the fleet-average annual improvement per available seat-kilometre was estimated at 2.4%. Concorde the supersonic transport managed about 17 passenger-miles to the Imperial gallon; similar to a business jet, but much worse than a subsonic turbofan aircraft. Airbus puts the fuel rate consumption of their A380 at less than 3 L/100 km per passenger (78 passenger-miles per US gallon). The mass of an aircraft can be reduced by using light-weight materials such as titanium, carbon fibre and other composite plastics. Expensive materials may be used, if the reduction of mass justifies the price of materials through improved fuel efficiency. The improvements achieved in fuel efficiency by mass reduction, reduces the amount of fuel that needs to be carried. This further reduces the mass of the aircraft and therefore enables further gains in fuel efficiency. For example, the Airbus A380 design includes multiple light-weight materials. Airbus has showcased wingtip devices (sharklets or winglets) that can achieve 3.5 percent reduction in fuel consumption. There are wingtip devices on the Airbus A380. Further developed Minix winglets have been said to offer 6 percent reduction in fuel consumption. Winglets at the tip of an aircraft wing smooth out the wing-tip vortex (reducing the aircraft's wing drag) and can be retrofitted to any airplane. NASA and Boeing are conducting tests on a 500 lb (230 kg) "blended wing" aircraft. This design allows for greater fuel efficiency since the whole craft produces lift, not just the wings. The blended wing body (BWB) concept offers advantages in structural, aerodynamic and operating efficiencies over today's more conventional fuselage-and-wing designs. These features translate into greater range, fuel economy, reliability and life cycle savings, as well as lower manufacturing costs. NASA has created a cruise efficient STOL (CESTOL) concept. Fraunhofer Institute for Manufacturing Engineering and Applied Materials Research (IFAM) have researched a shark skin imitating paint that would reduce drag through a riblet effect. Aircraft are a major potential application for new technologies such as aluminium metal foam and nanotechnology such as the shark skin imitating paint. Propeller systems, such as turboprops and propfans are a more fuel efficient technology than jets. But turboprops have an optimum speed below about 450 mph (700 km/h). This speed is less than used with jets by major airlines today. With the current high price for jet fuel and the emphasis on engine/airframe efficiency to reduce emissions, there is renewed interest in the propfan concept for jetliners that might come into service beyond the Boeing 787 and Airbus A350XWB. For instance, Airbus has patented aircraft designs with twin rear-mounted counter-rotating propfans. NASA has conducted an Advanced Turboprop Project (ATP), where they researched a variable pitch propfan that produced less noise and achieved high speeds. Related to fuel efficiency is the impact of aviation emissions on climate. ==== Small aircraft ==== Motor-gliders can reach an extremely low fuel consumption for cross-country flights, if favourable thermal air currents and winds are present. At 160 km/h, a diesel powered two-seater Dieselis burns 6 litres of fuel per hour, 1.9 litres per 100 passenger km. at 220 km/h, a four-seater 100 hp MCR-4S burns 20 litres of gas per hour, 2.2 litres per 100 passenger km. Under continuous motorised flight at 225 km/h, a Pipistrel Sinus burns 11 litres of fuel per flight hour. Carrying 2 people aboard, it operates at 2.4 litres per 100 passenger km. Ultralight aircraft Tecnam P92 Echo Classic at cruise speed of 185 km/h burns 17 litres of fuel per flight hour, 4.6 litres per 100 passenger km (2 people). Other modern ultralight aircraft have increased efficiency; Tecnam P2002 Sierra RG at cruise speed of 237 km/h burns 17 litres of fuel per flight hour, 3.6 litres per 100 passenger km (2 people). Two-seater and four-seater flying at 250 km/h with old generation engines can burn 25 to 40 litres per flight hour, 3 to 5 litres per 100 passenger km. The Sikorsky S-76C++ twin turbine helicopter gets about 1.65 mpg‑US (143 L/100 km; 1.98 mpg‑imp) at 140 knots (260 km/h; 160 mph) and carries 12 for about 19.8 passenger-miles per gallon (11.9 L per 100 passenger km). == Water transport means == === Ships === ==== Queen Elizabeth ==== Cunard stated that Queen Elizabeth 2 travelled 49.5 feet per imperial gallon of diesel oil (3.32 m/L or 41.2 ft/US gal), and that it had a passenger capacity of 1777. Thus carrying 1777 passengers we can calculate an efficiency of 16.7 passenger miles per imperial gallon (16.9 L/100 p·km or 13.9 p·mpg–US). ==== Cruise ships ==== MS Oasis of the Seas has a capacity of 6,296 passengers and a fuel efficiency of 14.4 passenger miles per US gallon. Voyager-class cruise ships have a capacity of 3,114 passengers and a fuel efficiency of 12.8 passenger miles per US gallon. ==== Emma Maersk ==== Emma Maersk uses a Wärtsilä-Sulzer RTA96-C, which consumes 163 g/kWh and 13,000 kg/h. If it carries 13,000 containers then 1 kg fuel transports one container for one hour over a distance of 45 km. The ship takes 18 days from Tanjung (Singapore) to Rotterdam (Netherlands), 11 from Tanjung to Suez, and 7 from Suez to Rotterdam, which is roughly 430 hours, and has 80 MW, +30 MW. 18 days at a mean speed of 25 knots (46 km/h) gives a total distance of 10,800 nautical miles (20,000 km). Assuming the Emma Maersk consumes diesel (as opposed to fuel oil which would be the more precise fuel) then 1 kg diesel = 1.202 litres = 0.317 US gallons. This corresponds to 46,525 kJ. Assuming a standard 14 tonnes per container (per teu) this yields 74 kJ per tonne-km at a speed of 45 km/h (24 knots). ==== Boats ==== A sailboat, much like a solar car, can locomote without consuming any fuel. A sail boat such as a dinghy using just wind power requires no input energy in terms of fuel. However some manual energy is required by the crew to steer the boat and adjust the sails using lines. In addition energy will be needed for demands other than propulsion, such as cooking, heating or lighting. The fuel efficiency of a single-occupancy boat is highly dependent on the size of its engine, the speed at which it travels, and its displacement. With a single passenger, the equivalent energy efficiency will be lower than in a car, train, or plane. == International transport comparisons == === European Public transport === Rail and bus are generally required to serve 'off peak' and rural services, which by their nature have lower loads than city bus routes and inter city train lines. Moreover, due to their 'walk on' ticketing it is much harder to match daily demand and passenger numbers. As a consequence, the overall load factor on UK railways is 35% or 90 people per train: Conversely, airline services generally work on point-to-point networks between large population centres and are 'pre-book' in nature. Using yield management, overall load factors can be raised to around 70–90%. Intercity train operators have begun to use similar techniques, with loads reaching typically 71% overall for TGV services in France and a similar figure for the UK's Virgin Rail Group services. For emissions, the electricity generating source needs to be taken into account. === US Passenger transport === The US Transport Energy Data Book states the following figures for passenger transport in 2018. These are based on actual consumption of energy, at whatever occupancy rates there were. For modes using electricity, losses during generation and distribution are included. Values are not directly comparable due to differences in types of services, routes, etc. === US Freight transport === The US Transport Energy book states the following figures for freight transport in 2010: From 1960 to 2010 the efficiency of air freight has increased 75%, mostly due to more efficient jet engines. 1 gal-US (3.785 L, 0.833 gal-imp) of fuel can move a ton of cargo 857 km or 462 nmi by barge, or 337 km (209 mi) by rail, or 98 km (61 mi) by lorry. Compare: Space Shuttle used to transport freight to the other side of the Earth (see above): 40 megajoules per tonne-kilometre. Net energy for lifting: 10 megajoules per tonne-kilometre. === Canadian transport === Natural Resources Canada's Office of Energy Efficiency publishes annual statistics regarding the efficiency of the entire Canadian fleet. For researchers, these fuel consumption estimates are more realistic than the fuel consumption ratings of new vehicles, as they represent the real world driving conditions, including extreme weather and traffic. The annual report is called Energy Efficiency Trends Analysis. There are dozens of tables illustrating trends in energy consumption expressed in energy per passenger km (passengers) or energy per tonne km (freight). === French environmental calculator === The environmental calculator of the French environment and energy agency (ADEME) published in 2007 using data from 2005 enables one to compare the different means of transport as regards the CO2 emissions (in terms of carbon dioxide equivalent) as well as the consumption of primary energy. In the case of an electric vehicle, the ADEME makes the assumption that 2.58 toe as primary energy are necessary for producing one toe of electricity as end energy in France (see Embodied energy: In the energy field). This computer tool devised by the ADEME shows the importance of public transport from an environmental point of view. It highlights the primary energy consumption as well as the CO2 emissions due to transport. Due to the relatively low environmental impact of radioactive waste, compared to that of fossil fuel combustion emissions, this is not a factor in the tool. Moreover, intermodal passenger transport is probably a key to sustainable transport, by allowing people to use less polluting means of transport. === German environmental costs === Deutsche Bahn calculates the energy consumption of their various means of transportation. == Note - External costs not included above == To include all the energy used in transport, we would need to also include the external energy costs of producing, transporting and packaging of fuel (food or fossil fuel or electricity), the energy incurred in disposing of exhaust waste, and the energy costs of manufacturing the vehicle. For example, a human walking requires little or no special equipment while automobiles require a great deal of energy to produce and have relatively short product lifespans. However, these external costs are independent of the energy cost per distance travelled, and can vary greatly for a particular vehicle depending on its lifetime, how often it is used and how it is energized over its lifetime. Thus this article's numbers include none of these external factors. == See also == == Footnotes == == External links == ECCM Study for rail, road and air journeys between main UK cities Traction Summary Report 2007– Prof. Roger Kemp Transport Energy Data Book (US) Fuel Consumption Ratings Infographic on Energy Efficiency in Transportation
Wikipedia/Energy_efficiency_in_transport
Energy security is the association between national security and the availability of natural resources for energy consumption (as opposed to household energy insecurity). Access to cheaper energy has become essential to the functioning of modern economies. However, the uneven distribution of energy supplies among countries has led to significant vulnerabilities. International energy relations have contributed to the globalization of the world leading to energy security and energy vulnerability at the same time. Renewable resources and significant opportunities for energy efficiency and transitions exist over wide geographical areas, in contrast to other energy sources, which are concentrated in a limited number of countries. Rapid deployment of wind power and solar power and energy efficiency, and technological diversification of energy sources, would result in significant energy security. == Threats == The modern world relies on a vast energy supply to fuel anything from transportation to communication, to security and health delivery systems. Peak oil expert Michael Ruppert has claimed that for every kilocalorie of food produced in the industrial world, 10 kilocalories of oil and gas energy are invested in the forms of fertilizer, pesticide, packaging, transportation, and running farm equipment. Energy plays an important role in the national security of any given country as a fuel to power the economic engine. Some sectors rely on energy more heavily than others; for example, the Department of Defense relies on petroleum for approximately 77% of its energy needs. Not every sector is as critical as the others; some have greater importance to energy security. Threats to a nation's energy security include: Political/Domestic instability of major energy-producing countries (e.g. change in leadership's environmental values, or regime change) Reliance on foreign countries for oil Foreign in-state conflict (e.g. religious civil wars) Foreign exporters' interests (e.g. Quid Pro Quo/blackmail/extortion) Foreign non-state actors targeting the supply and transportation of oil resources (e.g. theft) Manipulation of energy supplies (e.g. mega-corporation or state-backed racketeering) Competition over energy sources (e.g. biofuel (biodiesel, bioethanol) vs oil (crude, distilled fuel) vs coal vs natural gas vs nuclear vs wind vs solar vs hydro (dam, pumped)) Unreliable energy stores (e.g. long time to spin a turbine to create power, or Li-ion battery grid explosion, or pumped hydro dam becoming clogged) Attacks on supply infrastructure (e.g. hackers stopping flow pumps inside a pipeline or intentionally surging an electrical grid to over/underload it) Terrorism (e.g. napalming oil and/or fuel reserves) Accidents (e.g. shoddy weld causing debris buildup in a pipeline) Natural disasters (e.g. wind turbine collapsing from a major earthquake) Political and economic instability caused by war or other factors, such as strike action, can also prevent the proper functioning of the energy industry in a supplier country. For example, the nationalization of oil in Venezuela has triggered strikes and protests in which Venezuela's oil production rates have yet to recover. Exporters may have political or economic incentive to limit their foreign sales or cause disruptions in the supply chain. Since Venezuela's nationalization of oil, anti-American Hugo Chávez threatened to cut off supplies to the United States more than once. The 1973 oil embargo against the United States is an historical example in which oil supplies were cut off to the United States due to U.S. support of Israel during the Yom Kippur War. This has been done to apply pressure during economic negotiations—such as during the 2007 Russia–Belarus energy dispute. Terrorist attacks targeting oil facilities, pipelines, tankers, refineries, and oil fields are so common they are referred to as "industry risks". Infrastructure for producing the resource is extremely vulnerable to sabotage. One of the worst risks to oil transportation is the exposure of the five ocean chokepoints, like the Iranian-controlled Strait of Hormuz. Anthony Cordesman, a scholar at the Center for Strategic and International Studies in Washington, D.C., warns, "It may take only one asymmetric or conventional attack on a Ghawar Saudi oil field or tankers in the Strait of Hormuz to throw the market into a spiral." New threats to energy security have emerged in the form of the increased world competition for energy resources due to the increased pace of industrialization in countries such as India and China, as well as due to the increasing consequences of climate change. Although still a minority concern, the possibility of price rises resulting from the peaking of world oil production is also starting to attract the attention of at least the French government. Increased competition over energy resources may also lead to the formation of security compacts to enable an equitable distribution of oil and gas between major powers. However, this may happen at the expense of less developed economies. The Group of Five, precursors to the G8, first met in 1975 to coordinate economic and energy policies in the wake of the 1973 Arab oil embargo, a rise in inflation and a global economic slowdown. == Long-term security == The impact of the 1973 oil crisis and the emergence of the OPEC cartel was a particular milestone that prompted some countries to increase their energy security. Japan, almost totally dependent on imported oil, steadily introduced the use of natural gas, nuclear power, high-speed mass transit systems, and implemented energy conservation measures. The United Kingdom began exploiting North Sea oil and gas reserves, and became a net exporter of energy into the 2000s. Increasing energy security is also one of the reasons behind a block on the development of natural gas imports in Sweden. Greater investment in native renewable energy technologies and energy conservation is envisaged instead. India is carrying out a major hunt for domestic oil to decrease its dependency on OPEC, while Iceland is well advanced in its plans to become energy independent by 2050 through deploying 100% renewable energy. == Short-term security == === Petroleum === Petroleum, otherwise known as "crude oil", has become the resource most used by countries all around the world, including Russia, China and the United States of America. With all the oil wells located around the world, energy security has become a main issue to ensure the safety of the petroleum that is being harvested. In the middle east, oil fields have become main targets for sabotage due to how heavily countries rely on oil. Many countries hold strategic petroleum reserves as a buffer against the economic and political impacts of an energy crisis. For example, all 31 members of the International Energy Agency hold a minimum of 90 days of their oil imports. These countries also committed to passing legislation to develop an emergency response plan in the case of oil supply shocks and other short-term threats to energy security. The value of such reserves was demonstrated by the relative lack of disruption caused by the 2007 Russia-Belarus energy dispute, when Russia indirectly cut exports to several countries in the European Union. Due to the theories in peak oil and need to curb demand, the United States military and Department of Defense had made significant cuts, and have been making a number of attempts to come up with more efficient ways to use oil. === Natural gas === Compared to petroleum, reliance on imported natural gas creates significant short-term vulnerabilities. The gas conflicts between Ukraine and Russia of 2006 and 2009 serve as vivid examples of this. Many European countries saw an immediate drop in supply when Russian gas supplies were halted during the Russia-Ukraine gas dispute in 2006. Natural gas has been a viable source of energy in the world. Consisting of mostly methane, natural gas is produced using two methods: biogenic and thermogenic. Biogenic gas comes from methanogenic organisms located in marshes and landfills, whereas thermogenic gas comes from the anaerobic decay of organic matter deep under the Earth's surface. Russia is one of the three current leading country in production of natural gas alongside US and Saudi Arabia. In the European Union, security of gas supply is protected by Regulation 2017/1938 of 25 October 2017, which concerns "measures to safeguard the security of gas supply" and took the place of the previous regulation 994/2010 on the same subject. EU policy operates on a number of regional groupings, a network of common gas security risk assessments, and a "solidarity mechanism", which would be activated in the event of a significant gas supply crisis. A bilateral solidarity agreement was signed between Germany and Denmark on 14 December 2020. The proposed UK-EU Trade and Cooperation Agreement "provides for a new set of arrangements for extensive technical cooperation ... particularly with regard to security of supply". === Nuclear power === Uranium for nuclear power is mined and enriched in countries including Canada (23% of the world's total in 2007), Australia (21%), Kazakhstan (16%) and more than 10 other countries. Uranium is mined and fuel is manufactured significantly in advance of need. Nuclear fuel is considered by some to be a relatively reliable power source, being more common in the Earth's crust than tin, mercury or silver, though a debate over the timing of peak uranium does exist. Nuclear power is seen as a means to reduce carbon emissions. Although generally considered a viable energy resource, nuclear power remains controversial due to the risks associated with it. Another factor in the debate with nuclear power is the concern from people or companies regarding the location of a nuclear energy plant or the disposal radioactive waste nearby. In 2022, nuclear power provided 10% of the world's total electricity share. The most notable use of nuclear power within the United States is in U.S. Navy aircraft carriers and submarines, which have been exclusively nuclear-powered for several decades. These classes of ship provide the core of the Navy's power, and as such are the single most noteworthy application of nuclear power in the United States. === Renewable energy === The deployment of renewable fuels: Increases the diversity of electricity sources, reducing strangleholds of one fuel type. Increases backup energy via biofuel reserves. Increases backup electricity stores via batteries that can produce and/or store electricity. Contributes to the flexibility of the rigid electrical grid via local generation (independent of easily targeted centralized power distributors). Increases resistance to threats to energy security. For countries where growing dependence on imported gas is a significant energy security issue, renewable technologies can provide alternative sources of electric power as well as possibly displacing electricity demand through direct heat production (e.g. geothermal and burning fuels for heat and electricity). Renewable biofuels for transport represent a key source of diversification from petroleum products. As the finite resources that have been so crucial to survival in the world decline day by day, countries will begin to realize that the need for renewable fuel sources will be more vital than ever before. Moreover, renewable energy resources are more evenly distributed than fossil fuels and, as a result, can improve energy security and reduce geopolitical tensions among states. Geothermal (renewable and clean energy) can indirectly reduce the need for other sources of fuel. By using the heat from the outer core of the Earth to heat water, steam created from the heated water can not only power electricity-generating turbines, but also eliminate the need for consuming electricity to create hot water for showers, washing machines, dishwashers, sterilizers, and more; geothermal is one of the cleanest and most efficient options, needing fuel to dig deep holes, hot water pumps, and tubing to distribute the hot water. Geothermal not only helps energy security, but also food security via year-round heated greenhouses. Hydroelectric, already incorporated into many dams around the world, produces a lot of energy, usually on demand, and is very easy to produce energy as the dams control the gravity-fed water allowed through gates which spin up turbines located inside of the dam. Biofuels have been researched relatively thoroughly, using several different sources such as sugary corn (very inefficient) and cellulose-rich switchgrass (more efficient) to produce ethanol, and fat-rich algae to produce a synthetic crude oil (or algae-derived ethanol, which is very, very inefficient), these options are substantially cleaner than the consumption of petroleum. "Most life cycle analysis results for perennial and ligno-cellulosic crops conclude that biofuels can supplement anthropogenic energy demands and mitigate green house gas emissions to the atmosphere". Using net-carbon-positive oil to fuel transportation is a major source of green house gases, any one of these developments could replace the energy we derive from oil. Traditional fossil fuel exporters (e.g. Russia) who built their country's wealth from memorialized plant remains (fossil fuels) and have not yet diversified their energy portfolio to include renewable energy have greater national energy insecurity. In 2021, global renewable energy capacity made record-breaking growth, increasing by 295 gigawatts (295 billion Watts, equivalent to 295,000,000,000 Watts, or a third of a trillion Watts) despite supply chain issues and high raw material prices. The European Union was especially impactful—its annual additions increased nearly 30% to 36 gigawatts in 2021. The International Energy Agency's 2022 Renewable Energy Market Update predicts that the global capacity of renewables would increase an additional 320 gigawatts. For context, that would almost entirely cover the electricity demand of Germany. However, the report cautioned that current public policies are a threat to future renewable energy growth: "the amount of renewable power capacity added worldwide is expected to plateau in 2023, as continued progress for solar is offset by a 40% decline in hydropower expansion and little change in wind additions." Solar power is generally less vulnerable to enemy action than large fossil fuel and hydro plants and can be more quickly repaired. == See also == By area Economic Strategic == References == == Further reading == Deese, David A. (1979). "Energy: Economics, Politics, and Security". International Security. 4 (3): 140–153. == External links == Journal of Energy Security Institute for the Analysis of Global Security: Energy Security Research United States Energy Security Council Energy and Environmental Security Initiative (EESI) NATO and Energy Security
Wikipedia/Energy_security
Efficient energy use, or energy efficiency, is the process of reducing the amount of energy required to provide products and services. There are many technologies and methods available that are more energy efficient than conventional systems. For example, insulating a building allows it to use less heating and cooling energy while still maintaining a comfortable temperature. Another method made by Lev Levich is to remove energy subsidies that promote high energy consumption and inefficient energy use. Improved energy efficiency in buildings, industrial processes and transportation could reduce the world's energy needs in 2050 by one third. There are two main motivations to improve energy efficiency. Firstly, one motivation is to achieve cost savings during the operation of the appliance or process. However, installing an energy-efficient technology comes with an upfront cost, the capital cost. The different types of costs can be analyzed and compared with a life-cycle assessment. Another motivation for energy efficiency is to reduce greenhouse gas emissions and hence work towards climate action. A focus on energy efficiency can also have a national security benefit because it can reduce the amount of energy that has to be imported from other countries. Energy efficiency and renewable energy go hand in hand for sustainable energy policies. They are high priority actions in the energy hierarchy. == Aims == Energy productivity, which measures the output and quality of goods and services per unit of energy input, can come from either reducing the amount of energy required to produce something, or from increasing the quantity or quality of goods and services from the same amount of energy. From the point of view of an energy consumer, the main motivation of energy efficiency is often simply saving money by lowering the cost of purchasing energy. Additionally, from an energy policy point of view, there has been a long trend in a wider recognition of energy efficiency as the "first fuel", meaning the ability to replace or avoid the consumption of actual fuels. In fact, International Energy Agency has calculated that the application of energy efficiency measures in the years 1974-2010 has succeeded in avoiding more energy consumption in its member states than is the consumption of any particular fuel, including fossil fuels (i.e. oil, coal and natural gas). Moreover, it has long been recognized that energy efficiency brings other benefits additional to the reduction of energy consumption. Some estimates of the value of these other benefits, often called multiple benefits, co-benefits, ancillary benefits or non-energy benefits, have put their summed value even higher than that of the direct energy benefits. These multiple benefits of energy efficiency include things such as reduced greenhouse gas emissions, reduced air pollution and improved health, and improved energy security. Methods for calculating the monetary value of these multiple benefits have been developed, including e.g. the choice experiment method for improvements that have a subjective component (such as aesthetics or comfort) and Tuominen-Seppänen method for price risk reduction. When included in the analysis, the economic benefit of energy efficiency investments can be shown to be significantly higher than simply the value of the saved energy. Energy efficiency has proved to be a cost-effective strategy for building economies without necessarily increasing energy consumption. For example, the state of California began implementing energy-efficiency measures in the mid-1970s, including building code and appliance standards with strict efficiency requirements. During the following years, California's energy consumption has remained approximately flat on a per capita basis while national US consumption doubled. As part of its strategy, California implemented a "loading order" for new energy resources that puts energy efficiency first, renewable electricity supplies second, and new fossil-fired power plants last. States such as Connecticut and New York have created quasi-public Green Banks to help residential and commercial building-owners finance energy efficiency upgrades that reduce emissions and cut consumers' energy costs. == Related concepts == === Energy conservation === Energy conservation is broader than energy efficiency in including active efforts to decrease energy consumption, for example through behaviour change, in addition to using energy more efficiently. Examples of conservation without efficiency improvements are heating a room less in winter, using the car less, air-drying your clothes instead of using the dryer, or enabling energy saving modes on a computer. As with other definitions, the boundary between efficient energy use and energy conservation can be fuzzy, but both are important in environmental and economic terms. === Sustainable energy === Energy efficiency—using less energy to deliver the same goods or services, or delivering comparable services with less goods—is a cornerstone of many sustainable energy strategies. The International Energy Agency (IEA) has estimated that increasing energy efficiency could achieve 40% of greenhouse gas emission reductions needed to fulfil the Paris Agreement's goals. Energy can be conserved by increasing the technical efficiency of appliances, vehicles, industrial processes, and buildings. == Unintended consequences == If the demand for energy services remains constant, improving energy efficiency will reduce energy consumption and carbon emissions. However, many efficiency improvements do not reduce energy consumption by the amount predicted by simple engineering models. This is because they make energy services cheaper, and so consumption of those services increases. For example, since fuel efficient vehicles make travel cheaper, consumers may choose to drive farther, thereby offsetting some of the potential energy savings. Similarly, an extensive historical analysis of technological efficiency improvements has conclusively shown that energy efficiency improvements were almost always outpaced by economic growth, resulting in a net increase in resource use and associated pollution. These are examples of the direct rebound effect. Estimates of the size of the rebound effect range from roughly 5% to 40%. The rebound effect is likely to be less than 30% at the household level and may be closer to 10% for transport. A rebound effect of 30% implies that improvements in energy efficiency should achieve 70% of the reduction in energy consumption projected using engineering models. == Options == === Appliances === Modern appliances, such as, freezers, ovens, stoves, dishwashers, clothes washers and dryers, use significantly less energy than older appliances. Current energy-efficient refrigerators, for example, use 40 percent less energy than conventional models did in 2001. Following this, if all households in Europe changed their more than ten-year-old appliances into new ones, 20 billion kWh of electricity would be saved annually, hence reducing CO2 emissions by almost 18 billion kg. In the US, the corresponding figures would be 17 billion kWh of electricity and 27,000,000,000 lb (1.2×1010 kg) CO2. According to a 2009 study from McKinsey & Company the replacement of old appliances is one of the most efficient global measures to reduce emissions of greenhouse gases. Modern power management systems also reduce energy usage by idle appliances by turning them off or putting them into a low-energy mode after a certain time. Many countries identify energy-efficient appliances using energy input labeling. The impact of energy efficiency on peak demand depends on when the appliance is used. For example, an air conditioner uses more energy during the afternoon when it is hot. Therefore, an energy-efficient air conditioner will have a larger impact on peak demand than off-peak demand. An energy-efficient dishwasher, on the other hand, uses more energy during the late evening when people do their dishes. This appliance may have little to no impact on peak demand. Over the period 2001–2021, tech companies have replaced traditional silicon switches in an electric circuit with quicker gallium nitride transistors to make new gadgets as energy efficient as feasible. Gallium nitride transistors are, however, more costly. This is a significant change in lowering the carbon footprint. === Building design === A building's location and surroundings play a key role in regulating its temperature and illumination. For example, trees, landscaping, and hills can provide shade and block wind. In cooler climates, designing northern hemisphere buildings with south facing windows and southern hemisphere buildings with north facing windows increases the amount of sun (ultimately heat energy) entering the building, minimizing energy use, by maximizing passive solar heating. Tight building design, including energy-efficient windows, well-sealed doors, and additional thermal insulation of walls, basement slabs, and foundations can reduce heat loss by 25 to 50 percent. Dark roofs may become up to 39 °C (70 °F) hotter than the most reflective white surfaces. They transmit some of this additional heat inside the building. US Studies have shown that lightly colored roofs use 40 percent less energy for cooling than buildings with darker roofs. White roof systems save more energy in sunnier climates. Advanced electronic heating and cooling systems can moderate energy consumption and improve the comfort of people in the building. Proper placement of windows and skylights as well as the use of architectural features that reflect light into a building can reduce the need for artificial lighting. Increased use of natural and task lighting has been shown by one study to increase productivity in schools and offices. Compact fluorescent lamps use two-thirds less energy and may last 6 to 10 times longer than incandescent light bulbs. Newer fluorescent lights produce a natural light, and in most applications they are cost effective, despite their higher initial cost, with payback periods as low as a few months. LED lamps use only about 10% of the energy an incandescent lamp requires. Leadership in Energy and Environmental Design (LEED) is a rating system organized by the US Green Building Council (USGBC) to promote environmental responsibility in building design. They currently offer four levels of certification for existing buildings (LEED-EBOM) and new construction (LEED-NC) based on a building's compliance with the following criteria: Sustainable sites, water efficiency, energy and atmosphere, materials and resources, indoor environmental quality, and innovation in design. In 2013, USGBC developed the LEED Dynamic Plaque, a tool to track building performance against LEED metrics and a potential path to recertification. The following year, the council collaborated with Honeywell to pull data on energy and water use, as well as indoor air quality from a BAS to automatically update the plaque, providing a near-real-time view of performance. The USGBC office in Washington, D.C. is one of the first buildings to feature the live-updating LEED Dynamic Plaque. === Industry === Industries use a large amount of energy to power a diverse range of manufacturing and resource extraction processes. Many industrial processes require large amounts of heat and mechanical power, most of which is delivered as natural gas, petroleum fuels, and electricity. In addition some industries generate fuel from waste products that can be used to provide additional energy. Because industrial processes are so diverse it is impossible to describe the multitude of possible opportunities for energy efficiency in industry. Many depend on the specific technologies and processes in use at each industrial facility. There are, however, a number of processes and energy services that are widely used in many industries. Various industries generate steam and electricity for subsequent use within their facilities. When electricity is generated, the heat that is produced as a by-product can be captured and used for process steam, heating or other industrial purposes. Conventional electricity generation is about 30% efficient, whereas combined heat and power (also called co-generation) converts up to 90 percent of the fuel into usable energy. Advanced boilers and furnaces can operate at higher temperatures while burning less fuel. These technologies are more efficient and produce fewer pollutants. Over 45 percent of the fuel used by US manufacturers is burnt to make steam. The typical industrial facility can reduce this energy usage 20 percent (according to the US Department of Energy) by insulating steam and condensate return lines, stopping steam leakage, and maintaining steam traps. Electric motors usually run at a constant speed, but a variable speed drive allows the motor's energy output to match the required load. This achieves energy savings ranging from 3 to 60 percent, depending on how the motor is used. Motor coils made of superconducting materials can also reduce energy losses. Motors may also benefit from voltage optimization. Industry uses a large number of pumps and compressors of all shapes and sizes and in a wide variety of applications. The efficiency of pumps and compressors depends on many factors but often improvements can be made by implementing better process control and better maintenance practices. Compressors are commonly used to provide compressed air which is used for sand blasting, painting, and other power tools. According to the US Department of Energy, optimizing compressed air systems by installing variable speed drives, along with preventive maintenance to detect and fix air leaks, can improve energy efficiency 20 to 50 percent. === Transportation === ==== Automobiles ==== The estimated energy efficiency for an automobile is 280 Passenger-Mile/106 Btu. There are several ways to enhance a vehicle's energy efficiency. Using improved aerodynamics to minimize drag can increase vehicle fuel efficiency. Reducing vehicle weight can also improve fuel economy, which is why composite materials are widely used in car bodies. More advanced tires, with decreased tire to road friction and rolling resistance, can save gasoline. Fuel economy can be improved by up to 3.3% by keeping tires inflated to the correct pressure. Replacing a clogged air filter can improve a cars fuel consumption by as much as 10 percent on older vehicles. On newer vehicles (1980s and up) with fuel-injected, computer-controlled engines, a clogged air filter has no effect on mpg but replacing it may improve acceleration by 6-11 percent. Aerodynamics also aid in efficiency of a vehicle. The design of a car impacts the amount of gas needed to move it through air. Aerodynamics involves the air around the car, which can affect the efficiency of the energy expended. Turbochargers can increase fuel efficiency by allowing a smaller displacement engine. The 'Engine of the year 2011' is the Fiat TwinAir engine equipped with an MHI turbocharger. "Compared with a 1.2-liter 8v engine, the new 85 HP turbo has 23% more power and a 30% better performance index. The performance of the two-cylinder is not only equivalent to a 1.4-liter 16v engine, but fuel consumption is 30% lower." Energy-efficient vehicles may reach twice the fuel efficiency of the average automobile. Cutting-edge designs, such as the diesel Mercedes-Benz Bionic concept vehicle have achieved a fuel efficiency as high as 84 miles per US gallon (2.8 L/100 km; 101 mpg‑imp), four times the current conventional automotive average. The mainstream trend in automotive efficiency is the rise of electric vehicles (all-electric or hybrid electric). Electric engines have more than double the efficiency of internal combustion engines. Hybrids, like the Toyota Prius, use regenerative braking to recapture energy that would dissipate in normal cars; the effect is especially pronounced in city driving. Plug-in hybrids also have increased battery capacity, which makes it possible to drive for limited distances without burning any gasoline; in this case, energy efficiency is dictated by whatever process (such as coal-burning, hydroelectric, or renewable source) created the power. Plug-ins can typically drive for around 40 miles (64 km) purely on electricity without recharging; if the battery runs low, a gas engine kicks in allowing for extended range. Finally, all-electric cars are also growing in popularity; the Tesla Model S sedan is the only high-performance all-electric car currently on the market. ==== Street lighting ==== Cities around the globe light up millions of streets with 300 million lights. Some cities are seeking to reduce street light power consumption by dimming lights during off-peak hours or switching to LED lamps. LED lamps are known to reduce the energy consumption by 50% to 80%. ==== Aircraft ==== There are several ways to improve aviation's use of energy through modifications aircraft and air traffic management. Aircraft improve with better aerodynamics, engines and weight. Seat density and cargo load factors contribute to efficiency. Air traffic management systems can allow automation of takeoff, landing, and collision avoidance, as well as within airports, from simple things like HVAC and lighting to more complex tasks such as security and scanning. == International Action == === International agreements and pledges === At the 2023 United Nations Climate Change Conference, one of the adopted declaration was the GLOBAL RENEWABLES AND ENERGY EFFICIENCY PLEDGE signed by 123 countries. The declaration includes obligations to consider energy efficiency as "first fuel" and double the rate of increase in energy efficiency from 2% per year to 4% per year by the year 2030. China and India did not signed this pledge. === International standards === International standards ISO 17743 and ISO 17742 provide a documented methodology for calculating and reporting on energy savings and energy efficiency for countries and cities. == Examples by country or region == === Europe === The first EU-wide energy efficiency target was set in 1998. Member states agreed to improve energy efficiency by 1 percent a year over twelve years. In addition, legislation about products, industry, transport and buildings has contributed to a general energy efficiency framework. More effort is needed to address heating and cooling: there is more heat wasted during electricity production in Europe than is required to heat all buildings in the continent. All in all, EU energy efficiency legislation is estimated to deliver savings worth the equivalent of up to 326 million tons of oil per year by 2020. The EU set itself a 20% energy savings target by 2020 compared to 1990 levels, but member states decide individually how energy savings will be achieved. At an EU summit in October 2014, EU countries agreed on a new energy efficiency target of 27% or greater by 2030. One mechanism used to achieve the target of 27% is the 'Suppliers Obligations & White Certificates'. The ongoing debate around the 2016 Clean Energy Package also puts an emphasis on energy efficiency, but the goal will probably remain around 30% greater efficiency compared to 1990 levels. Some have argued that this will not be enough for the EU to meet its Paris Agreement goals of reducing greenhouse gas emissions by 40% compared to 1990 levels. In the European Union, 78% of enterprises proposed energy-saving methods in 2023, 67% listed energy contract renegotiation as a strategy, and 62% stated passing on costs to consumers as a plan to deal with energy market trends. Larger organisations were found more likely to invest in energy efficiency, green innovation, and climate change, with a significant rise in energy efficiency investments reported by SMEs and mid-cap companies. ==== Germany ==== Energy efficiency is central to energy policy in Germany. As of late 2015, national policy includes the following efficiency and consumption targets (with actual values for 2014):: 4  Progress toward improved efficiency has been steady. Some however believe energy efficiency is still under-recognized in terms of its contribution to Germany's energy transformation (or Energiewende). Efforts to reduce final energy consumption in transport sector have not been successful, with a growth of 1.7% between 2005 and 2014. This growth is due to both road passenger and road freight transport. Both sectors increased their overall distance travelled to record the highest figures ever for Germany. Rebound effects played a significant role, both between improved vehicle efficiency and the distance travelled, and between improved vehicle efficiency and an increase in vehicle weights and engine power.: 12  In 2014, the German federal government released its National Action Plan on Energy Efficiency (NAPE). The areas covered are the energy efficiency of buildings, energy conservation for companies, consumer energy efficiency, and transport energy efficiency. The central short-term measures of NAPE include the introduction of competitive tendering for energy efficiency, the raising of funding for building renovation, the introduction of tax incentives for efficiency measures in the building sector, and the setting up energy efficiency networks together with business and industry. In 2016, the German government released a green paper on energy efficiency for public consultation (in German). It outlines the potential challenges and actions needed to reduce energy consumption in Germany over the coming decades. At the document's launch, economics and energy minister Sigmar Gabriel said "we do not need to produce, store, transmit and pay for the energy that we save". The green paper prioritizes the efficient use of energy as the "first" response and also outlines opportunities for sector coupling, including using renewable power for heating and transport. Other proposals include a flexible energy tax which rises as petrol prices fall, thereby incentivizing fuel conservation despite low oil prices. ==== Spain ==== In Spain, four out of every five buildings use more energy than they should. They are either inadequately insulated or consume energy inefficiently. The Unión de Créditos Immobiliarios (UCI), which has operations in Spain and Portugal, is increasing loans to homeowners and building management groups for energy-efficiency initiatives. Their Residential Energy Rehabilitation initiative aims to remodel and encourage the use of renewable energy in at least 3720 homes in Madrid, Barcelona, Valencia, and Seville. The works are expected to mobilize around €46.5 million in energy efficiency upgrades by 2025 and save approximately 8.1 GWh of energy. It has the ability to reduce carbon emissions by 7,545 tonnes per year. ==== Poland ==== In May 2016 Poland adopted a new Act on Energy Efficiency, to enter into force on 1 October 2016. === Australia === In July 2009, the Council of Australian Governments, which represents the individual states and territories of Australia, agreed to a National Strategy on Energy Efficiency (NSEE). This is a ten-year plan accelerating the implementation of a nationwide adoption of energy-efficient practices and a preparation for the country's transformation into a low carbon future. The overriding agreement that governs this strategy is the National Partnership Agreement on Energy Efficiency. === Canada === In August 2017, the Government of Canada released Build Smart - Canada's Buildings Strategy, as a key driver of the Pan-Canadian Framework on Clean Growth and Climate Change, Canada's national climate strategy. === United States === A 2011 Energy Modeling Forum study covering the United States examined how energy efficiency opportunities will shape future fuel and electricity demand over the next several decades. The US economy is already set to lower its energy and carbon intensity, but explicit policies will be necessary to meet climate goals. These policies include: a carbon tax, mandated standards for more efficient appliances, buildings and vehicles, and subsidies or reductions in the upfront costs of new more energy-efficient equipment. Programs and organizations: Alliance to Save Energy American Council for an Energy-Efficient Economy Building Codes Assistance Project Building Energy Codes Program Consortium for Energy Efficiency Energy Star, from United States Environmental Protection Agency == See also == Carbon footprint – Concept to quantify greenhouse gas emissions from activities or products Energy audit – Inspection, survey and analysis of energy flows in a building Energy conservation measure – Reducing energy consumptionPages displaying short descriptions of redirect targets Energy conversion efficiency – Ratio between the useful output and the input of a machine Energy efficiency implementation – industry comprising firms which retrofit or replace inefficient equipment with more efficient parts or equipment, with the goal of reducing energy consumptionPages displaying wikidata descriptions as a fallback Energy law – Law governing the use and taxation of energy Energy recovery Energy recycling – Process of using energy that would normally be wasted Energy resilience – Methods bringing energy into productionPages displaying short descriptions of redirect targets List of least carbon efficient power stations Waste-to-energy – Process of generating energy from the primary treatment of waste == References ==
Wikipedia/Efficient_energy_use
In physics, a force is an influence that can cause an object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the magnitude and direction of a force are both important, force is a vector quantity. The SI unit of force is the newton (N), and force is often represented by the symbol F. Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include elastic, frictional, contact or "normal" forces, and gravitational. The rotational version of force is torque, which produces changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent parts; the distribution of such forces through the body is the internal mechanical stress. In the case of multiple forces, if the net force on an extended body is zero the body is in equilibrium. In modern physics, which includes relativity and quantum mechanics, the laws governing motion are revised to rely on fundamental interactions as the ultimate origin of force. However, the understanding of force provided by classical mechanics is useful for practical purposes. == Development of the concept == Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part, this was due to an incomplete understanding of the sometimes non-obvious force of friction and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Newton formulated laws of motion that were not improved for over two hundred years. By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light and also provided insight into the forces produced by gravitation and inertia. With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational.: 2–10 : 79  High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. == Pre-Newtonian concepts == Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, were in their natural place when on the ground, and that they stay that way if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. An archer causes the arrow to move at the start of the flight, and it then sails through the air even though no discernible efficient cause acts upon it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path carries the projectile to its target. This explanation requires a continuous medium such as air to sustain the motion. Though Aristotelian physics was criticized as early as the 6th century, its shortcomings would not be corrected until the 17th century work of Galileo Galilei, who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion. He showed that the bodies were accelerated by gravity to an extent that was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction. Galileo's idea that force is needed to change motion rather than to sustain it, further improved upon by Isaac Beeckman, René Descartes, and Pierre Gassendi, became a key principle of Newtonian physics. In the early 17th century, before Newton's Principia, the term "force" (Latin: vis) was applied to many physical and non-physical phenomena, e.g., for an acceleration of a point. The product of a point mass and the square of its velocity was named vis viva (live force) by Leibniz. The modern concept of force corresponds to Newton's vis motrix (accelerating force). == Newtonian mechanics == Sir Isaac Newton described the motion of all objects using the concepts of inertia and force. In 1687, Newton published his magnum opus, Philosophiæ Naturalis Principia Mathematica. In this work Newton set out three laws of motion that have dominated the way forces are described in physics to this day. The precise ways in which Newton's laws are expressed have evolved in step with new mathematical approaches. === First law === Newton's first law of motion states that the natural behavior of an object at rest is to continue being at rest, and the natural behavior of an object moving at constant speed in a straight line is to continue moving at that constant speed along that straight line. The latter follows from the former because of the principle that the laws of physics are the same for all inertial observers, i.e., all observers who do not feel themselves to be in motion. An observer moving in tandem with an object will see it as being at rest. So, its natural behavior will be to remain at rest with respect to that observer, which means that an observer who sees it moving at constant speed in a straight line will see it continuing to do so.: 1–7  === Second law === According to the first law, motion at constant speed in a straight line does not need a cause. It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.: 204–207  A modern statement of Newton's second law is a vector equation: F = d p d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},} where p {\displaystyle \mathbf {p} } is the momentum of the system, and F {\displaystyle \mathbf {F} } is the net (vector sum) force.: 399  If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time. In common engineering applications the mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum, F = d p d t = d ( m v ) d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}={\frac {\mathrm {d} \left(m\mathbf {v} \right)}{\mathrm {d} t}},} where m is the mass and v {\displaystyle \mathbf {v} } is the velocity.: 9-1,9-2  If Newton's second law is applied to a system of constant mass, m may be moved outside the derivative operator. The equation then becomes F = m d v d t . {\displaystyle \mathbf {F} =m{\frac {\mathrm {d} \mathbf {v} }{\mathrm {d} t}}.} By substituting the definition of acceleration, the algebraic version of Newton's second law is derived: F = m a . {\displaystyle \mathbf {F} =m\mathbf {a} .} === Third law === Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if F 1 , 2 {\displaystyle \mathbf {F} _{1,2}} is the force of body 1 on body 2 and F 2 , 1 {\displaystyle \mathbf {F} _{2,1}} that of body 2 on body 1, then F 1 , 2 = − F 2 , 1 . {\displaystyle \mathbf {F} _{1,2}=-\mathbf {F} _{2,1}.} This law is sometimes referred to as the action-reaction law, with F 1 , 2 {\displaystyle \mathbf {F} _{1,2}} called the action and − F 2 , 1 {\displaystyle -\mathbf {F} _{2,1}} the reaction. Newton's third law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. and thus that there is no such thing as a unidirectional force or a force that acts on only one body. In a system composed of object 1 and object 2, the net force on the system due to their mutual interactions is zero: F 1 , 2 + F 2 , 1 = 0. {\displaystyle \mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} More generally, in a closed system of particles, all internal forces are balanced. The particles may accelerate with respect to each other but the center of mass of the system will not accelerate. If an external force acts on the system, it will make the center of mass accelerate in proportion to the magnitude of the external force divided by the mass of the system.: 19-1  Combining Newton's second and third laws, it is possible to show that the linear momentum of a system is conserved in any closed system. In a system of two particles, if p 1 {\displaystyle \mathbf {p} _{1}} is the momentum of object 1 and p 2 {\displaystyle \mathbf {p} _{2}} the momentum of object 2, then d p 1 d t + d p 2 d t = F 1 , 2 + F 2 , 1 = 0. {\displaystyle {\frac {\mathrm {d} \mathbf {p} _{1}}{\mathrm {d} t}}+{\frac {\mathrm {d} \mathbf {p} _{2}}{\mathrm {d} t}}=\mathbf {F} _{1,2}+\mathbf {F} _{2,1}=0.} Using similar arguments, this can be generalized to a system with an arbitrary number of particles. In general, as long as all forces are due to the interaction of objects with mass, it is possible to define a system such that net momentum is never lost nor gained.: ch.12  === Defining "force" === Some textbooks use Newton's second law as a definition of force. However, for the equation F = m a {\displaystyle \mathbf {F} =m\mathbf {a} } for a constant mass m {\displaystyle m} to then have any predictive content, it must be combined with further information.: 12-1  Moreover, inferring that a force is present because a body is accelerating is only valid in an inertial frame of reference.: 59  The question of which aspects of Newton's laws to take as definitions and which to regard as holding physical content has been answered in various ways,: vii  which ultimately do not affect how the theory is used in practice. Notable physicists, philosophers and mathematicians who have sought a more explicit definition of the concept of force include Ernst Mach and Walter Noll. == Combining forces == Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous.: 197  Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the resultant (also called the net force), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action.: ch.12  Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right angles to the other two.: ch.12  === Equilibrium === When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium.: 566  Hence, equilibrium occurs when the resultant force acting on a point particle is zero (that is, the vector sum of all forces is zero). When dealing with an extended body, it is also necessary that the net torque be zero. A body is in static equilibrium with respect to a frame of reference if it at rest and not accelerating, whereas a body in dynamic equilibrium is moving at a constant speed in a straight line, i.e., moving but not accelerating. What one observer sees as static equilibrium, another can see as dynamic equilibrium and vice versa.: 566  ==== Static ==== Static equilibrium was understood well before the invention of classical mechanics. Objects that are not accelerating have zero net force acting on them. The simplest case of static equilibrium occurs when two forces are equal in magnitude but opposite in direction. For example, an object on a level surface is pulled (attracted) downward toward the center of the Earth by the force of gravity. At the same time, a force is applied by the surface that resists the downward force with equal upward force (called a normal force). The situation produces zero net force and hence no acceleration. Pushing against an object that rests on a frictional surface can result in a situation where the object does not move because the applied force is opposed by static friction, generated between the object and the table surface. For a situation with no movement, the static friction force exactly balances the applied force resulting in no acceleration. The static friction increases or decreases in response to the applied force up to an upper limit determined by the characteristics of the contact between the surface and the object. A static equilibrium between two forces is the most usual way of measuring forces, using simple devices such as weighing scales and spring balances. For example, an object suspended on a vertical spring scale experiences the force of gravity acting on the object balanced by a force applied by the "spring reaction force", which equals the object's weight. Using such tools, some quantitative force laws were discovered: that the force of gravity is proportional to volume for objects of constant density (widely exploited for millennia to define standard weights); Archimedes' principle for buoyancy; Archimedes' analysis of the lever; Boyle's law for gas pressure; and Hooke's law for springs. These were all formulated and experimentally verified before Isaac Newton expounded his three laws of motion.: ch.12  ==== Dynamic ==== Dynamic equilibrium was first described by Galileo who noticed that certain assumptions of Aristotelian physics were contradicted by observations and logic. Galileo realized that simple velocity addition demands that the concept of an "absolute rest frame" did not exist. Galileo concluded that motion in a constant velocity was completely equivalent to rest. This was contrary to Aristotle's notion of a "natural state" of rest that objects with mass naturally approached. Simple experiments showed that Galileo's understanding of the equivalence of constant velocity and rest were correct. For example, if a mariner dropped a cannonball from the crow's nest of a ship moving at a constant velocity, Aristotelian physics would have the cannonball fall straight down while the ship moved beneath it. Thus, in an Aristotelian universe, the falling cannonball would land behind the foot of the mast of a moving ship. When this experiment is actually conducted, the cannonball always falls at the foot of the mast, as if the cannonball knows to travel with the ship despite being separated from it. Since there is no forward horizontal force being applied on the cannonball as it falls, the only conclusion left is that the cannonball continues to move with the same velocity as the boat as it falls. Thus, no force is required to keep the cannonball moving at the constant forward velocity. Moreover, any object traveling at a constant velocity must be subject to zero net force (resultant force). This is the definition of dynamic equilibrium: when all the forces on an object balance but it still moves at a constant velocity. A simple case of dynamic equilibrium occurs in constant velocity motion across a surface with kinetic friction. In such a situation, a force is applied in the direction of motion while the kinetic friction force exactly opposes the applied force. This results in zero net force, but since the object started with a non-zero velocity, it continues to move with a non-zero velocity. Aristotle misinterpreted this motion as being caused by the applied force. When kinetic friction is taken into consideration it is clear that there is no net force causing constant velocity motion.: ch.12  == Examples of forces in classical mechanics == Some forces are consequences of the fundamental ones. In such situations, idealized models can be used to gain physical insight. For example, each solid object is considered a rigid body. === Gravitational force or Gravity === What we now call gravity was not identified as a universal force until the work of Isaac Newton. Before Newton, the tendency for objects to fall towards the Earth was not understood to be related to the motions of celestial objects. Galileo was instrumental in describing the characteristics of falling objects by determining that the acceleration of every object in free-fall was constant and independent of the mass of the object. Today, this acceleration due to gravity towards the surface of the Earth is usually designated as g {\displaystyle \mathbf {g} } and has a magnitude of about 9.81 meters per second squared (this measurement is taken from sea level and may vary depending on location), and points toward the center of the Earth. This observation means that the force of gravity on an object at the Earth's surface is directly proportional to the object's mass. Thus an object that has a mass of m {\displaystyle m} will experience a force: F = m g . {\displaystyle \mathbf {F} =m\mathbf {g} .} For an object in free-fall, this force is unopposed and the net force on the object is its weight. For objects not in free-fall, the force of gravity is opposed by the reaction forces applied by their supports. For example, a person standing on the ground experiences zero net force, since a normal force (a reaction force) is exerted by the ground upward on the person that counterbalances his weight that is directed downward.: ch.12  Newton's contribution to gravitational theory was to unify the motions of heavenly bodies, which Aristotle had assumed were in a natural state of constant motion, with falling motion observed on the Earth. He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion. Newton came to realize that the effects of gravity might be observed in different ways at larger distances. In particular, Newton determined that the acceleration of the Moon around the Earth could be ascribed to the same force of gravity if the acceleration due to gravity decreased as an inverse square law. Further, Newton realized that the acceleration of a body due to gravity is proportional to the mass of the other attracting body. Combining these ideas gives a formula that relates the mass ( m ⊕ {\displaystyle m_{\oplus }} ) and the radius ( R ⊕ {\displaystyle R_{\oplus }} ) of the Earth to the gravitational acceleration: g = − G m ⊕ R ⊕ 2 r ^ , {\displaystyle \mathbf {g} =-{\frac {Gm_{\oplus }}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},} where the vector direction is given by r ^ {\displaystyle {\hat {\mathbf {r} }}} , is the unit vector directed outward from the center of the Earth. In this equation, a dimensional constant G {\displaystyle G} is used to describe the relative strength of gravity. This constant has come to be known as the Newtonian constant of gravitation, though its value was unknown in Newton's lifetime. Not until 1798 was Henry Cavendish able to make the first measurement of G {\displaystyle G} using a torsion balance; this was widely reported in the press as a measurement of the mass of the Earth since knowing G {\displaystyle G} could allow one to solve for the Earth's mass given the above equation. Newton realized that since all celestial bodies followed the same laws of motion, his law of gravity had to be universal. Succinctly stated, Newton's law of gravitation states that the force on a spherical object of mass m 1 {\displaystyle m_{1}} due to the gravitational pull of mass m 2 {\displaystyle m_{2}} is F = − G m 1 m 2 r 2 r ^ , {\displaystyle \mathbf {F} =-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},} where r {\displaystyle r} is the distance between the two objects' centers of mass and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointed in the direction away from the center of the first object toward the center of the second object. This formula was powerful enough to stand as the basis for all subsequent descriptions of motion within the Solar System until the 20th century. During that time, sophisticated methods of perturbation analysis were invented to calculate the deviations of orbits due to the influence of multiple bodies on a planet, moon, comet, or asteroid. The formalism was exact enough to allow mathematicians to predict the existence of the planet Neptune before it was observed. === Electromagnetic === The electrostatic force was first described in 1784 by Coulomb as a force that existed intrinsically between two charges.: 519  The properties of the electrostatic force were that it varied as an inverse square law directed in the radial direction, was both attractive and repulsive (there was intrinsic polarity), was independent of the mass of the charged objects, and followed the superposition principle. Coulomb's law unifies all these observations into one succinct statement. Subsequent mathematicians and physicists found the construct of the electric field to be useful for determining the electrostatic force on an electric charge at any point in space. The electric field was based on using a hypothetical "test charge" anywhere in space and then using Coulomb's Law to determine the electrostatic force.: 4-6–4-8  Thus the electric field anywhere in space is defined as E = F q , {\displaystyle \mathbf {E} ={\mathbf {F} \over {q}},} where q {\displaystyle q} is the magnitude of the hypothetical test charge. Similarly, the idea of the magnetic field was introduced to express how magnets can influence one another at a distance. The Lorentz force law gives the force upon a body with charge q {\displaystyle q} due to electric and magnetic fields: F = q ( E + v × B ) , {\displaystyle \mathbf {F} =q\left(\mathbf {E} +\mathbf {v} \times \mathbf {B} \right),} where F {\displaystyle \mathbf {F} } is the electromagnetic force, E {\displaystyle \mathbf {E} } is the electric field at the body's location, B {\displaystyle \mathbf {B} } is the magnetic field, and v {\displaystyle \mathbf {v} } is the velocity of the particle. The magnetic contribution to the Lorentz force is the cross product of the velocity vector with the magnetic field.: 482  The origin of electric and magnetic fields would not be fully explained until 1864 when James Clerk Maxwell unified a number of earlier theories into a set of 20 scalar equations, which were later reformulated into 4 vector equations by Oliver Heaviside and Josiah Willard Gibbs. These "Maxwell's equations" fully described the sources of the fields as being stationary and moving charges, and the interactions of the fields themselves. This led Maxwell to discover that electric and magnetic fields could be "self-generating" through a wave that traveled at a speed that he calculated to be the speed of light. This insight united the nascent fields of electromagnetic theory with optics and led directly to a complete description of the electromagnetic spectrum. === Normal === When objects are in contact, the force directly between them is called the normal force, the component of the total force in the system exerted normal to the interface between the objects.: 264  The normal force is closely related to Newton's third law. The normal force, for example, is responsible for the structural integrity of tables and floors as well as being the force that responds whenever an external force pushes on a solid object. An example of the normal force in action is the impact force on an object crashing into an immobile surface.: ch.12  === Friction === Friction is a force that opposes relative motion of two bodies. At the macroscopic scale, the frictional force is directly related to the normal force at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction.: 267  The static friction force ( F s f {\displaystyle \mathbf {F} _{\mathrm {sf} }} ) will exactly oppose forces applied to an object parallel to a surface up to the limit specified by the coefficient of static friction ( μ s f {\displaystyle \mu _{\mathrm {sf} }} ) multiplied by the normal force ( F N {\displaystyle \mathbf {F} _{\text{N}}} ). In other words, the magnitude of the static friction force satisfies the inequality: 0 ≤ F s f ≤ μ s f F N . {\displaystyle 0\leq \mathbf {F} _{\mathrm {sf} }\leq \mu _{\mathrm {sf} }\mathbf {F} _{\mathrm {N} }.} The kinetic friction force ( F k f {\displaystyle F_{\mathrm {kf} }} ) is typically independent of both the forces applied and the movement of the object. Thus, the magnitude of the force equals: F k f = μ k f F N , {\displaystyle \mathbf {F} _{\mathrm {kf} }=\mu _{\mathrm {kf} }\mathbf {F} _{\mathrm {N} },} where μ k f {\displaystyle \mu _{\mathrm {kf} }} is the coefficient of kinetic friction. The coefficient of kinetic friction is normally less than the coefficient of static friction.: 267–271  === Tension === Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and do not stretch. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action–reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by the second object. By connecting the same string multiple times to the same object through the use of a configuration that uses movable pulleys, the tension force on a load can be multiplied. For every string that acts on a load, another factor of the tension force in the string acts on the load. Such machines allow a mechanical advantage for a corresponding increase in the length of displaced string needed to move the load. These tandem effects result ultimately in the conservation of mechanical energy since the work done on the load is the same no matter how complicated the machine.: ch.12  === Spring === A simple elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring from its equilibrium position. This linear relationship was described by Robert Hooke in 1676, for whom Hooke's law is named. If Δ x {\displaystyle \Delta x} is the displacement, the force exerted by an ideal spring equals: F = − k Δ x , {\displaystyle \mathbf {F} =-k\Delta \mathbf {x} ,} where k {\displaystyle k} is the spring constant (or force constant), which is particular to the spring. The minus sign accounts for the tendency of the force to act in opposition to the applied load.: ch.12  === Centripetal === For an object in uniform circular motion, the net force acting on the object equals: F = − m v 2 r r ^ , {\displaystyle \mathbf {F} =-{\frac {mv^{2}}{r}}{\hat {\mathbf {r} }},} where m {\displaystyle m} is the mass of the object, v {\displaystyle v} is the velocity of the object and r {\displaystyle r} is the distance to the center of the circular path and r ^ {\displaystyle {\hat {\mathbf {r} }}} is the unit vector pointing in the radial direction outwards from the center. This means that the net force felt by the object is always directed toward the center of the curving path. Such forces act perpendicular to the velocity vector associated with the motion of an object, and therefore do not change the speed of the object (magnitude of the velocity), but only the direction of the velocity vector. More generally, the net force that accelerates an object can be resolved into a component that is perpendicular to the path, and one that is tangential to the path. This yields both the tangential force, which accelerates the object by either slowing it down or speeding it up, and the radial (centripetal) force, which changes its direction.: ch.12  === Continuum mechanics === Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. In real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows: F V = − ∇ P , {\displaystyle {\frac {\mathbf {F} }{V}}=-\mathbf {\nabla } P,} where V {\displaystyle V} is the volume of the object in the fluid and P {\displaystyle P} is the scalar function that describes the pressure at all locations in space. Pressure gradients and differentials result in the buoyant force for fluids suspended in gravitational fields, winds in atmospheric science, and the lift associated with aerodynamics and flight.: ch.12  A specific instance of such a force that is associated with dynamic pressure is fluid resistance: a body force that resists the motion of an object through a fluid due to viscosity. For so-called "Stokes' drag" the force is approximately proportional to the velocity, but opposite in direction: F d = − b v , {\displaystyle \mathbf {F} _{\mathrm {d} }=-b\mathbf {v} ,} where: b {\displaystyle b} is a constant that depends on the properties of the fluid and the dimensions of the object (usually the cross-sectional area), and v {\displaystyle \mathbf {v} } is the velocity of the object.: ch.12  More formally, forces in continuum mechanics are fully described by a stress tensor with terms that are roughly defined as σ = F A , {\displaystyle \sigma ={\frac {F}{A}},} where A {\displaystyle A} is the relevant cross-sectional area for the volume for which the stress tensor is being calculated. This formalism includes pressure terms associated with forces that act normal to the cross-sectional area (the matrix diagonals of the tensor) as well as shear terms associated with forces that act parallel to the cross-sectional area (the off-diagonal elements). The stress tensor accounts for forces that cause all strains (deformations) including also tensile stresses and compressions.: 133–134 : 38-1–38-11  === Fictitious === There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force. These forces are considered fictitious because they do not exist in frames of reference that are not accelerating.: ch.12  Because these forces are not genuine they are also referred to as "pseudo forces".: 12-11  In general relativity, gravity becomes a fictitious force that arises in situations where spacetime deviates from a flat geometry. == Concepts derived from force == === Rotation and torque === Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force F {\displaystyle \mathbf {F} } is defined relative to an arbitrary reference point as the cross product: τ = r × F , {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} ,} where r {\displaystyle \mathbf {r} } is the position vector of the force application point relative to the reference point.: 497  Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's first law of motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's second law of motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body: τ = I α , {\displaystyle {\boldsymbol {\tau }}=I{\boldsymbol {\alpha }},} where I {\displaystyle I} is the moment of inertia of the body α {\displaystyle {\boldsymbol {\alpha }}} is the angular acceleration of the body.: 502  This provides a definition for the moment of inertia, which is the rotational equivalent for mass. In more advanced treatments of mechanics, where the rotation over a time interval is described, the moment of inertia must be substituted by the tensor that, when properly analyzed, fully determines the characteristics of rotations including precession and nutation.: 96–113  Equivalently, the differential form of Newton's second law provides an alternative definition of torque: τ = d L d t , {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {dt} }},} where L {\displaystyle \mathbf {L} } is the angular momentum of the particle. Newton's third law of motion requires that all objects exerting torques themselves experience equal and opposite torques, and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques. === Yank === The yank is defined as the rate of change of force: 131  Y = d F d t {\displaystyle \mathbf {Y} ={\frac {\mathrm {d} \mathbf {F} }{\mathrm {d} t}}} The term is used in biomechanical analysis, athletic assessment and robotic control. The second ("tug"), third ("snatch"), fourth ("shake"), and higher derivatives are rarely used. === Kinematic integrals === Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse: J = ∫ t 1 t 2 F d t , {\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}{\mathbf {F} \,\mathrm {d} t},} which by Newton's second law must be equivalent to the change in momentum (yielding the Impulse momentum theorem). Similarly, integrating with respect to position gives a definition for the work done by a force:: 13-3  W = ∫ x 1 x 2 F ⋅ d x , {\displaystyle W=\int _{\mathbf {x} _{1}}^{\mathbf {x} _{2}}{\mathbf {F} \cdot {\mathrm {d} \mathbf {x} }},} which is equivalent to changes in kinetic energy (yielding the work energy theorem).: 13-3  Power P is the rate of change dW/dt of the work W, as the trajectory is extended by a position change d x {\displaystyle d\mathbf {x} } in a time interval dt:: 13-2  d W = d W d x ⋅ d x = F ⋅ d x , {\displaystyle \mathrm {d} W={\frac {\mathrm {d} W}{\mathrm {d} \mathbf {x} }}\cdot \mathrm {d} \mathbf {x} =\mathbf {F} \cdot \mathrm {d} \mathbf {x} ,} so P = d W d t = d W d x ⋅ d x d t = F ⋅ v , {\displaystyle P={\frac {\mathrm {d} W}{\mathrm {d} t}}={\frac {\mathrm {d} W}{\mathrm {d} \mathbf {x} }}\cdot {\frac {\mathrm {d} \mathbf {x} }{\mathrm {d} t}}=\mathbf {F} \cdot \mathbf {v} ,} with v = d x / d t {\displaystyle \mathbf {v} =\mathrm {d} \mathbf {x} /\mathrm {d} t} the velocity. === Potential energy === Instead of a force, often the mathematically related concept of a potential energy field is used. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field U ( r ) {\displaystyle U(\mathbf {r} )} is defined as that field whose gradient is equal and opposite to the force produced at every point: F = − ∇ U . {\displaystyle \mathbf {F} =-\mathbf {\nabla } U.} Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not.: ch.12  === Conservation === A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same way that the direction and amount of a flow of water can be considered to be an artifact of the contour map of the elevation of an area.: ch.12  Conservative forces include gravity, the electromagnetic force, and the spring force. Each of these forces has models that are dependent on a position often given as a radial vector r {\displaystyle \mathbf {r} } emanating from spherically symmetric potentials. Examples of this follow: For gravity: F g = − G m 1 m 2 r 2 r ^ , {\displaystyle \mathbf {F} _{\text{g}}=-{\frac {Gm_{1}m_{2}}{r^{2}}}{\hat {\mathbf {r} }},} where G {\displaystyle G} is the gravitational constant, and m n {\displaystyle m_{n}} is the mass of object n. For electrostatic forces: F e = q 1 q 2 4 π ε 0 r 2 r ^ , {\displaystyle \mathbf {F} _{\text{e}}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}r^{2}}}{\hat {\mathbf {r} }},} where ε 0 {\displaystyle \varepsilon _{0}} is electric permittivity of free space, and q n {\displaystyle q_{n}} is the electric charge of object n. For spring forces: F s = − k r r ^ , {\displaystyle \mathbf {F} _{\text{s}}=-kr{\hat {\mathbf {r} }},} where k {\displaystyle k} is the spring constant.: ch.12  For certain physical scenarios, it is impossible to model forces as being due to a simple gradient of potentials. This is often due a macroscopic statistical average of microstates. For example, static friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include other contact forces, tension, compression, and drag. For any sufficiently detailed description, all these forces are the results of conservative ones since each of these macroscopic forces are the net results of the gradients of microscopic potentials.: ch.12  The connection between macroscopic nonconservative forces and microscopic conservative forces is described by detailed treatment with statistical mechanics. In macroscopic closed systems, nonconservative forces act to change the internal energies of the system, and are often associated with the transfer of heat. According to the Second law of thermodynamics, nonconservative forces necessarily result in energy transformations within closed systems from ordered to more random conditions as entropy increases.: ch.12  == Units == The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or kg·m·s−2.The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or g·cm·s−2. A newton is thus equal to 100,000 dynes. The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of 9.80665 m·s−2. The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. An alternative unit of force in a different foot–pound–second system, the absolute fps system, is the poundal, defined as the force required to accelerate a one-pound mass at a rate of one foot per second squared. The pound-force has a metric counterpart, less commonly used than the newton: the kilogram-force (kgf) (sometimes kilopond), is the force exerted by standard gravity on one kilogram of mass. The kilogram-force leads to an alternate, but rarely used unit of mass: the metric slug (sometimes mug or hyl) is that mass that accelerates at 1 m·s−2 when subjected to a force of 1 kgf. The kilogram-force is not a part of the modern SI system, and is generally deprecated, sometimes used for expressing aircraft weight, jet thrust, bicycle spoke tension, torque wrench settings and engine output torque. See also Ton-force. == Revisions of the force concept == At the beginning of the 20th century, new physical ideas emerged to explain experimental results in astronomical and submicroscopic realms. As discussed below, relativity alters the definition of momentum and quantum mechanics reuses the concept of "force" in microscopic contexts where Newton's laws do not apply directly. === Special theory of relativity === In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's second law, F = d p d t , {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}},} remains valid because it is a mathematical definition.: 855–876  But for momentum to be conserved at relativistic relative velocity, v {\displaystyle v} , momentum must be redefined as: p = m 0 v 1 − v 2 / c 2 , {\displaystyle \mathbf {p} ={\frac {m_{0}\mathbf {v} }{\sqrt {1-v^{2}/c^{2}}}},} where m 0 {\displaystyle m_{0}} is the rest mass and c {\displaystyle c} the speed of light. The expression relating force and acceleration for a particle with constant non-zero rest mass m {\displaystyle m} moving in the x {\displaystyle x} direction at velocity v {\displaystyle v} is:: 216  F = ( γ 3 m a x , γ m a y , γ m a z ) , {\displaystyle \mathbf {F} =\left(\gamma ^{3}ma_{x},\gamma ma_{y},\gamma ma_{z}\right),} where γ = 1 1 − v 2 / c 2 . {\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}.} is called the Lorentz factor. The Lorentz factor increases steeply as the relative velocity approaches the speed of light. Consequently, the greater and greater force must be applied to produce the same acceleration at extreme velocity. The relative velocity cannot reach c {\displaystyle c} .: 26 : §15–8  If v {\displaystyle v} is very small compared to c {\displaystyle c} , then γ {\displaystyle \gamma } is very close to 1 and F = m a {\displaystyle \mathbf {F} =m\mathbf {a} } is a close approximation. Even for use in relativity, one can restore the form of F μ = m A μ {\displaystyle F^{\mu }=mA^{\mu }} through the use of four-vectors. This relation is correct in relativity when F μ {\displaystyle F^{\mu }} is the four-force, m {\displaystyle m} is the invariant mass, and A μ {\displaystyle A^{\mu }} is the four-acceleration. The general theory of relativity incorporates a more radical departure from the Newtonian way of thinking about force, specifically gravitational force. This reimagining of the nature of gravity is described more fully below. === Quantum mechanics === Quantum mechanics is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The conceptual underpinning of quantum physics is different from that of classical physics. Instead of thinking about quantities like position, momentum, and energy as properties that an object has, one considers what result might appear when a measurement of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The expectation value for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence. In quantum mechanics, interactions are typically described in terms of energy rather than force. The Ehrenfest theorem provides a connection between quantum expectation values and the classical concept of force, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law, with a force defined as the negative derivative of the potential energy. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance. Quantum mechanics also introduces two new constraints that interact with forces at the submicroscopic scale and which are especially important for atoms. Despite the strong attraction of the nucleus, the uncertainty principle limits the minimum extent of an electron probability distribution and the Pauli exclusion principle prevents electrons from sharing the same probability distribution. This gives rise to an emergent pressure known as degeneracy pressure. The dynamic equilibrium between the degeneracy pressure and the attractive electromagnetic force give atoms, molecules, liquids, and solids stability. === Quantum field theory === In modern particle physics, forces and the acceleration of particles are explained as a mathematical by-product of exchange of momentum-carrying gauge bosons. With the development of quantum field theory and general relativity, it was realized that force is a redundant concept arising from conservation of momentum (4-momentum in relativity and momentum of virtual particles in quantum electrodynamics). The conservation of momentum can be directly derived from the homogeneity or symmetry of space and so is usually considered more fundamental than the concept of a force. Thus the currently known fundamental forces are considered more accurately to be "fundamental interactions".: 199–128  While sophisticated mathematical descriptions are needed to predict, in full detail, the result of such interactions, there is a conceptually simple way to describe them through the use of Feynman diagrams. In a Feynman diagram, each matter particle is represented as a straight line (see world line) traveling through time, which normally increases up or to the right in the diagram. Matter and anti-matter particles are identical except for their direction of propagation through the Feynman diagram. World lines of particles intersect at interaction vertices, and the Feynman diagram represents any force arising from an interaction as occurring at the vertex with an associated instantaneous change in the direction of the particle world lines. Gauge bosons are emitted away from the vertex as wavy lines and, in the case of virtual particle exchange, are absorbed at an adjacent vertex. The utility of Feynman diagrams is that other types of physical phenomena that are part of the general picture of fundamental interactions but are conceptually separate from forces can also be described using the same rules. For example, a Feynman diagram can describe in succinct detail how a neutron decays into an electron, proton, and antineutrino, an interaction mediated by the same gauge boson that is responsible for the weak nuclear force. == Fundamental interactions == All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions operating within quantum mechanics, including the constraints introduced by the Schrödinger equation and the Pauli exclusion principle. For example, friction is a manifestation of the electromagnetic force acting between atoms of two surfaces. The forces in springs, modeled by Hooke's law, are also the result of electromagnetic forces. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference.: 12-11 : 359  The fundamental theories for forces developed from the unification of different ideas. For example, Newton's universal theory of gravitation showed that the force responsible for objects falling near the surface of the Earth is also the force responsible for the falling of celestial bodies about the Earth (the Moon) and around the Sun (the planets). Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through a theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons. This Standard Model of particle physics assumes a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory, which was subsequently confirmed by observation. === Gravitational === Newton's law of gravitation is an example of action at a distance: one body, like the Sun, exerts an influence upon any other body, like the Earth, no matter how far apart they are. Moreover, this action at a distance is instantaneous. According to Newton's theory, the one body shifting position changes the gravitational pulls felt by all other bodies, all at the same instant of time. Albert Einstein recognized that this was inconsistent with special relativity and its prediction that influences cannot travel faster than the speed of light. So, he sought a new theory of gravitation that would be relativistically consistent. Mercury's orbit did not match that predicted by Newton's law of gravitation. Some astrophysicists predicted the existence of an undiscovered planet (Vulcan) that could explain the discrepancies. When Einstein formulated his theory of general relativity (GR) he focused on Mercury's problematic orbit and found that his theory added a correction, which could account for the discrepancy. This was the first time that Newton's theory of gravity had been shown to be inexact. Since then, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved spacetime – defined as the shortest spacetime path between two spacetime events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of spacetime can be observed and the force is inferred from the object's curved path. Thus, the straight line path in spacetime is seen as a curved line in space, and it is called the ballistic trajectory of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its spacetime trajectory is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force". === Electromagnetic === Maxwell's equations and the set of techniques built around them adequately describe a wide range of physics involving force in electricity and magnetism. This classical theory already includes relativity effects. Understanding quantized electromagnetic interactions between elementary particles requires quantum electrodynamics (QED). In QED, photons are fundamental exchange particles, describing all interactions relating to electromagnetism including the electromagnetic force. === Strong nuclear === There are two "nuclear forces", which today are usually described as interactions that take place in quantum theories of particle physics. The strong nuclear force is the force responsible for the structural integrity of atomic nuclei, and gains its name from its ability to overpower the electromagnetic repulsion between protons.: 940  The strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). The strong force is the fundamental force mediated by gluons, acting upon quarks, antiquarks, and the gluons themselves. The strong force only acts directly upon elementary particles. A residual is observed between hadrons (notably, the nucleons in atomic nuclei), known as the nuclear force. Here the strong force acts indirectly, transmitted as gluons that form part of the virtual pi and rho mesons, the classical transmitters of the nuclear force. The failure of many searches for free quarks has shown that the elementary particles affected are not directly observable. This phenomenon is called color confinement.: 232  === Weak nuclear === Unique among the fundamental interactions, the weak nuclear force creates no bound states. The weak force is due to the exchange of the heavy W and Z bosons. Since the weak force is mediated by two types of bosons, it can be divided into two types of interaction or "vertices" — charged current, involving the electrically charged W+ and W− bosons, and neutral current, involving electrically neutral Z0 bosons. The most familiar effect of weak interaction is beta decay (of neutrons in atomic nuclei) and the associated radioactivity.: 951  This is a type of charged-current interaction. The word "weak" derives from the fact that the field strength is some 1013 times less than that of the strong force. Still, it is stronger than gravity over short distances. A consistent electroweak theory has also been developed, which shows that electromagnetic forces and the weak force are indistinguishable at a temperatures in excess of approximately 1015 K. Such temperatures occurred in the plasma collisions in the early moments of the Big Bang.: 201  == See also == Contact force – Force between two objects that are in physical contact Force control – Force control is given by the machine Force gauge – Instrument for measuring force Orders of magnitude (force) – Comparison of a wide range of physical forces Parallel force system – Situation in mechanical engineering Rigid body – Physical object which does not deform when forces or moments are exerted on it Specific force – Concept in physics == References == == External links == "Classical Mechanics, Week 2: Newton's Laws". MIT OpenCourseWare. Retrieved 2023-08-09. "Fundamentals of Physics I, Lecture 3: Newton's Laws of Motion". Open Yale Courses. Retrieved 2023-08-09.
Wikipedia/Force_(physics)
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the very early universe. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old (5.4 billion years ago). Inflation theory was developed in the late 1970s and early 1980s, with notable contributions by several theoretical physicists, including Alexei Starobinsky at Landau Institute for Theoretical Physics, Alan Guth at Cornell University, and Andrei Linde at Lebedev Physical Institute. Starobinsky, Guth, and Linde won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation". It was developed further in the early 1980s. It explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see galaxy formation and evolution and structure formation). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (isotropic), why the cosmic microwave background radiation is distributed evenly, why the universe is flat, and why no magnetic monopoles have been observed. The detailed particle physics mechanism responsible for inflation is unknown. A number of inflation model predictions have been confirmed by observation; for example temperature anisotropies observed by the COBE satellite in 1992 exhibit nearly scale-invariant spectra as predicted by the inflationary paradigm and WMAP results also show strong evidence for inflation. However, some scientists dissent from this position. The hypothetical field thought to be responsible for inflation is called the inflaton. In 2002, three of the original architects of the theory were recognized for their major contributions; physicists Alan Guth of M.I.T., Andrei Linde of Stanford, and Paul Steinhardt of Princeton shared the Dirac Prize "for development of the concept of inflation in cosmology". In 2012, Guth and Linde were awarded the Breakthrough Prize in Fundamental Physics for their invention and development of inflationary cosmology. == Overview == Cosmic inflation is the hypothesis that the very early universe expanded exponentially fast. Distances between points doubled every 10-37 seconds; the expansion lasted at least 10-35 seconds, but its full duration is not certain. A distance of 1 cm expanded to a distance more than 20 times the distance from the Earth to the Moon.: 3  All of the mass-energy in all of the galaxies currently visible started in a sphere with a radius around 4 x 10-29m which grew to a sphere with a radius around 0.9m.: 202  The hypothesis was originally proposed to solve issues in cosmology. The originally proposal by Alan Guth in 1979 was motivated by predictions by particle physics theories that the universe should have high densities of magnetic monopoles, contrary to observations. An exponential expansion would dilute the monopoles to the extent they could no longer be detected. It was quickly realized that such exponential expansion would resolve two other problems, the flatness problem and horizon problem. The rapid expansion means a universe with any amount of curved spacetime will emerge from inflation very "flat", that is with much smaller curvature consistent with observations. The rapid expansion also means that parts of the universe in thermal equilibrium before inflation can end up after inflation very far apart, so far apart that no particles could ever have made the journey in the lifetime of the universe. This matches observations that points separated by more than a "horizon" distance have almost identical cosmic microwave background temperatures. The underlying physics of inflation is not well understood. According to the Friedmann equations that describe the dynamics of an expanding universe, a fluid with sufficiently negative pressure exerts gravitational repulsion in the cosmological context. A field in a positive-energy false vacuum state could represent such a fluid, and the resulting repulsion would set the universe into exponential expansion. Thus one simple theory is a new field, active only during inflation. The energy of this field produces the initial energy of the Big Bang. == Theory == An expanding universe generally has a cosmological horizon, which, by analogy with the more familiar horizon caused by the curvature of Earth's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an accelerating universe never reaches the observer, because the space in between the observer and the object is expanding too rapidly. The observable universe is one causal patch of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon, which is believed to be 46 billion light years in all directions from Earth. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: Its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They could not have learned it by getting signals, because they were not previously in communication with our past light cone. Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the cosmological horizon is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communication. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous. As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space. The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter, dark matter and residual vacuum energy in the Universe have to add up to the critical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed. === Space expands === In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially). In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following metric: d s 2 = − ( 1 − Λ r 2 ) c 2 d t 2 + 1 1 − Λ r 2 d r 2 + r 2 d Ω 2 . {\displaystyle ds^{2}=-(1-\Lambda r^{2})\,c^{2}dt^{2}+{1 \over 1-\Lambda r^{2}}\,dr^{2}+r^{2}\,d\Omega ^{2}.} This exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure p equal in magnitude to its energy density ρ; the equation of state is p=−ρ. Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases. === Few inhomogeneities remain === Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths out inhomogeneities and anisotropies, and reduces the curvature of space. This pushes the Universe into a very simple state in which it is completely dominated by the inflaton field and the only significant inhomogeneities are tiny quantum fluctuations. Inflation also dilutes exotic heavy particles, such as the magnetic monopoles predicted by many extensions to the Standard Model of particle physics. If the Universe was only hot enough to form such particles before a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the observable universe. Together, these effects are called the inflationary "no-hair theorem" by analogy with the no hair theorem for black holes. The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for not testable disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, energy densities generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) declines as the inverse of the volume: when linear dimensions double, the energy density declines by a factor of eight; the radiation energy density declines even more rapidly as the Universe expands since the wavelength of each photon is stretched (redshifted), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins. === Reheating === Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from 1027 K down to 1022 K.) This relatively low temperature is maintained during the inflationary phase. When inflation ends, the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe. Because the nature of the inflaton field is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance. == Motivations == Inflation tries to resolve several problems in Big Bang cosmology that were discovered in the 1970s. Inflation was first proposed by Alan Guth in 1979 while investigating the problem of why no magnetic monopoles are seen today; he found that a positive-energy false vacuum would, according to general relativity, generate an exponential expansion of space. It was quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory. === Magnetic-monopole problem === Stable magnetic monopoles are a problem for Grand Unified Theories, which propose that at high temperatures (such as in the early universe), the electromagnetic force, strong, and weak nuclear forces are not actually fundamental forces but arise due to spontaneous symmetry breaking from a single gauge theory. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field. Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature, and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe. Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe. A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: Monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude.: 202  While solving the monopole problem motivated the original hypothesis, not every cosmologists was impressed. Martin Rees has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!" However, the flatness and especially the horizon problem are also solved by inflation theory.: 202  === Flatness problem === The flatness problem is sometimes called one of the Dicke coincidences (along with the cosmological constant problem). It became known in the 1960s that the density of matter in the Universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large-scale geometry is the usual Euclidean geometry, rather than a non-Euclidean hyperbolic or spherical geometry).(p 61) Therefore, regardless of the shape of the universe, the contribution of spatial curvature to the expansion of the Universe could not be much greater than the contribution of matter. But as the Universe expands, the curvature redshifts away more slowly than matter and radiation. Extrapolated into the past, this presents a fine-tuning problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at Big Bang nucleosynthesis, for example). Observations of the cosmic microwave background have demonstrated that the Universe is flat to within a few percent. === Horizon problem === The horizon problem is the problem of determining why the universe appears statistically homogeneous and isotropic in accordance with the cosmological principle. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. In the Big Bang model without inflation, gravitational expansion separates regions too quickly: the early universe does not have enough time to equilibrate. In a Big Bang with only the matter and radiation known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the speed of light and thus have never come into causal contact. Historically, proposed solutions included the Phoenix universe of Georges Lemaître, the related oscillatory universe of Richard Chase Tolman, and the Mixmaster universe of Charles Misner. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of entropy over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe more chaotic, could lead to statistical homogeneity and isotropy. The inflation solution starts with a tiny universe in thermal equilibrium then expands it much faster than the speed of light, so fast that the equilibrated parts are widely separated by the time gravitational expansion takes over. The results is a homogeneous and isotropic universe as the initial conditions for the expansion predicted by general relativity.: 202  == History == === Precursors === In the early days of general relativity, Albert Einstein introduced the cosmological constant to allow a static solution, which was a three-dimensional sphere with a uniform density of matter. Later, Willem de Sitter found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty. It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe. In 1965, Erast Gliner proposed a unique assumption regarding the early Universe's pressure in the context of the Einstein–Friedmann equations. According to his idea, the pressure was negatively proportional to the energy density. This relationship between pressure and energy density served as the initial theoretical prediction of dark energy. In the early 1970s, Yakov Zeldovich noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds. In the Soviet Union, this and other considerations led Vladimir Belinski and Isaak Khalatnikov to analyze the chaotic BKL singularity in general relativity. Misner's Mixmaster universe attempted to use this chaotic behavior to solve the cosmological problems, with limited success. ==== False vacuum ==== In the late 1970s, Sidney Coleman applied the instanton techniques developed by Alexander Polyakov and collaborators to study the fate of the false vacuum in quantum field theory. Like a metastable phase in statistical mechanics—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology. The universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum. ==== The Causal Universe of Brout Englert and Gunzig ==== In 1978 and 1979, Robert Brout, François Englert and Edgard Gunzig suggested that the universe could originate from a fluctuation of Minkowski space which would be followed by a period in which the geometry would resemble De Sitter space. This initial period would then evolve into the standard expanding universe. They noted that their proposal makes the universe causal, as there are neither particle nor event horizons in their model. ==== Starobinsky inflation ==== In the Soviet Union, Alexei Starobinsky noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to the Einstein–Hilbert action and a form of f(R) modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era. This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action S = 1 2 ∫ d 4 x ( R + R 2 6 M 2 ) {\displaystyle S={\frac {1}{2}}\int d^{4}x\left(R+{\frac {R^{2}}{6M^{2}}}\right)} which corresponds to the potential V ( ϕ ) = Λ 4 ( 1 − e − 2 / 3 ϕ / M p 2 ) 2 {\displaystyle \quad V(\phi )=\Lambda ^{4}\left(1-e^{-{\sqrt {2/3}}\phi /M_{p}^{2}}\right)^{2}} in the Einstein frame. This results in the observables: n s = 1 − 2 N , r = 12 N 2 . {\displaystyle n_{s}=1-{\frac {2}{N}},\qquad r={\frac {12}{N^{2}}}.} ==== Monopole problem ==== In 1978, Zeldovich noted the magnetic monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980, Alan Guth realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details. === Early inflationary models === Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles; it was Guth who coined the term "inflation". At the same time, Starobinsky argued that quantum corrections to gravity would replace the supposed initial singularity of the Universe with an exponentially expanding de Sitter phase. In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the particle horizon and perhaps solve the horizon problem, while Katsuhiko Sato suggested that an exponential expansion could eliminate domain walls (another kind of exotic relic). In 1981, Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the magnetic monopole abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions. Guth proposed that as the early universe cooled, it was trapped in a false vacuum with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a metastable state (it was supercooled), which it could only decay out of through the process of bubble nucleation via quantum tunneling. Bubbles of true vacuum spontaneously form in the sea of false vacuum and rapidly begin expanding at the speed of light. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate. ... Kazanas (1980) called this phase of the early Universe "de Sitter's phase". The name "inflation" was given by Guth (1981). ... Guth himself did not refer to work of Kazanas until he published a book on the subject, under the title The Inflationary Universe: The quest for a new theory of cosmic origin (1997), where he apologizes for not having referenced the work of Kazanas and of others, related to inflation. === Slow-roll inflation === The bubble collision problem was solved by Andrei Linde and independently by Andreas Albrecht and Paul Steinhardt in a model named new inflation or slow-roll inflation (Guth's model then became known as old inflation). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a scalar field rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur. === Effects of asymmetries === Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by Viatcheslav Mukhanov and G. V. Chibisov in analyzing Starobinsky's similar model. In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at Cambridge University. The fluctuations were calculated by four groups working separately over the course of the workshop: Stephen Hawking; Starobinsky; Alan Guth and So-Young Pi; and James Bardeen, Paul Steinhardt and Michael Turner. == Observational status == Inflation is a mechanism for realizing the cosmological principle, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the cosmic microwave background made by the Planck spacecraft. This analysis shows that the Universe is flat to within ⁠ 1 /2⁠ percent, and that it is homogeneous and isotropic to one part in 100,000. Inflation predicts that the structures visible in the Universe today formed through the gravitational collapse of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a nearly-scale-invariant Gaussian random field is very specific and has only two free parameters. One is the amplitude of the spectrum and the spectral index, which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe). The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without fine-tuning, predict a tensor to scalar ratio near 0.1 . Inflation predicts that the observed perturbations should be in thermal equilibrium with each other (these are called adiabatic or isentropic perturbations). This structure for the perturbations has been confirmed by the Planck spacecraft, WMAP spacecraft and other cosmic microwave background (CMB) experiments, and galaxy surveys, especially the ongoing Sloan Digital Sky Survey. These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The spectral index, ns is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that ns is between 0.92 and 0.98 . This is the range that is possible without fine-tuning of the parameters related to energy. From Planck data it can be inferred that ns=0.968 ± 0.006, and a tensor to scalar ratio that is less than 0.11 . These are considered an important confirmation of the theory of inflation. Various inflation theories have been proposed that make radically different predictions, but they generally have much more fine-tuning than should be necessary. As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics. Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature. However, the third-year data revealed that the effect was a statistical anomaly. Another effect remarked upon since the first cosmic microwave background satellite, the Cosmic Background Explorer is that the amplitude of the quadrupole moment of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to quantum corrections or new physics, foreground contamination, or even publication bias. An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the polarization of the background radiation could provide evidence of the gravitational radiation produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (1015~1016 GeV) is correct. In March 2014, the BICEP2 team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio r was between 0.15 and 0.27 (rejecting the null hypothesis; r is expected to be 0 in the absence of inflation). However, on 19 June 2014, lowered confidence in confirming the findings was reported; on 19 September 2014, a further reduction in confidence was reported and, on 30 January 2015, even less confidence yet was reported. By 2018, additional data suggested, with 95% confidence, that r {\displaystyle r} is 0.06 or lower: Consistent with the null hypothesis, but still also consistent with many remaining models of inflation. Other potentially corroborating measurements are expected from the Planck spacecraft, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with radio sources on Earth and in the galaxy will be too great. == Theoretical status == In Guth's early proposal, it was thought that the inflaton was the Higgs field, the field that explains the mass of the elementary particles. It is now believed by some that the inflaton cannot be the Higgs field. One problem of this identification is the current tension with experimental data at the electroweak scale,. Other models of inflation relied on the properties of Grand Unified Theories. === Fine-tuning problem === One of the most severe challenges for inflation arises from the need for fine tuning. In new inflation, the slow-roll conditions must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton potential must be flat (compared to the large vacuum energy) and that the inflaton particles must have a small mass. New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through perturbation theory. Linde proposed a theory known as chaotic inflation in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually any universe that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy. However, in his model, the inflaton field necessarily takes values larger than one Planck unit: For this reason, these are often called large field models and the competing new inflation models are called small field models. In this situation, the predictions of effective field theory are thought to be invalid, as renormalization should cause large corrections that could prevent inflation. This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models. While inflation depends on quantum field theory (and the semiclassical approximation to quantum gravity) in an important way, it has not been completely reconciled with these theories. Brandenberger commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around 1016 GeV or 10−3 times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): The energy density given by the scalar potential is down by 10−12 compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification. === Eternal inflation === In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time. All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model. Paul Steinhardt, one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983. He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year, Alexander Vilenkin showed that eternal inflation is generic. Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards, expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions. In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating do not. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible. Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that the multiverse is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model, later became one of its most vocal critics for this reason. === Initial conditions === Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever. Other proposals attempt to describe the ex nihilo creation of the Universe based on quantum cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally. Guth described the inflationary universe as the "ultimate free lunch": new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy and the arrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a quantum fluctuation. Don Page was an outspoken critic of inflation because of this anomaly. He stressed that the thermodynamic arrow of time necessitates low entropy initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase. Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle–Hawking initial state. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe.: 223–225  However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations. Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable. === Hybrid inflation === Another kind of inflation, called hybrid inflation, is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state. In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation. === Relation to dark energy === Dark energy is broadly similar to inflation and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower, 10−12 GeV, roughly 27 orders of magnitude less than the scale of inflation. === Inflation and string cosmology === The discovery of flux compactifications opened the way for reconciling inflation and string theory. Brane inflation suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the Dirac–Born–Infeld action, is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism. === Inflation and loop quantum gravity === When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back. == Alternatives and adjuncts == Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation. === Big bounce === The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang. The flatness and horizon problems are naturally solved in the Einstein–Cartan–Sciama–Kibble theory of gravity, without needing an exotic form of matter or free parameters. This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era. === Ekpyrotic and cyclic models === The ekpyrotic and cyclic models are also considered adjuncts to inflation. These models solve the horizon problem through an expanding epoch well before the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The Universe passes through the Big Crunch and emerges in a hot Big Bang phase. In this sense they are reminiscent of Richard Chace Tolman's oscillatory universe; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the magnetic monopole problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years. === String gas cosmology === String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up or compactified (see also Kaluza–Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to quantum gravity. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called string gas cosmology, was proposed by Robert Brandenberger and Cumrun Vafa. This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other, which became known as Brandenberger–Vafa mechanism. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will generically intersect (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. The original model did not "solve the entropy and flatness problems of standard cosmology", although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario. === Varying c === Cosmological models employing a variable speed of light have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constant c, denoting the speed of light in vacuum, is greater in the early universe than its present value, effectively increasing the particle horizon at the time of decoupling sufficiently to account for the observed isotropy of the CMB. == Criticisms == Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support. In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding, "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology." As pointed out by Roger Penrose from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved: "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after." The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that "inflation isn't falsifiable, it's falsified. ... BICEP did a wonderful service by bringing all the inflation-ists out of their shell, and giving them a black eye." A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable. Paul Steinhardt, one of the founding fathers of inflationary cosmology, calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them: "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of 10 to the googol power!" Together with Anna Ijjas and Abraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the Planck satellite. Counter-arguments were presented by Alan Guth, David Kaiser, and Yasunori Nomura and by Linde, saying that "cosmic inflation is on a stronger footing than ever before". == See also == == Notes == == References == == Sources == == External links == Was Cosmic Inflation The 'Bang' Of The Big Bang?, by Alan Guth, 1997 Andrew R Liddle (1999). "An introduction to cosmological inflation". p. 260. arXiv:astro-ph/9901124. update 2004 by Andrew Liddle Covi, Laura (2003). "Status of observational cosmology and inflation". p. 67. arXiv:hep-ph/0309238. Lyth, David H. (2003). "Which is the best inflation model?". p. 260. arXiv:hep-th/0311040. The Growth of Inflation Symmetry, December 2004 Guth's logbook showing the original idea WMAP Bolsters Case for Cosmic Inflation, March 2006 NASA March 2006 WMAP press release Archived 22 November 2013 at the Wayback Machine Max Tegmark. Our Mathematical Universe (2014), "Chapter 5: Inflation"
Wikipedia/Inflation_theory
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0); and an exact form is a differential form, α, that is the exterior derivative of another differential form β, i.e. α = dβ. Thus, an exact form is in the image of d, and a closed form is in the kernel of d (also known as null space). For an exact form α, α = dβ for some differential form β of degree one less than that of α. The form β is called a "potential form" or "primitive" for α. Since the exterior derivative of a closed form is zero, β is not unique, but can be modified by the addition of any closed form of degree one less than that of α. Because d2 = 0, every exact form is necessarily closed. The question of whether every closed form is exact depends on the topology of the domain of interest. On a contractible domain, every closed form is exact by the Poincaré lemma. More general questions of this kind on an arbitrary differentiable manifold are the subject of de Rham cohomology, which allows one to obtain purely topological information using differential methods. == Examples == A simple example of a form that is closed but not exact is the 1-form d θ {\displaystyle d\theta } given by the derivative of argument on the punctured plane R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} . Since θ {\displaystyle \theta } is not actually a function (see the next paragraph) d θ {\displaystyle d\theta } is not an exact form. Still, d θ {\displaystyle d\theta } has vanishing derivative and is therefore closed. Note that the argument θ {\displaystyle \theta } is only defined up to an integer multiple of 2 π {\displaystyle 2\pi } since a single point p {\displaystyle p} can be assigned different arguments r {\displaystyle r} , r + 2 π {\displaystyle r+2\pi } , etc. We can assign arguments in a locally consistent manner around p {\displaystyle p} , but not in a globally consistent manner. This is because if we trace a loop from p {\displaystyle p} counterclockwise around the origin and back to p {\displaystyle p} , the argument increases by 2 π {\displaystyle 2\pi } . Generally, the argument θ {\displaystyle \theta } changes by ∮ S 1 d θ {\displaystyle \oint _{S^{1}}d\theta } over a counter-clockwise oriented loop S 1 {\displaystyle S^{1}} . Even though the argument θ {\displaystyle \theta } is not technically a function, the different local definitions of θ {\displaystyle \theta } at a point p {\displaystyle p} differ from one another by constants. Since the derivative at p {\displaystyle p} only uses local data, and since functions that differ by a constant have the same derivative, the argument has a globally well-defined derivative " d θ {\displaystyle d\theta } ". The upshot is that d θ {\displaystyle d\theta } is a one-form on R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} that is not actually the derivative of any well-defined function θ {\displaystyle \theta } . We say that d θ {\displaystyle d\theta } is not exact. Explicitly, d θ {\displaystyle d\theta } is given as: d θ = − y d x + x d y x 2 + y 2 , {\displaystyle d\theta ={\frac {-y\,dx+x\,dy}{x^{2}+y^{2}}},} which by inspection has derivative zero. Notice that if we restrict the domain to the right half-plane, we can write d θ = d ( tan − 1 ⁡ ( y / x ) ) {\displaystyle d\theta =d\left(\tan ^{-1}(y/x)\right)} , but the angle function θ = tan − 1 ⁡ ( y / x ) {\displaystyle \theta =\tan ^{-1}(y/x)} is neither smooth nor continuous over R 2 ∖ { 0 } {\displaystyle \mathbb {R} ^{2}\smallsetminus \{0\}} (as is any choice of angle function). Because d θ {\displaystyle d\theta } has vanishing derivative, we say that it is closed. On the other hand, for the one-form α = − y d x + x d y , {\displaystyle \alpha =-y\,dx+x\,dy,} d α ≠ 0 {\displaystyle d\alpha \neq 0} . Thus α {\displaystyle \alpha } is not even closed, never mind exact. The form d θ {\displaystyle d\theta } generates the de Rham cohomology group H d R 1 ( R 2 ∖ { 0 } ) ≅ R , {\displaystyle H_{dR}^{1}(\mathbb {R} ^{2}\smallsetminus \{0\})\cong \mathbb {R} ,} meaning that any closed form ω {\displaystyle \omega } is the sum of an exact form d f {\displaystyle df} and a multiple of d θ {\displaystyle d\theta } : ω = d f + k d θ {\displaystyle \omega =df+k\ d\theta } , where k = 1 2 π ∮ S 1 ω {\textstyle k={\frac {1}{2\pi }}\oint _{S^{1}}\omega } accounts for a non-trivial contour integral around the origin, which is the only obstruction to a closed form on the punctured plane (locally the derivative of a potential function) being the derivative of a globally defined function. == Examples in low dimensions == Differential forms in R 2 {\displaystyle \mathbb {R} ^{2}} and R 3 {\displaystyle \mathbb {R} ^{3}} were well known in the mathematical physics of the nineteenth century. In the plane, 0-forms are just functions, and 2-forms are functions times the basic area element d x ∧ d y {\displaystyle dx\wedge dy} , so that it is the 1-forms α = f ( x , y ) d x + g ( x , y ) d y {\displaystyle \alpha =f(x,y)\,dx+g(x,y)\,dy} that are of real interest. The formula for the exterior derivative d {\displaystyle d} here is d α = ( g x − f y ) d x ∧ d y {\displaystyle d\alpha =(g_{x}-f_{y})\,dx\wedge dy} where the subscripts denote partial derivatives. Therefore the condition for α {\displaystyle \alpha } to be closed is f y = g x . {\displaystyle f_{y}=g_{x}.} In this case if h ( x , y ) {\displaystyle h(x,y)} is a function then d h = h x d x + h y d y . {\displaystyle dh=h_{x}\,dx+h_{y}\,dy.} The implication from 'exact' to 'closed' is then a consequence of the symmetry of second derivatives, with respect to x {\displaystyle x} and y {\displaystyle y} . The gradient theorem asserts that a 1-form is exact if and only if the line integral of the form depends only on the endpoints of the curve, or equivalently, if the integral around any smooth closed curve is zero. === Vector field analogies === On a Riemannian manifold, or more generally a pseudo-Riemannian manifold, k-forms correspond to k-vector fields (by duality via the metric), so there is a notion of a vector field corresponding to a closed or exact form. In 3 dimensions, an exact vector field (thought of as a 1-form) is called a conservative vector field, meaning that it is the derivative (gradient) of a 0-form (smooth scalar field), called the scalar potential. A closed vector field (thought of as a 1-form) is one whose derivative (curl) vanishes, and is called an irrotational vector field. Thinking of a vector field as a 2-form instead, a closed vector field is one whose derivative (divergence) vanishes, and is called an incompressible flow (sometimes solenoidal vector field). The term incompressible is used because a non-zero divergence corresponds to the presence of sources and sinks in analogy with a fluid. The concepts of conservative and incompressible vector fields generalize to n dimensions, because gradient and divergence generalize to n dimensions; curl is defined only in three dimensions, thus the concept of irrotational vector field does not generalize in this way. == Poincaré lemma == The Poincaré lemma states that if B is an open ball in Rn, any closed p-form ω defined on B is exact, for any integer p with 1 ≤ p ≤ n. More generally, the lemma states that on a contractible open subset of a manifold (e.g., R n {\displaystyle \mathbb {R} ^{n}} ), a closed p-form, p > 0, is exact. == Formulation as cohomology == When the difference of two closed forms is an exact form, they are said to be cohomologous to each other. That is, if ζ and η are closed forms, and one can find some β such that ζ − η = d β {\displaystyle \zeta -\eta =d\beta } then one says that ζ and η are cohomologous to each other. Exact forms are sometimes said to be cohomologous to zero. The set of all forms cohomologous to a given form (and thus to each other) is called a de Rham cohomology class; the general study of such classes is known as cohomology. It makes no real sense to ask whether a 0-form (smooth function) is exact, since d increases degree by 1; but the clues from topology suggest that only the zero function should be called "exact". The cohomology classes are identified with locally constant functions. Using contracting homotopies similar to the one used in the proof of the Poincaré lemma, it can be shown that de Rham cohomology is homotopy-invariant. == Relevance to thermodynamics == Consider a thermodynamic system whose equilibrium states are specified by n {\displaystyle n} thermodynamic variables, x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} . The first law of thermodynamics can be stated as follows: In any process that results in an infinitesimal change of state where the internal energy of the system changes by an amount d U ( x 1 , x 2 , … , x n ) , {\displaystyle dU(x_{1},x_{2},\ldots ,x_{n}),} and an amount of work d W ( x 1 , x 2 , … , x n ) {\displaystyle dW(x_{1},x_{2},\ldots ,x_{n})} is done on the system, one must also supply an amount of heat d U − d W . {\displaystyle dU-dW.} The second law of thermodynamics is an empirical law of nature which says that there is no thermodynamic system for which d U = d W {\displaystyle dU=dW} in every circumstance, or in mathematical terms that, the differential form d U − d W {\displaystyle dU-dW} is not closed. Caratheodory's theorem further states that there exists an integrating denominator T {\displaystyle T} such that d S ≡ d U − d W T {\displaystyle dS\equiv {\frac {dU-dW}{T}}} is a closed 1-form. The integrating denominator T {\displaystyle T} is the temperature, and the state function S ( x 1 , x 2 , … , x n ) {\displaystyle S(x_{1},x_{2},\ldots ,x_{n})} is the equilibrium entropy. == Application in electrodynamics == In electrodynamics, the case of the magnetic field B → ( r ) {\displaystyle {\vec {B}}(\mathbf {r} )} produced by a stationary electrical current is important. There one deals with the vector potential A → ( r ) {\displaystyle {\vec {A}}(\mathbf {r} )} of this field. This case corresponds to k = 2, and the defining region is the full R 3 {\displaystyle \mathbb {R} ^{3}} . The current-density vector is j → {\displaystyle {\vec {j}}} . It corresponds to the current two-form I := j 1 ( x 1 , x 2 , x 3 ) d x 2 ∧ d x 3 + j 2 ( x 1 , x 2 , x 3 ) d x 3 ∧ d x 1 + j 3 ( x 1 , x 2 , x 3 ) d x 1 ∧ d x 2 . {\displaystyle \mathbf {I} :=j_{1}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{2}\wedge {\rm {d}}x_{3}+j_{2}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{3}\wedge {\rm {d}}x_{1}+j_{3}(x_{1},x_{2},x_{3})\,{\rm {d}}x_{1}\wedge {\rm {d}}x_{2}.} For the magnetic field B → {\displaystyle {\vec {B}}} one has analogous results: it corresponds to the induction two-form Φ B := B 1 d x 2 ∧ d x 3 + ⋯ {\displaystyle \Phi _{B}:=B_{1}{\rm {d}}x_{2}\wedge {\rm {d}}x_{3}+\cdots } , and can be derived from the vector potential A → {\displaystyle {\vec {A}}} , or the corresponding one-form A {\displaystyle \mathbf {A} } , B → = curl ⁡ A → = { ∂ A 3 ∂ x 2 − ∂ A 2 ∂ x 3 , ∂ A 1 ∂ x 3 − ∂ A 3 ∂ x 1 , ∂ A 2 ∂ x 1 − ∂ A 1 ∂ x 2 } , or Φ B = d A . {\displaystyle {\vec {B}}=\operatorname {curl} {\vec {A}}=\left\{{\frac {\partial A_{3}}{\partial x_{2}}}-{\frac {\partial A_{2}}{\partial x_{3}}},{\frac {\partial A_{1}}{\partial x_{3}}}-{\frac {\partial A_{3}}{\partial x_{1}}},{\frac {\partial A_{2}}{\partial x_{1}}}-{\frac {\partial A_{1}}{\partial x_{2}}}\right\},{\text{ or }}\Phi _{B}={\rm {d}}\mathbf {A} .} Thereby the vector potential A → {\displaystyle {\vec {A}}} corresponds to the potential one-form A := A 1 d x 1 + A 2 d x 2 + A 3 d x 3 . {\displaystyle \mathbf {A} :=A_{1}\,{\rm {d}}x_{1}+A_{2}\,{\rm {d}}x_{2}+A_{3}\,{\rm {d}}x_{3}.} The closedness of the magnetic-induction two-form corresponds to the property of the magnetic field that it is source-free: div ⁡ B → ≡ 0 {\displaystyle \operatorname {div} {\vec {B}}\equiv 0} , i.e., that there are no magnetic monopoles. In a special gauge, div ⁡ A → = ! 0 {\displaystyle \operatorname {div} {\vec {A}}{~{\stackrel {!}{=}}~}0} , this implies for i = 1, 2, 3 A i ( r → ) = ∫ μ 0 j i ( r → ′ ) d x 1 ′ d x 2 ′ d x 3 ′ 4 π | r → − r → ′ | . {\displaystyle A_{i}({\vec {r}})=\int {\frac {\mu _{0}j_{i}\left({\vec {r}}'\right)\,\,dx_{1}'\,dx_{2}'\,dx_{3}'}{4\pi |{\vec {r}}-{\vec {r}}'|}}\,.} (Here μ 0 {\displaystyle \mu _{0}} is the magnetic constant.) This equation is remarkable, because it corresponds completely to a well-known formula for the electrical field E → {\displaystyle {\vec {E}}} , namely for the electrostatic Coulomb potential φ ( x 1 , x 2 , x 3 ) {\displaystyle \varphi (x_{1},x_{2},x_{3})} of a charge density ρ ( x 1 , x 2 , x 3 ) {\displaystyle \rho (x_{1},x_{2},x_{3})} . At this place one can already guess that E → {\displaystyle {\vec {E}}} and B → , {\displaystyle {\vec {B}},} ρ {\displaystyle \rho } and j → , {\displaystyle {\vec {j}},} φ {\displaystyle \varphi } and A → {\displaystyle {\vec {A}}} can be unified to quantities with six rsp. four nontrivial components, which is the basis of the relativistic invariance of the Maxwell equations. If the condition of stationarity is left, on the left-hand side of the above-mentioned equation one must add, in the equations for A i {\displaystyle A_{i}} , to the three space coordinates, as a fourth variable also the time t, whereas on the right-hand side, in j i ′ {\displaystyle j_{i}'} , the so-called "retarded time", t ′ := t − | r → − r → ′ | c {\displaystyle t':=t-{\frac {|{\vec {r}}-{\vec {r}}'|}{c}}} , must be used, i.e. it is added to the argument of the current-density. Finally, as before, one integrates over the three primed space coordinates. (As usual c is the vacuum velocity of light.) == Notes == == Citations == == References == Chandrasekhar, S. (1939). An Introduction to the Study of Stellar Structure. Dover. Flanders, Harley (1989) [1963]. Differential forms with applications to the physical sciences. New York: Dover Publications. ISBN 978-0-486-66169-8.. Warner, Frank W. (1983), Foundations of differentiable manifolds and Lie groups, Graduate Texts in Mathematics, vol. 94, Springer, ISBN 0-387-90894-3 Napier, Terrence; Ramachandran, Mohan (2011), An introduction to Riemann surfaces, Birkhäuser, ISBN 978-0-8176-4693-6 Singer, I. M.; Thorpe, J. A. (1976), Lecture Notes on Elementary Topology and Geometry, University of Bangalore Press, ISBN 0721114784
Wikipedia/Exact_differential_form
Marine energy, also known as ocean energy, ocean power, or marine and hydrokinetic energy, refers to energy harnessed from waves, tides, salinity gradients, and temperature differences in the ocean. The movement of water in the world's oceans stores vast amounts of kinetic energy, which can be converted into electricity to power homes, transportation, and industries. Marine energy includes wave power, which is derived from surface waves, and tidal power, which is obtained from the kinetic energy of moving water. Offshore wind power, however, is not considered marine energy because it is generated from wind, even if the wind turbines are located over water. The oceans have a tremendous amount of energy and are close to many if not most concentrated populations. Ocean energy has the potential of providing a substantial amount of new renewable energy around the world. While marine energy is a sustainable alternative to fossil fuels, its development can impact marine ecosystems, wildlife, and the physical environment. Potential effects include habitat disruption, noise pollution, and electromagnetic fields from subsea cables, which may require mitigation strategies such as fish-friendly turbine designs and environmental impact assessments. Government policies, economic incentives, and regulatory frameworks contribute significantly to advancing marine energy, with countries like the UK, Canada, and South Korea leading in tidal and wave energy projects. == Global potential == The global potential for marine energy is significant, with estimates suggesting that 20,000 to 80,000 terawatt-hours per year (TWh/y) of electricity could be generated from ocean temperature differences, salinity gradients, tides, currents, waves, and swells. Indonesia, as an archipelagic country that is three quarters ocean, has 49 GW recognized potential ocean energy and has 727 GW theoretical potential ocean energy. == Forms of ocean energy == The oceans are a vast, largely untapped source of energy, including surface waves, fluid flow, salinity gradients, and thermal differences. Marine and Hydrokinetic (MHK) or marine energy development in U.S. and international waters includes projects using the following devices: Wave power converters in open coastal areas with significant waves; Tidal turbines placed in coastal and estuarine areas; In-stream turbines in fast-moving rivers; Ocean current turbines in areas of strong marine currents; Ocean thermal energy converters in deep tropical waters. === Marine current power === Strong ocean currents are driven by temperature, wind, salinity, bathymetry, and the rotation of the Earth. The Sun acts as the primary driving force, causing winds and temperature differences. Because there are only small fluctuations in current speed and stream location with no changes in direction, ocean currents may be suitable locations for deploying energy extraction devices such as turbines. Ocean currents are instrumental in determining the climate in many regions around the world. While little is known about the effects of removing ocean current energy, the impacts of removing current energy on the farfield environment may be a significant environmental concern. The typical turbine issues with blade strike, entanglement of marine organisms, and acoustic effects still exists; however, these may be magnified due to the presence of more diverse populations of marine organisms using ocean currents for migration purposes. Locations can be further offshore and therefore require longer power cables that could affect the marine environment with electromagnetic output. === Osmotic power === At the mouth of rivers where fresh water mixes with salt water, energy associated with the salinity gradient can be harnessed using pressure-retarded reverse osmosis process and associated conversion technologies. Another system is based on using freshwater upwelling through a turbine immersed in seawater, and one involving electrochemical reactions is also in development. Significant research took place from 1975 to 1985 and gave various results regarding the economy of PRO and RED plants. Small-scale investigations into salinity power production take place in other countries like Japan, Israel, and the United States. In Europe the research is concentrated in Norway and the Netherlands, in both places small pilots are tested. Salinity gradient energy is the energy available from the difference in salt concentration between freshwater with saltwater. This energy source is not easy to understand, as it is not directly occurring in nature in the form of heat, waterfalls, wind, waves, or radiation. === Ocean thermal energy === Water typically varies in temperature from the surface warmed by direct sunlight to greater depths where sunlight cannot penetrate. This differential is greatest in tropical waters, making this technology most applicable in water locations. A fluid is often vaporized to drive a turbine that may generate electricity or produce desalinized water. Systems may be either open-cycle, closed-cycle, or hybrid. === Tidal power === The energy from moving masses of water – a popular form of hydroelectric power generation. Tidal power generation comprises three main forms, namely tidal stream power, tidal barrage power, and dynamic tidal power. === Wave power === Solar energy from the Sun creates temperature differentials that result in wind. The interaction between wind and the surface of water creates waves, which are larger when there is a greater distance for them to build up. Wave energy potential is greatest between 30° and 60° latitude in both hemispheres on the west coast because of the global direction of wind. When evaluating wave energy as a technology type, it is important to distinguish between the four most common approaches: point absorber buoys, surface attenuators, oscillating water columns, and overtopping devices. The wave energy sector is reaching a significant milestone in the development of the industry, with positive steps towards commercial viability being taken. The more advanced device developers are now progressing beyond single unit demonstration devices and are proceeding to array development and multi-megawatt projects. The backing of major utility companies is now manifesting itself through partnerships within the development process, unlocking further investment and, in some cases, international co-operation. At a simplified level, wave energy technology can be located near-shore and offshore. Wave energy converters can also be designed for operation in specific water depth conditions: deep water, intermediate water or shallow water. The fundamental device design will be dependent on the location of the device and the intended resource characteristics. == Environmental effects == Marine energy, harnessed from renewable sources such as waves, tides, and ocean currents, is widely regarded as a sustainable alternative to fossil fuels. However, similar to other energy technologies, marine energy may have environmental impacts that need to be carefully assessed. These effects can be broadly categorized into impacts on marine ecosystems, wildlife, and the physical environment. Impacts on Marine Ecosystems The deployment of marine energy infrastructure can alter local ecosystems by modifying water flow, sediment transport, and habitat structures. For instance, tidal barrages, which block the natural flow of water, can lead to changes in salinity levels and sediment deposition in estuaries. Such alterations can disrupt benthic habitats, affecting species that rely on these environments for survival. Research has shown that tidal energy projects can result in localized habitat loss, particularly for species sensitive to changes in sediment composition and water flow. Wave energy converters (WECs) can also influence marine ecosystems. While they may create artificial reefs that attract certain species, they can simultaneously displace others, leading to competition for resources. In some cases, these structures have been observed to enhance biodiversity, but the overall impact depends on the specific design and location of the devices. The ecological trade-offs associated with WECs highlight the importance of careful planning and monitoring to balance energy production with environmental conservation. Effects on Marine Wildlife Marine energy technologies pose risks to marine wildlife, particularly through collisions with underwater turbines, noise pollution, and electromagnetic fields (EMFs) generated by subsea cables. For example, tidal turbines, which operate in high-flow environments, can pose a threat to fish and marine mammals that may collide with rotating blades. While the risk of collision is generally considered low, it can be significant for slow-moving or migratory species, necessitating the development of fish-friendly turbine designs. Noise pollution is another concern associated with marine energy installations. The construction and operation of devices can generate underwater noise, which may disrupt marine life. Cetaceans, such as whales and dolphins, rely heavily on sound for communication, navigation, and foraging. Prolonged exposure to noise can lead to behavioral changes, increased stress levels, and even habitat abandonment. Mitigation measures, such as noise-reduction technologies and strategic placement of devices, are required to minimize these impacts. Electromagnetic fields (EMFs) from subsea power cables can also affect marine species, particularly those sensitive to electromagnetic stimuli, such as sharks and rays. Physical and Chemical Changes The installation of marine energy infrastructure can lead to physical changes in the marine environment, such as altered wave patterns and coastal erosion. For example, large-scale wave energy farms can reduce the amount of wave energy reaching the shore, which may impact coastal processes like sediment transport. In some cases, this could exacerbate coastal erosion, particularly in areas already vulnerable to such changes. Chemical impacts, such as the release of antifouling agents or other pollutants from marine energy devices, are another potential concern. While these impacts are generally minor compared to those associated with fossil fuel extraction, they still require careful management to minimize harm to marine ecosystems. Regular maintenance and the use of environmentally friendly materials can help mitigate these risks. Mitigation and Best Practices Governments and organizations have developed regulatory frameworks and best practices to address these environmental effects. Regulatory bodies typically require environmental impact assessments (EIAs) before deploying marine energy projects. These assessments help identify potential risks and guide mitigation strategies, such as the use of fish-friendly turbine designs, noise-reduction technologies, and strategic placement of devices to minimize ecological disruption. International organizations, such as the International Renewable Energy Agency (IRENA), have published guidelines for sustainable marine energy development. These guidelines emphasize the importance of stakeholder engagement, adaptive management, and long-term monitoring to ensure that marine energy projects are environmentally responsible. By adhering to these principles, the marine energy industry can balance the need for renewable energy with the protection of marine ecosystems and wildlife. == Policies, Economics, and Government Initiatives == The development of marine energy is heavily influenced by government policies, economic incentives, and regulatory frameworks. These factors play a critical role in fostering innovation, attracting investment, and ensuring the sustainable deployment of marine energy technologies. Economic Considerations Marine energy is still in the early stages of commercialization, and its economic viability depends on reducing costs and improving efficiency. The high capital expenditure (CapEx) and operational expenditure (OpEx) associated with marine energy projects have historically been barriers to widespread adoption. However, technological advancements, economies of scale, and government support are helping to drive down costs. For example, the levelized cost of energy (LCOE) for tidal and wave energy has decreased significantly in recent years, though it remains higher than that of more established renewable energy sources like wind and solar. Government subsidies, grants, and tax incentives are often used to offset the high initial costs of marine energy projects. These financial mechanisms are designed to encourage private sector investment and accelerate the deployment of marine energy technologies. Government Policies and Regulatory Frameworks Government policies significantly influence the development of marine energy. Many countries have implemented renewable energy targets, feed-in tariffs, and renewable portfolio standards (RPS) to promote the development of marine energy. For instance, the European Union has set ambitious renewable energy targets as part of its Green Deal, with marine energy identified as a key component of its strategy to achieve carbon neutrality by 2050. In the United Kingdom, the Marine Energy Programme has been instrumental in supporting the development of tidal and wave energy. The program provides funding for research and development (R&D), as well as demonstration projects. The UK government has also established the Contracts for Difference (CfD) scheme, which guarantees a fixed price for electricity generated from marine energy, providing long-term revenue certainty for developers. United States has implemented policies to support marine energy through the Department of Energy’s Water Power Technologies Office (WPTO). The WPTO funds R&D initiatives and provides grants for pilot projects. The Marine Renewable Energy Act has also been proposed to create a regulatory framework for the development of marine energy resources in U.S. waters. Case Studies United Kingdom: The UK is a global leader in marine energy, particularly tidal energy. The MeyGen tidal energy project in Scotland is one of the largest tidal stream projects in the world. Supported by government funding and private investment, the project has demonstrated the potential for large-scale tidal energy generation. The UK’s supportive policy environment, including the CfD scheme, has played a key role in the project’s success. Canada: Canada has significant marine energy resources, particularly in the Bay of Fundy, which has some of the highest tidal ranges in the world. The Fundy Ocean Research Center for Energy (FORCE) in Nova Scotia serves as a test site for tidal energy technologies. The Canadian government has provided funding for FORCE and established regulatory frameworks to facilitate the deployment of marine energy projects. South Korea: South Korea has made substantial investments in marine energy as part of its renewable energy strategy. The Sihwa Lake Tidal Power Station is the world’s largest tidal power plant, with a capacity of 254 MW. The project was developed with significant government support and is a representative example of large-scale tidal energy deployment. France: France has a long history of tidal energy development, dating back to the Rance Tidal Power Station, which was commissioned in 1966 and remains one of the oldest and most successful tidal power plants in the world. The French government continues to support marine energy through R&D funding and policy initiatives aimed at expanding renewable energy capacity. == See also == Energy harvesting Marine current power Tidal power Wave power Ocean thermal energy conversion Osmotic power Renewable energy Renewable energy commercialization == References == == Further reading == Omar Ellabban, Haitham Abu-Rub, Frede Blaabjerg: Renewable energy resources: Current status, future prospects and their enabling technology. Renewable and Sustainable Energy Reviews 39, (2014), 748–764, doi:10.1016/j.rser.2014.07.113. == External links == The Ocean Energy Systems European Ocean Energy Association The European Marine Energy Centre (EMEC) Ocean Energy Council SuperGen UK Centre for Marine Energy Research Portal and Repository for Information on Marine Renewable Energy Marine Energy Projects Database Tethys - Environmental Effects of Wind and Marine Renewable Energy Tethys Engineering - Technical information on marine energy Marine and Hydrokinetic Data Repository
Wikipedia/Marine_energy
Electric potential energy is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may be said to have electric potential energy by virtue of either its own electric charge or its relative position to other electrically charged objects. The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields. == Definition == The electric potential energy of a system of point charges is defined as the work required to assemble this system of charges by bringing them close together, as in the system from an infinite distance. Alternatively, the electric potential energy of any given charge or system of charges is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration. The electrostatic potential energy can also be defined from the electric potential as follows: == Units == The SI unit of electric potential energy is joule (named after the English physicist James Prescott Joule). In the CGS system the erg is the unit of energy, being equal to 10−7 Joules. Also electronvolts may be used, 1 eV = 1.602×10−19 Joules. == Electrostatic potential energy of one point charge == === One point charge q in the presence of another point charge Q === The electrostatic potential energy, UE, of one point charge q at position r in the presence of a point charge Q, taking an infinite separation between the charges as the reference position, is: U E ( r ) = 1 4 π ε 0 q Q r {\displaystyle U_{E}(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ}{r}}} where r is the distance between the point charges q and Q, and q and Q are the charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula. === One point charge q in the presence of n point charges Qi === The electrostatic potential energy, UE, of one point charge q in the presence of n point charges Qi, taking an infinite separation between the charges as the reference position, is: U E ( r ) = q 4 π ε 0 ∑ i = 1 n Q i r i , {\displaystyle U_{E}(r)={\frac {q}{4\pi \varepsilon _{0}}}\sum _{i=1}^{n}{\frac {Q_{i}}{r_{i}}},} where ri is the distance between the point charges q and Qi, and q and Qi are the assigned values of the charges. == Electrostatic potential energy stored in a system of point charges == The electrostatic potential energy UE stored in a system of N charges q1, q2, …, qN at positions r1, r2, …, rN respectively, is: where, for each i value, V(ri) is the electrostatic potential due to all point charges except the one at ri, and is equal to: V ( r i ) = k e ∑ j ≠ i j = 1 N q j r i j , {\displaystyle V(\mathbf {r} _{i})=k_{e}\sum _{\stackrel {j=1}{j\neq i}}^{N}{\frac {q_{j}}{r_{ij}}},} where rij is the distance between qi and qj. === Energy stored in a system of one point charge === The electrostatic potential energy of a system containing only one point charge is zero, as there are no other sources of electrostatic force against which an external agent must do work in moving the point charge from infinity to its final location. A common question arises concerning the interaction of a point charge with its own electrostatic potential. Since this interaction doesn't act to move the point charge itself, it doesn't contribute to the stored energy of the system. === Energy stored in a system of two point charges === Consider bringing a point charge, q, into its final position near a point charge, Q1. The electric potential V(r) due to Q1 is V ( r ) = k e Q 1 r {\displaystyle V(\mathbf {r} )=k_{e}{\frac {Q_{1}}{r}}} Hence we obtain, the electrostatic potential energy of q in the potential of Q1 as U E = 1 4 π ε 0 q Q 1 r 1 {\displaystyle U_{E}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {qQ_{1}}{r_{1}}}} where r1 is the separation between the two point charges. === Energy stored in a system of three point charges === The electrostatic potential energy of a system of three charges should not be confused with the electrostatic potential energy of Q1 due to two charges Q2 and Q3, because the latter doesn't include the electrostatic potential energy of the system of the two charges Q2 and Q3. The electrostatic potential energy stored in the system of three charges is: U E = 1 4 π ε 0 [ Q 1 Q 2 r 12 + Q 1 Q 3 r 13 + Q 2 Q 3 r 23 ] {\displaystyle U_{\mathrm {E} }={\frac {1}{4\pi \varepsilon _{0}}}\left[{\frac {Q_{1}Q_{2}}{r_{12}}}+{\frac {Q_{1}Q_{3}}{r_{13}}}+{\frac {Q_{2}Q_{3}}{r_{23}}}\right]} == Energy stored in an electrostatic field distribution in vacuum == The energy density, or energy per unit volume, d U d V {\textstyle {\frac {dU}{dV}}} , of the electrostatic field of a continuous charge distribution is: u e = d U d V = 1 2 ε 0 | E | 2 . {\displaystyle u_{e}={\frac {dU}{dV}}={\frac {1}{2}}\varepsilon _{0}\left|{\mathbf {E} }\right|^{2}.} == Energy stored in electronic elements == Some elements in a circuit can convert energy from one form to another. For example, a resistor converts electrical energy to heat. This is known as the Joule effect. A capacitor stores it in its electric field. The total electrostatic potential energy stored in a capacitor is given by U E = 1 2 Q V = 1 2 C V 2 = Q 2 2 C {\displaystyle U_{E}={\frac {1}{2}}QV={\frac {1}{2}}CV^{2}={\frac {Q^{2}}{2C}}} where C is the capacitance, V is the electric potential difference, and Q the charge stored in the capacitor. The total electrostatic potential energy may also be expressed in terms of the electric field in the form U E = 1 2 ∫ V E ⋅ D d V {\displaystyle U_{E}={\frac {1}{2}}\int _{V}\mathrm {E} \cdot \mathrm {D} \,dV} where D {\displaystyle \mathrm {D} } is the electric displacement field within a dielectric material and integration is over the entire volume of the dielectric. The total electrostatic potential energy stored within a charged dielectric may also be expressed in terms of a continuous volume charge, ρ {\displaystyle \rho } , U E = 1 2 ∫ V ρ Φ d V {\displaystyle U_{E}={\frac {1}{2}}\int _{V}\rho \Phi \,dV} where integration is over the entire volume of the dielectric. These latter two expressions are valid only for cases when the smallest increment of charge is zero ( d q → 0 {\displaystyle dq\to 0} ) such as dielectrics in the presence of metallic electrodes or dielectrics containing many charges. Note that a virtual experiment based on the energy transfer between capacitor plates reveals that an additional term should be taken into account when dealing with semiconductors for instance. While this extra energy cancels when dealing with insulators, the derivation predicts that it cannot be ignored as it may exceed the polarization energy. == Notes == == References == == External links == Media related to Electric potential energy at Wikimedia Commons
Wikipedia/Electric_potential_energy
An intermolecular force (IMF; also secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles (e.g. atoms or ions). Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics. The first reference to the nature of microscopic forces is found in Alexis Clairaut's work Théorie de la figure de la Terre, published in Paris in 1743. Other scientists who have contributed to the investigation of microscopic forces include: Laplace, Gauss, Maxwell, Boltzmann and Pauling. Attractive intermolecular forces are categorized into the following types: Hydrogen bonding Ion–dipole forces and ion–induced dipole force Cation–π, σ–π and π–π bonding Van der Waals forces – Keesom force, Debye force, and London dispersion force Cation–cation bonding Salt bridge (protein and supramolecular) Information on intermolecular forces is obtained by macroscopic measurements of properties like viscosity, pressure, volume, temperature (PVT) data. The link to microscopic aspects is given by virial coefficients and intermolecular pair potentials, such as the Mie potential, Buckingham potential or Lennard-Jones potential. In the broadest sense, it can be understood as such interactions between any particles (molecules, atoms, ions and molecular ions) in which the formation of chemical (that is, ionic, covalent or metallic) bonds does not occur. In other words, these interactions are significantly weaker than covalent ones and do not lead to a significant restructuring of the electronic structure of the interacting particles. (This is only partially true. For example, all enzymatic and catalytic reactions begin with a weak intermolecular interaction between a substrate and an enzyme or a molecule with a catalyst, but several such weak interactions with the required spatial configuration of the active center of the enzyme lead to significant restructuring changes the energy state of molecules or substrate, which ultimately leads to the breaking of some and the formation of other covalent chemical bonds. Strictly speaking, all enzymatic reactions begin with intermolecular interactions between the substrate and the enzyme, therefore the importance of these interactions is especially great in biochemistry and molecular biology, and is the basis of enzymology). == Hydrogen bonding == A hydrogen bond refers to the attraction between a hydrogen atom that is covalently bonded to an element with high electronegativity, usually nitrogen, oxygen, or fluorine, and another highly electronegative atom. The hydrogen bond is often described as a strong electrostatic interaction. However, it also has some features of covalent bonding: it is directional, stronger than a van der Waals force interaction, produces interatomic distances shorter than the sum of their van der Waals radii, and usually involves a limited number of interaction partners, which can be interpreted as a kind of valence. The number of hydrogen bonds formed between molecules is equal to the number of active pairs. The molecule which donates its hydrogen is termed the donor molecule, while the molecule containing lone pair participating in H bonding is termed the acceptor molecule. The number of active pairs is equal to the common number between number of hydrogens the donor has and the number of lone pairs the acceptor has. Though both are not depicted in the diagram, water molecules have four active bonds. The oxygen atom’s two lone pairs interact with a hydrogen each, forming two additional hydrogen bonds, and the second hydrogen atom also interacts with a neighbouring oxygen. Intermolecular hydrogen bonding is responsible for the high boiling point of water (100 °C) compared to the other group 16 hydrides, which have little capability to hydrogen bond. Intramolecular hydrogen bonding is partly responsible for the secondary, tertiary, and quaternary structures of proteins and nucleic acids. It also plays an important role in the structure of polymers, both synthetic and natural. == Salt bridge == The attraction between cationic and anionic sites is a noncovalent, or intermolecular interaction which is usually referred to as ion pairing or salt bridge. It is essentially due to electrostatic forces, although in aqueous medium the association is driven by entropy and often even endothermic. Most salts form crystals with characteristic distances between the ions; in contrast to many other noncovalent interactions, salt bridges are not directional and show in the solid state usually contact determined only by the van der Waals radii of the ions. Inorganic as well as organic ions display in water at moderate ionic strength I similar salt bridge as association ΔG values around 5 to 6 kJ/mol for a 1:1 combination of anion and cation, almost independent of the nature (size, polarizability, etc.) of the ions. The ΔG values are additive and approximately a linear function of the charges, the interaction of e.g. a doubly charged phosphate anion with a single charged ammonium cation accounts for about 2x5 = 10 kJ/mol. The ΔG values depend on the ionic strength I of the solution, as described by the Debye-Hückel equation, at zero ionic strength one observes ΔG = 8 kJ/mol. == Dipole–dipole and similar interactions == Dipole–dipole interactions (or Keesom interactions) are electrostatic interactions between molecules which have permanent dipoles. This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved. These interactions tend to align the molecules to increase attraction (reducing potential energy). An example of a dipole–dipole interaction can be seen in hydrogen chloride (HCl): the positive end of a polar molecule will attract the negative end of the other molecule and influence its position. Polar molecules have a net attraction between them. Examples of polar molecules include hydrogen chloride (HCl) and chloroform (CHCl3). H δ + − Cl δ − ⋯ H δ + − Cl δ − {\displaystyle {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}\cdots {\overset {\color {Red}\delta +}{{\ce {H}}}}-{\overset {\color {Red}\delta -}{{\ce {Cl}}}}} Often molecules contain dipolar groups of atoms, but have no overall dipole moment on the molecule as a whole. This occurs if there is symmetry within the molecule that causes the dipoles to cancel each other out. This occurs in molecules such as tetrachloromethane and carbon dioxide. The dipole–dipole interaction between two individual atoms is usually zero, since atoms rarely carry a permanent dipole. The Keesom interaction is a van der Waals force. It is discussed further in the section "Van der Waals forces". === Ion–dipole and ion–induced dipole forces === Ion–dipole and ion–induced dipole forces are similar to dipole–dipole and dipole–induced dipole interactions but involve ions, instead of only polar and non-polar molecules. Ion–dipole and ion–induced dipole forces are stronger than dipole–dipole interactions because the charge of any ion is much greater than the charge of a dipole moment. Ion–dipole bonding is stronger than hydrogen bonding. An ion–dipole force consists of an ion and a polar molecule interacting. They align so that the positive and negative groups are next to one another, allowing maximum attraction. An important example of this interaction is hydration of ions in water which give rise to hydration enthalpy. The polar water molecules surround themselves around ions in water and the energy released during the process is known as hydration enthalpy. The interaction has its immense importance in justifying the stability of various ions (like Cu2+) in water. An ion–induced dipole force consists of an ion and a non-polar molecule interacting. Like a dipole–induced dipole force, the charge of the ion causes distortion of the electron cloud on the non-polar molecule. == Van der Waals forces == The van der Waals forces arise from interaction between uncharged atoms or molecules, leading not only to such phenomena as the cohesion of condensed phases and physical absorption of gases, but also to a universal force of attraction between macroscopic bodies. === Keesom force (permanent dipole – permanent dipole) === The first contribution to van der Waals forces is due to electrostatic interactions between rotating permanent dipoles, quadrupoles (all molecules with symmetry lower than cubic), and multipoles. It is termed the Keesom interaction, named after Willem Hendrik Keesom. These forces originate from the attraction between permanent dipoles (dipolar molecules) and are temperature dependent. They consist of attractive interactions between dipoles that are ensemble averaged over different rotational orientations of the dipoles. It is assumed that the molecules are constantly rotating and never get locked into place. This is a good assumption, but at some point molecules do get locked into place. The energy of a Keesom interaction depends on the inverse sixth power of the distance, unlike the interaction energy of two spatially fixed dipoles, which depends on the inverse third power of the distance. The Keesom interaction can only occur among molecules that possess permanent dipole moments, i.e., two polar molecules. Also Keesom interactions are very weak van der Waals interactions and do not occur in aqueous solutions that contain electrolytes. The angle averaged interaction is given by the following equation: − d 1 2 d 2 2 24 π 2 ε 0 2 ε r 2 k B T r 6 = V , {\displaystyle {\frac {-d_{1}^{2}d_{2}^{2}}{24\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}k_{\text{B}}Tr^{6}}}=V,} where d = electric dipole moment, ε 0 {\displaystyle \varepsilon _{0}} = permittivity of free space, ε r {\displaystyle \varepsilon _{r}} = dielectric constant of surrounding material, T = temperature, k B {\displaystyle k_{\text{B}}} = Boltzmann constant, and r = distance between molecules. === Debye force (permanent dipoles–induced dipoles) === The second contribution is the induction (also termed polarization) or Debye force, arising from interactions between rotating permanent dipoles and from the polarizability of atoms and molecules (induced dipoles). These induced dipoles occur when one molecule with a permanent dipole repels another molecule's electrons. A molecule with permanent dipole can induce a dipole in a similar neighboring molecule and cause mutual attraction. Debye forces cannot occur between atoms. The forces between induced and permanent dipoles are not as temperature dependent as Keesom interactions because the induced dipole is free to shift and rotate around the polar molecule. The Debye induction effects and Keesom orientation effects are termed polar interactions. The induced dipole forces appear from the induction (also termed polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced (by the former di/multi-pole) 31 on another. This interaction is called the Debye force, named after Peter J. W. Debye. One example of an induction interaction between permanent dipole and induced dipole is the interaction between HCl and Ar. In this system, Ar experiences a dipole as its electrons are attracted (to the H side of HCl) or repelled (from the Cl side) by HCl. The angle averaged interaction is given by the following equation: − d 1 2 α 2 16 π 2 ε 0 2 ε r 2 r 6 = V , {\displaystyle {\frac {-d_{1}^{2}\alpha _{2}}{16\pi ^{2}\varepsilon _{0}^{2}\varepsilon _{r}^{2}r^{6}}}=V,} where α 2 {\displaystyle \alpha _{2}} = polarizability. This kind of interaction can be expected between any polar molecule and non-polar/symmetrical molecule. The induction-interaction force is far weaker than dipole–dipole interaction, but stronger than the London dispersion force. === London dispersion force (fluctuating dipole–induced dipole interaction) === The third and dominant contribution is the dispersion or London force (fluctuating dipole–induced dipole), which arises due to the non-zero instantaneous dipole moments of all atoms and molecules. Such polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in non-polar molecules. Thus, London interactions are caused by random fluctuations of electron density in an electron cloud. An atom with a large number of electrons will have a greater associated London force than an atom with fewer electrons. The dispersion (London) force is the most important component because all materials are polarizable, whereas Keesom and Debye forces require permanent dipoles. The London interaction is universal and is present in atom-atom interactions as well. For various reasons, London interactions (dispersion) have been considered relevant for interactions between macroscopic bodies in condensed systems. Hamaker developed the theory of van der Waals between macroscopic bodies in 1937 and showed that the additivity of these interactions renders them considerably more long-range. == Relative strength of forces == This comparison is approximate. The actual relative strengths will vary depending on the molecules involved. For instance, the presence of water creates competing interactions that greatly weaken the strength of both ionic and hydrogen bonds. We may consider that for static systems, Ionic bonding and covalent bonding will always be stronger than intermolecular forces in any given substance. But it is not so for big moving systems like enzyme molecules interacting with substrate molecules. Here the numerous intramolecular (most often - hydrogen bonds) bonds form an active intermediate state where the intermolecular bonds cause some of the covalent bond to be broken, while the others are formed, in this way enabling the thousands of enzymatic reactions, so important for living organisms. == Effect on the behavior of gases == Intermolecular forces are repulsive at short distances and attractive at long distances (see the Lennard-Jones potential). In a gas, the repulsive force chiefly has the effect of keeping two molecules from occupying the same volume. This gives a real gas a tendency to occupy a larger volume than an ideal gas at the same temperature and pressure. The attractive force draws molecules closer together and gives a real gas a tendency to occupy a smaller volume than an ideal gas. Which interaction is more important depends on temperature and pressure (see compressibility factor). In a gas, the distances between molecules are generally large, so intermolecular forces have only a small effect. The attractive force is not overcome by the repulsive force, but by the thermal energy of the molecules. Temperature is the measure of thermal energy, so increasing temperature reduces the influence of the attractive force. In contrast, the influence of the repulsive force is essentially unaffected by temperature. When a gas is compressed to increase its density, the influence of the attractive force increases. If the gas is made sufficiently dense, the attractions can become large enough to overcome the tendency of thermal motion to cause the molecules to disperse. Then the gas can condense to form a solid or liquid, i.e., a condensed phase. Lower temperature favors the formation of a condensed phase. In a condensed phase, there is very nearly a balance between the attractive and repulsive forces. == Quantum mechanical theories == Intermolecular forces observed between atoms and molecules can be described phenomenologically as occurring between permanent and instantaneous dipoles, as outlined above. Alternatively, one may seek a fundamental, unifying theory that is able to explain the various types of interactions such as hydrogen bonding, van der Waals force and dipole–dipole interactions. Typically, this is done by applying the ideas of quantum mechanics to molecules, and Rayleigh–Schrödinger perturbation theory has been especially effective in this regard. When applied to existing quantum chemistry methods, such a quantum mechanical explanation of intermolecular interactions provides an array of approximate methods that can be used to analyze intermolecular interactions. One of the most helpful methods to visualize this kind of intermolecular interactions, that we can find in quantum chemistry, is the non-covalent interaction index, which is based on the electron density of the system. London dispersion forces play a big role with this. Concerning electron density topology, recent methods based on electron density gradient methods have emerged recently, notably with the development of IBSI (Intrinsic Bond Strength Index), relying on the IGM (Independent Gradient Model) methodology. == See also == == References ==
Wikipedia/Intermolecular_forces
In physics and chemistry, ionization energy (IE) is the minimum energy required to remove the most loosely bound electron of an isolated gaseous atom, positive ion, or molecule. The first ionization energy is quantitatively expressed as X(g) + energy ⟶ X+(g) + e− where X is any atom or molecule, X+ is the resultant ion when the original atom was stripped of a single electron, and e− is the removed electron. Ionization energy is positive for neutral atoms, meaning that the ionization is an endothermic process. Roughly speaking, the closer the outermost electrons are to the nucleus of the atom, the higher the atom's ionization energy. In physics, ionization energy (IE) is usually expressed in electronvolts (eV) or joules (J). In chemistry, it is expressed as the energy to ionize a mole of atoms or molecules, usually as kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Comparison of ionization energies of atoms in the periodic table reveals two periodic trends which follow the rules of Coulombic attraction: Ionization energy generally increases from left to right within a given period (that is, row). Ionization energy generally decreases from top to bottom in a given group (that is, column). The latter trend results from the outer electron shell being progressively farther from the nucleus, with the addition of one inner shell per row as one moves down the column. The nth ionization energy refers to the amount of energy required to remove the most loosely bound electron from the species having a positive charge of (n − 1). For example, the first three ionization energies are defined as follows: 1st ionization energy is the energy that enables the reaction X ⟶ X+ + e− 2nd ionization energy is the energy that enables the reaction X+ ⟶ X2+ + e− 3rd ionization energy is the energy that enables the reaction X2+ ⟶ X3+ + e− The most notable influences that determine ionization energy include: Electron configuration: This accounts for most elements' IE, as all of their chemical and physical characteristics can be ascertained just by determining their respective electron configuration (EC). Nuclear charge: If the nuclear charge (atomic number) is greater, the electrons are held more tightly by the nucleus and hence the ionization energy will be greater (leading to the mentioned trend 1 within a given period). Number of electron shells: If the size of the atom is greater due to the presence of more shells, the electrons are held less tightly by the nucleus and the ionization energy will be smaller. Effective nuclear charge (Zeff): If the magnitude of electron shielding and penetration are greater, the electrons are held less tightly by the nucleus, the Zeff of the electron and the ionization energy is smaller. Stability: An atom having a more stable electronic configuration has a reduced tendency to lose electrons and consequently has a higher ionization energy. Minor influences include: Relativistic effects: Heavier elements (especially those whose atomic number is greater than about 70) are affected by these as their electrons are approaching the speed of light. They therefore have smaller atomic radii and higher ionization energies. Lanthanide and actinide contraction (and scandide contraction): The shrinking of the elements affects the ionization energy, as the net charge of the nucleus is more strongly felt. Electron pairing energies: Half-filled subshells usually result in higher ionization energies. The term ionization potential is an older and obsolete term for ionization energy, because the oldest method of measuring ionization energy was based on ionizing a sample and accelerating the electron removed using an electrostatic potential. == Determination of ionization energies == The ionization energy of atoms, denoted Ei, is measured by finding the minimal energy of light quanta (photons) or electrons accelerated to a known energy that will kick out the least bound atomic electrons. The measurement is performed in the gas phase on single atoms. While only noble gases occur as monatomic gases, other gases can be split into single atoms. Also, many solid elements can be heated and vaporized into single atoms. Monatomic vapor is contained in a previously evacuated tube that has two parallel electrodes connected to a voltage source. The ionizing excitation is introduced through the walls of the tube or produced within. When ultraviolet light is used, the wavelength is swept down the ultraviolet range. At a certain wavelength (λ) and frequency of light (ν=c/λ, where c is the speed of light), the light quanta, whose energy is proportional to the frequency, will have energy high enough to dislodge the least bound electrons. These electrons will be attracted to the positive electrode, and the positive ions remaining after the photoionization will get attracted to the negatively charged electrode. These electrons and ions will establish a current through the tube. The ionization energy will be the energy of photons hνi (h is the Planck constant) that caused a steep rise in the current: Ei = hνi. When high-velocity electrons are used to ionize the atoms, they are produced by an electron gun inside a similar evacuated tube. The energy of the electron beam can be controlled by the acceleration voltages. The energy of these electrons that gives rise to a sharp onset of the current of ions and freed electrons through the tube will match the ionization energy of the atoms. == Atoms: values and trends == Generally, the (N+1)th ionization energy of a particular element is larger than the Nth ionization energy (it may also be noted that the ionization energy of an anion is generally less than that of cations and neutral atom for the same element). When the next ionization energy involves removing an electron from the same electron shell, the increase in ionization energy is primarily due to the increased net charge of the ion from which the electron is being removed. Electrons removed from more highly charged ions experience greater forces of electrostatic attraction; thus, their removal requires more energy. In addition, when the next ionization energy involves removing an electron from a lower electron shell, the greatly decreased distance between the nucleus and the electron also increases both the electrostatic force and the distance over which that force must be overcome to remove the electron. Both of these factors further increase the ionization energy. Some values for elements of the third period are given in the following table: Large jumps in the successive molar ionization energies occur when passing noble gas configurations. For example, as can be seen in the table above, the first two molar ionization energies of magnesium (stripping the two 3s electrons from a magnesium atom) are much smaller than the third, which requires stripping off a 2p electron from the neon configuration of Mg2+. That 2p electron is much closer to the nucleus than the 3s electrons removed previously. Ionization energy is also a periodic trend within the periodic table. Moving left to right within a period, or upward within a group, the first ionization energy generally increases, with exceptions such as aluminium and sulfur in the table above. As the nuclear charge of the nucleus increases across the period, the electrostatic attraction increases between electrons and protons, hence the atomic radius decreases, and the electron cloud comes closer to the nucleus because the electrons, especially the outermost one, are held more tightly by the higher effective nuclear charge. On moving downward within a given group, the electrons are held in higher-energy shells with higher principal quantum number n, further from the nucleus and therefore are more loosely bound so that the ionization energy decreases. The effective nuclear charge increases only slowly so that its effect is outweighed by the increase in n. === Exceptions in ionization energies === There are exceptions to the general trend of rising ionization energies within a period. For example, the value decreases from beryllium ( 4Be: 9.3 eV) to boron ( 5B: 8.3 eV), and from nitrogen ( 7N: 14.5 eV) to oxygen ( 8O: 13.6 eV). These dips can be explained in terms of electron configurations. Boron has its last electron in a 2p orbital, which has its electron density further away from the nucleus on average than the 2s electrons in the same shell. The 2s electrons then shield the 2p electron from the nucleus to some extent, and it is easier to remove the 2p electron from boron than to remove a 2s electron from beryllium, resulting in a lower ionization energy for B. In oxygen, the last electron shares a doubly occupied p-orbital with an electron of opposing spin. The two electrons in the same orbital are closer together on average than two electrons in different orbitals, so that they shield each other from the nucleus more effectively and it is easier to remove one electron, resulting in a lower ionization energy. Furthermore, after every noble gas element, the ionization energy drastically drops. This occurs because the outer electron in the alkali metals requires a much lower amount of energy to be removed from the atom than the inner shells. This also gives rise to low electronegativity values for the alkali metals. The trends and exceptions are summarized in the following subsections: ==== Ionization energy decreases when ==== Transitioning to a new period: an alkali metal easily loses one electron to leave an octet or pseudo-noble gas configuration, so those elements have only small values for IE. Moving from the s-block to the p-block: a p-orbital loses an electron more easily. An example is beryllium to boron, with electron configuration 1s2 2s2 2p1. The 2s electrons shield the higher-energy 2p electron from the nucleus, making it slightly easier to remove. This also happens from magnesium to aluminium. Occupying a p-subshell with its first electron with spin opposed to the other electrons: such as in nitrogen ( 7N: 14.5 eV) to oxygen ( 8O: 13.6 eV), as well as phosphorus ( 15P: 10.48 eV) to sulfur ( 16S: 10.36 eV). The reason for this is because oxygen, sulfur and selenium all have dipping ionization energies because of shielding effects. However, this discontinues starting from tellurium where the shielding is too small to produce a dip. Moving from the d-block to the p-block: as in the case of zinc ( 30Zn: 9.4 eV) to gallium ( 31Ga: 6.0 eV) Special case: decrease from lead ( 82Pb: 7.42 eV) to bismuth ( 83Bi: 7.29 eV). This cannot be attributed to size (the difference is minimal: lead has a covalent radius of 146 pm whereas bismuth's is 148 pm). This is due to the spin-orbit splitting of the 6p shell (lead is removing an electron from the stabilised 6p1/2 level, but bismuth is removing one from the destabilised 6p3/2 level). Predicted ionization energies show a much greater decrease from flerovium to moscovium, one row further down the periodic table and with much larger spin-orbit effects. Special case: decrease from radium ( 88Ra: 5.27 eV) to actinium ( 89Ac: 5.17 eV), which is a switch from an s to a d orbital. However the analogous switch from barium ( 56Ba: 5.2 eV) to lanthanum ( 57La: 5.6 eV) does not show a downward change. Lutetium ( 71Lu) and lawrencium ( 103Lr) both have ionization energies lower than the previous elements. In both cases the last electron added starts a new subshell: 5d for Lu with electron configuration [Xe] 4f14 5d1 6s2, and 7p for Lr with configuration [Rn] 5f4 7s2 7p1. These dips in ionization energies for lutetium and especially lawrencium show that these elements belong in the d-block, and not lanthanum and actinium. ==== Ionization energy increases when ==== Reaching Group 18 noble gas elements: This is due to their complete electron subshells, so that these elements require large amounts of energy to remove one electron. Group 12: The elements here, zinc ( 30Zn: 9.4 eV), cadmium ( 48Cd: 9.0 eV) and mercury ( 80Hg: 10.4 eV) all record sudden rising IE values in contrast to their preceding elements: copper ( 29Cu: 7.7 eV), silver ( 47Ag: 7.6 eV) and gold ( 79Au: 9.2 eV), respectively. For mercury, it can be extrapolated that the relativistic stabilization of the 6s electrons increases the ionization energy, in addition to poor shielding by 4f electrons that increases the effective nuclear charge on the outer valence electrons. In addition, the closed-subshells electron configurations: [Ar] 3d10 4s2, [Kr] 4d105s2 and [Xe] 4f14 5d10 6s2 provide increased stability. Special case: shift from rhodium ( 45Rh: 7.5 eV) to palladium ( 46Pd: 8.3 eV). Unlike other Group 10 elements, palladium has a higher ionization energy than the preceding atom, due to its electron configuration. In contrast to nickel's [Ar] 3d8 4s2, and platinum's [Xe] 4f14 5d9 6s1, palladium's electron configuration is [Kr] 4d10 5s0 (even though the Madelung rule predicts [Kr] 4d8 5s2). Finally, silver's lower IE ( 47Ag: 7.6 eV) further accentuates the high value for palladium; the single added s electron is removed with a lower ionization energy than palladium, which emphasizes palladium's high IE (as shown in the above linear table values for IE) The IE of gadolinium ( 64Gd: 6.15 eV) is somewhat higher than both the preceding ( 62Sm: 5.64 eV), ( 63Eu: 5.67 eV) and following elements ( 65Tb: 5.86 eV), ( 66Dy: 5.94 eV). This anomaly is due to the fact that gadolinium valence d-subshell borrows 1 electron from the valence f-subshell. Now the valence subshell is the d-subshell, and due to the poor shielding of positive nuclear charge by electrons of the f-subshell, the electron of the valence d-subshell experiences a greater attraction to the nucleus, therefore increasing the energy required to remove the (outermost) valence electron. Moving into d-block elements: The elements Sc with a 3d1 electronic configuration has a higher IP ( 21Sc: 6.56 eV) than the preceding element ( 20Ca: 6.11 eV), contrary to the decreases on moving into s-block and p-block elements. The 4s and 3d electrons have similar shielding ability: the 3d orbital forms part of the n=3 shell whose average position is closer to the nucleus than the 4s orbital and the n=4 shell, but electrons in s orbitals experience greater penetration into the nucleus than electrons in d orbitals. So the mutual shielding of 3d and 4s electrons is weak, and the effective nuclear charge acting on the ionized electron is relatively large. Yttrium ( 39Y) similarly has a higher IP (6.22 eV) than 38Sr: 5.69 eV. Moving into f-block elements; The elements ( 57La: 5.18 eV) and ( 89Ac: 5.17 eV) have only very slightly lower IP's than their preceding elements ( 56Ba: 5.21 eV) and ( 88Ra: 5.18 eV), though their atoms are anomalies in that they add a d-electron rather than an f-electron. As can be seen in the above graph for ionization energies, the sharp rise in IE values from ( 55Cs: 3.89 eV) to ( 56Ba: 5.21 eV) is followed by a small increase (with some fluctuations) as the f-block proceeds from 56Ba to 70Yb. This is due to the lanthanide contraction (for lanthanides). This decrease in ionic radius is associated with an increase in ionization energy in turn increases, since the two properties correlate to each other. As for d-block elements, the electrons are added in an inner shell, so that no new shells are formed. The shape of the added orbitals prevents them from penetrating to the nucleus so that the electrons occupying them have less shielding capacity. ==== Ionization energy anomalies in groups ==== Ionization energy values tend to decrease on going to heavier elements within a group as shielding is provided by more electrons and overall, the valence shells experience a weaker attraction from the nucleus, attributed to the larger covalent radius which increase on going down a group Nonetheless, this is not always the case. As one exception, in Group 10 palladium ( 46Pd: 8.34 eV) has a higher ionization energy than nickel ( 28Ni: 7.64 eV), contrary to the general decrease for the elements from technetium 43Tc to xenon 54Xe. Such anomalies are summarized below: Group 1: Hydrogen's ionization energy is very high (at 13.59844 eV), compared to the alkali metals. This is due to its single electron (and hence, very small electron cloud), which is close to the nucleus. Likewise, since there are not any other electrons that may cause shielding, that single electron experiences the full net positive charge of the nucleus. Francium's ionization energy is higher than the precedent alkali metal, cesium. This is due to its (and radium's) small ionic radii owing to relativistic effects. Because of their large mass and size, this means that its electrons are traveling at extremely high speeds, which results in the electrons coming closer to the nucleus than expected, and they are consequently harder to remove (higher IE). Group 2: Radium's ionization energy is higher than its antecedent alkaline earth metal barium, like francium, which is also due to relativistic effects. The electrons, especially the 1s electrons, experience very high effective nuclear charges. To avoid falling into the nucleus, the 1s electrons must move at very high speeds, which causes the special relativistic corrections to be substantially higher than the approximate classical momenta. By the uncertainty principle, this causes a relativistic contraction of the 1s orbital (and other orbitals with electron density close to the nucleus, especially ns and np orbitals). Hence this causes a cascade of electron changes, which finally results in the outermost electron shells contracting and getting closer to the nucleus. Group 4: Hafnium's near similarity in IE with zirconium. The effects of the lanthanide contraction can still be felt after the lanthanides. It can be seen through the former's smaller atomic radius (which contradicts the observed periodic trend Archived 2018-10-11 at the Wayback Machine) at 159 pm (empirical value), which differs from the latter's 155 pm. This in turn makes its ionization energies increase by 18 kJ/mol−1. Titanium's IE is smaller than that of both hafnium and zirconium. Hafnium's ionization energy is similar to zirconium's due to lanthanide contraction. However, why zirconium's ionization energy is higher than the preceding elements' remains unclear; we cannot attribute it to atomic radius as it is higher for zirconium and hafnium by 15 pm. We also cannot invoke the condensed ionization energy, as it is more or less the same ([Ar] 3d2 4s2 for titanium, whereas [Kr] 4d2 5s2 for zirconium). Additionally, there are no half-filled nor fully filled orbitals we might compare. Hence, we can only invoke zirconium's full electron configuration, which is 1s22s22p63s23p63d104s24p64d25s2. The presence of a full 3d-block sublevel is tantamount to a higher shielding efficiency compared to the 4d-block elements (which are only two electrons). Group 5: akin to Group 4, niobium and tantalum are analogous to each other, due to their electron configuration and to the lanthanide contraction affecting the latter element. Ipso facto, their significant rise in IE compared to the foremost element in the group, vanadium, can be attributed due to their full d-block electrons, in addition to their electron configuration. Another intriguing notion is niobium's half-filled 5s orbital; due to repulsion and exchange energy (in other words the "costs" of putting an electron in a low-energy sublevel to completely fill it instead of putting the electron in a high-energy one) overcoming the energy gap between s- and d-(or f) block electrons, the EC does not follow the Madelung rule. Group 6: like its forerunners groups 4 and 5, group 6 also record high values when moving downward. Tungsten is once again similar to molybdenum due to their electron configurations. Likewise, it is also attributed to the full 3d-orbital in its electron configuration. Another reason is molybdenum's half filled 4d orbital due to electron pair energies violating the aufbau principle. Groups 7-12 6th period elements (rhenium, osmium, iridium, platinum, gold and mercury): All of these elements have extremely high ionization energies compared to the elements preceding them in their respective groups. The essence of this is due to the lanthanide contraction's influence on post lanthanides, in addition to the relativistic stabilization of the 6s orbital. Group 13: Gallium's IE is higher than aluminum's. This is once again due to d-orbitals, in addition to scandide contraction, providing weak shielding, and hence the effective nuclear charges are augmented. Thallium's IE, due to poor shielding of 4f electrons in addition to lanthanide contraction, causes its IE to be increased in contrast to its precursor indium. Group 14: Lead's unusually high ionization energy ( 82Pb: 7.42 eV) is, akin to that of group 13's thallium, a result of the full 5d and 4f subshells. The lanthanide contraction and the inefficient screening of the nucleus by the 4f electrons results in slightly higher ionization energy for lead than for tin ( 50Sn: 7.34 eV). == Bohr model for hydrogen atom == The ionization energy of the hydrogen atom (⁠ Z = 1 {\displaystyle Z=1} ⁠) can be evaluated in the Bohr model, which predicts that the atomic energy level n {\displaystyle n} has energy E = − 1 n 2 Z 2 e 2 2 a 0 = − Z 2 R H n 2 = − Z 2 × 13.6 e V n 2 {\displaystyle E=-{\frac {1}{n^{2}}}{\frac {Z^{2}e^{2}}{2a_{0}}}=-{\frac {Z^{2}R_{\text{H}}}{n^{2}}}=-{\frac {Z^{2}\times \mathrm {13.6\ eV} }{n^{2}}}} ⁠ R H {\displaystyle R_{\text{H}}} ⁠ is the Rydberg constant for the hydrogen atom. For hydrogen in the ground state Z = 1 {\displaystyle Z=1} and n = 1 {\displaystyle n=1} so that the energy of the atom before ionization is simply ⁠ E = − 13.6 e V {\displaystyle E=\mathrm {-13.6\ eV} } ⁠. After ionization, the energy is zero for a motionless electron infinitely far from the proton, so that the ionization energy is ⁠ I = E ( H + ) − E ( H ) = + 13.6 e V {\displaystyle I=E(\mathrm {H} ^{+})-E(\mathrm {H} )=\mathrm {+13.6\ eV} } ⁠. This agrees with the experimental value for the hydrogen atom. == Quantum-mechanical explanation == According to the more complete theory of quantum mechanics, the location of an electron is best described as a probability distribution within an electron cloud, i.e. atomic orbital. The energy can be calculated by integrating over this cloud. The cloud's underlying mathematical representation is the wavefunction, which is built from Slater determinants consisting of molecular spin orbitals. These are related by Pauli's exclusion principle to the antisymmetrized products of the atomic or molecular orbitals. There are two main ways in which ionization energy is calculated. In general, the computation for the Nth ionization energy requires calculating the energies of Z − N + 1 {\displaystyle Z-N+1} and Z − N {\displaystyle Z-N} electron systems. Calculating these energies exactly is not possible except for the simplest systems (i.e. hydrogen and hydrogen-like elements), primarily because of difficulties in integrating the electron correlation terms. Therefore, approximation methods are routinely employed, with different methods varying in complexity (computational time) and accuracy compared to empirical data. This has become a well-studied problem and is routinely done in computational chemistry. The second way of calculating ionization energies is mainly used at the lowest level of approximation, where the ionization energy is provided by Koopmans' theorem, which involves the highest occupied molecular orbital or "HOMO" and the lowest unoccupied molecular orbital or "LUMO", and states that the ionization energy of an atom or molecule is equal to the negative value of energy of the orbital from which the electron is ejected. This means that the ionization energy is equal to the negative of HOMO energy, which in a formal equation can be written as: I i = − E i {\displaystyle I_{i}=-E_{i}} == Molecules: vertical and adiabatic ionization energy == Ionization of molecules often leads to changes in molecular geometry, and two types of (first) ionization energy are defined – adiabatic and vertical. === Adiabatic ionization energy === The adiabatic ionization energy of a molecule is the minimum amount of energy required to remove an electron from a neutral molecule, i.e. the difference between the energy of the vibrational ground state of the neutral species (v" = 0 level) and that of the positive ion (v' = 0). The specific equilibrium geometry of each species does not affect this value. === Vertical ionization energy === Due to the possible changes in molecular geometry that may result from ionization, additional transitions may exist between the vibrational ground state of the neutral species and vibrational excited states of the positive ion. In other words, ionization is accompanied by vibrational excitation. The intensity of such transitions is explained by the Franck–Condon principle, which predicts that the most probable and intense transition corresponds to the vibrationally excited state of the positive ion that has the same geometry as the neutral molecule. This transition is referred to as the "vertical" ionization energy since it is represented by a completely vertical line on a potential energy diagram (see Figure). For a diatomic molecule, the geometry is defined by the length of a single bond. The removal of an electron from a bonding molecular orbital weakens the bond and increases the bond length. In Figure 1, the lower potential energy curve is for the neutral molecule and the upper surface is for the positive ion. Both curves plot the potential energy as a function of bond length. The horizontal lines correspond to vibrational levels with their associated vibrational wave functions. Since the ion has a weaker bond, it will have a longer bond length. This effect is represented by shifting the minimum of the potential energy curve to the right of the neutral species. The adiabatic ionization is the diagonal transition to the vibrational ground state of the ion. Vertical ionization may involve vibrational excitation of the ionic state and therefore requires greater energy. In many circumstances, the adiabatic ionization energy is often a more interesting physical quantity since it describes the difference in energy between the two potential energy surfaces. However, due to experimental limitations, the adiabatic ionization energy is often difficult to determine, whereas the vertical detachment energy is easily identifiable and measurable. == Analogs of ionization energy to other systems == While the term ionization energy is largely used only for gas-phase atomic, cationic, or molecular species, there are a number of analogous quantities that consider the amount of energy required to remove an electron from other physical systems. === Electron binding energy === Electron binding energy is a generic term for the minimum energy needed to remove an electron from a particular electron shell for an atom or ion, due to these negatively charged electrons being held in place by the electrostatic pull of the positively charged nucleus. For example, the electron binding energy for removing a 3p3/2 electron from the chloride ion is the minimum amount of energy required to remove an electron from the chlorine atom when it has a charge of −1. In this particular example, the electron binding energy has the same magnitude as the electron affinity for the neutral chlorine atom. In another example, the electron binding energy refers to the minimum amount of energy required to remove an electron from the dicarboxylate dianion −O2C(CH2)8CO−2. The graph to the right shows the binding energy for electrons in different shells in neutral atoms. The ionization energy is the lowest binding energy for a particular atom (although these are not all shown in the graph). === Solid surfaces: work function === Work function is the minimum amount of energy required to remove an electron from a solid surface, where the work function W for a given surface is defined by the difference W = − e ϕ − E F , {\displaystyle W=-e\phi -E_{\rm {F}},} where −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material. == Note == == See also == Rydberg equation, a calculation that could determine the ionization energies of hydrogen and hydrogen-like elements. This is further elaborated through this site. Electron affinity, a closely related concept describing the energy released by adding an electron to a neutral atom or molecule. Lattice energy, a measure of the energy released when ions are combined to make a compound. Electronegativity is a number that shares some similarities with ionization energy. Koopmans' theorem, regarding the predicted ionization energies in Hartree–Fock theory. Ditungsten tetra(hpp) has the lowest recorded ionization energy for a stable chemical compound. Bond-dissociation energy, the measure of the strength of a chemical bond calculated through cleaving by homolysis giving two radical fragments A and B and subsequent evaluation of the enthalpy change Bond energy, the average measure of a chemical bond's strength, calculated through the amount of heat needed to break all of the chemical bonds into individual atoms. == References == == Sources == Levine, Ira N. (1991). Quantum Chemistry. Prentice Hall. ISBN 978-0-205-12770-2.
Wikipedia/Ionization_energy
Concentrated solar power (CSP, also known as concentrating solar power, concentrated solar thermal) systems generate solar power by using mirrors or lenses to concentrate a large area of sunlight into a receiver. Electricity is generated when the concentrated light is converted to heat (solar thermal energy), which drives a heat engine (usually a steam turbine) connected to an electrical power generator or powers a thermochemical reaction. As of 2021, global installed capacity of concentrated solar power stood at 6.8 GW. As of 2023, the total was 8.1 GW, with the inclusion of three new CSP projects in construction in China and in Dubai in the UAE. The U.S.-based National Renewable Energy Laboratory (NREL), which maintains a global database of CSP plants, counts 6.6 GW of operational capacity and another 1.5 GW under construction. == Comparison between CSP and other electricity sources == As a thermal energy generating power station, CSP has more in common with thermal power stations such as coal, gas, or geothermal. A CSP plant can incorporate thermal energy storage, which stores energy either in the form of sensible heat or as latent heat (for example, using molten salt), which enables these plants to continue supplying electricity whenever it is needed, day or night. This makes CSP a dispatchable form of solar. Dispatchable renewable energy is particularly valuable in places where there is already a high penetration of photovoltaics (PV), such as California, because demand for electric power peaks near sunset just as PV capacity ramps down (a phenomenon referred to as duck curve). CSP is often compared to photovoltaic solar (PV) since they both use solar energy. While solar PV experienced huge growth during the 2010s due to falling prices, solar CSP growth has been slow due to technical difficulties and high prices. In 2017, CSP represented less than 2% of worldwide installed capacity of solar electricity plants. However, CSP can more easily store energy during the night, making it more competitive with dispatchable generators and baseload plants. The DEWA project in Dubai, under construction in 2019, held the world record for lowest CSP price in 2017 at US$73 per MWh for its 700 MW combined trough and tower project: 600 MW of trough, 100 MW of tower with 15 hours of thermal energy storage daily. Base-load CSP tariff in the extremely dry Atacama region of Chile reached below $50/MWh in 2017 auctions. == History == A legend has it that Archimedes used a "burning glass" to concentrate sunlight on the invading Roman fleet and repel them from Syracuse. In 1973 a Greek scientist, Dr. Ioannis Sakkas, curious about whether Archimedes could really have destroyed the Roman fleet in 212 BC, lined up nearly 60 Greek sailors, each holding an oblong mirror tipped to catch the sun's rays and direct them at a tar-covered plywood silhouette 49 m (160 ft) away. The ship caught fire after a few minutes; however, historians continue to doubt the Archimedes story. In 1866, Auguste Mouchout used a parabolic trough to produce steam for the first solar steam engine. The first patent for a solar collector was obtained by the Italian Alessandro Battaglia in Genoa, Italy, in 1886. Over the following years, invеntors such as John Ericsson and Frank Shuman developed concentrating solar-powered dеvices for irrigation, refrigеration, and locomоtion. In 1913 Shuman finished a 55 horsepower (41 kW) parabolic solar thermal energy station in Maadi, Egypt for irrigation. The first solar-power system using a mirror dish was built by Dr. R.H. Goddard, who was already well known for his research on liquid-fueled rockets and wrote an article in 1929 in which he asserted that all the previous obstacles had been addressed. Professor Giovanni Francia (1911–1980) designed and built the first concentrated-solar plant, which entered into operation in Sant'Ilario, near Genoa, Italy in 1968. This plant had the architecture of today's power tower plants, with a solar receiver in the center of a field of solar collectors. The plant was able to produce 1 MW with superheated steam at 100 bar and 500 °C. The 10 MW Solar One power tower was developed in Southern California in 1981. Solar One was converted into Solar Two in 1995, implementing a new design with a molten salt mixture (60% sodium nitrate, 40% potassium nitrate) as the receiver working fluid and as a storage medium. The molten salt approach proved effective, and Solar Two operated successfully until it was decommissioned in 1999. The parabolic-trough technology of the nearby Solar Energy Generating Systems (SEGS), begun in 1984, was more workable. The 354 MW SEGS was the largest solar power plant in the world until 2014. No commercial concentrated solar was constructed from 1990, when SEGS was completed, until 2006, when the Compact linear Fresnel reflector system at Liddell Power Station in Australia was built. Few other plants were built with this design, although the 5 MW Kimberlina Solar Thermal Energy Plant opened in 2009. In 2007, 75 MW Nevada Solar One was built, a trough design and the first large plant since SEGS. Between 2010 and 2013, Spain built over 40 parabolic trough systems, size constrained at no more than 50 MW by the support scheme. Where not bound in other countries, the manufacturers have adopted up to 200 MW size for a single unit, with a cost soft point around 125 MW for a single unit. Due to the success of Solar Two, a commercial power plant, called Solar Tres Power Tower, was built in Spain in 2011, later renamed Gemasolar Thermosolar Plant. Gemasolar's results paved the way for further plants of its type. Ivanpah Solar Power Facility was constructed at the same time but without thermal storage, using natural gas to preheat water each morning. Most concentrated solar power plants use the parabolic trough design, instead of the power tower or Fresnel systems. There have also been variations of parabolic trough systems like the integrated solar combined cycle (ISCC) which combines troughs and conventional fossil fuel heat systems. CSP was originally treated as a competitor to photovoltaics, and Ivanpah was built without energy storage, although Solar Two included several hours of thermal storage. By 2015, prices for photovoltaic plants had fallen and PV commercial power was selling for 1⁄3 of contemporary CSP contracts. However, increasingly, CSP was being bid with 3 to 12 hours of thermal energy storage, making CSP a dispatchable form of solar energy. As such, it is increasingly seen as competing with natural gas and PV with batteries for flexible, dispatchable power. == Current technology == CSP is used to produce electricity (sometimes called solar thermoelectricity, usually generated through steam). Concentrated solar technology systems use mirrors or lenses with tracking systems to focus a large area of sunlight onto a small area. The concentrated light is then used as heat or as a heat source for a conventional power plant (solar thermoelectricity). The solar concentrators used in CSP systems can often also be used to provide industrial process heating or cooling, such as in solar air conditioning. Concentrating technologies exist in four optical types, namely parabolic trough, dish, concentrating linear Fresnel reflector, and solar power tower. Parabolic trough and concentrating linear Fresnel reflectors are classified as linear focus collector types, while dish and solar tower are point focus types. Linear focus collectors achieve medium concentration factors (50 suns and over), and point focus collectors achieve high concentration factors (over 500 suns). Although simple, these solar concentrators are quite far from the theoretical maximum concentration. For example, the parabolic-trough concentration gives about 1⁄3 of the theoretical maximum for the design acceptance angle, that is, for the same overall tolerances for the system. Approaching the theoretical maximum may be achieved by using more elaborate concentrators based on nonimaging optics. Different types of concentrators produce different peak temperatures and correspondingly varying thermodynamic efficiencies due to differences in the way that they track the sun and focus light. New innovations in CSP technology are leading systems to become more and more cost-effective. In 2023, Australia’s national science agency CSIRO tested a CSP arrangement in which tiny ceramic particles fall through the beam of concentrated solar energy, the ceramic particles capable of storing a greater amount of heat than molten salt, while not requiring a container that would diminish heat transfer. === Parabolic trough === A parabolic trough consists of a linear parabolic reflector that concentrates light onto a receiver positioned along the reflector's focal line. The receiver is a tube positioned at the longitudinal focal line of the parabolic mirror and filled with a working fluid. The reflector follows the sun during the daylight hours by tracking along a single axis. A working fluid (e.g. molten salt) is heated to 150–350 °C (302–662 °F) as it flows through the receiver and is then used as a heat source for a power generation system. Trough systems are the most developed CSP technology. The Solar Energy Generating Systems (SEGS) plants in California, some of the longest-running in the world until their 2021 closure; Acciona's Nevada Solar One near Boulder City, Nevada; and Andasol, Europe's first commercial parabolic trough plant are representative, along with Plataforma Solar de Almería's SSPS-DCS test facilities in Spain. ==== Enclosed trough ==== The design encapsulates the solar thermal system within a greenhouse-like glasshouse. The glasshouse creates a protected environment to withstand the elements that can negatively impact reliability and efficiency of the solar thermal system. Lightweight curved solar-reflecting mirrors are suspended from the ceiling of the glasshouse by wires. A single-axis tracking system positions the mirrors to retrieve the optimal amount of sunlight. The mirrors concentrate the sunlight and focus it on a network of stationary steel pipes, also suspended from the glasshouse structure. Water is carried throughout the length of the pipe, which is boiled to generate steam when intense solar radiation is applied. Sheltering the mirrors from the wind allows them to achieve higher temperature rates and prevents dust from building up on the mirrors. GlassPoint Solar, the company that created the Enclosed Trough design, states its technology can produce heat for Enhanced Oil Recovery (EOR) for about $5 per 290 kWh (1,000,000 BTU) in sunny regions, compared to between $10 and $12 for other conventional solar thermal technologies. === Solar power tower === A solar power tower consists of an array of dual-axis tracking reflectors (heliostats) that concentrate sunlight on a central receiver atop a tower; the receiver contains a heat-transfer fluid, which can consist of water-steam or molten salt. Optically a solar power tower is the same as a circular Fresnel reflector. The working fluid in the receiver is heated to 500–1000 °C (773–1,273 K or 932–1,832 °F) and then used as a heat source for a power generation or energy storage system. An advantage of the solar tower is the reflectors can be adjusted instead of the whole tower. Power-tower development is less advanced than trough systems, but they offer higher efficiency and better energy storage capability. Beam down tower application is also feasible with heliostats to heat the working fluid. CSP with dual towers are also used to enhance the conversion efficiency by nearly 24%. The Solar Two in Daggett, California and the CESA-1 in Plataforma Solar de Almeria Almeria, Spain, are the most representative demonstration plants. The Planta Solar 10 (PS10) in Sanlucar la Mayor, Spain, is the first commercial utility-scale solar power tower in the world. The 377 MW Ivanpah Solar Power Facility, located in the Mojave Desert, was the largest CSP facility in the world, and uses three power towers. Ivanpah generated only 0.652 TWh (63%) of its energy from solar means, and the other 0.388 TWh (37%) was generated by burning natural gas. Supercritical carbon dioxide can be used instead of steam as heat-transfer fluid for increased electricity production efficiency. However, because of the high temperatures in arid areas where solar power is usually located, it is impossible to cool down carbon dioxide below its critical temperature in the compressor inlet. Therefore, supercritical carbon dioxide blends with higher critical temperatures are currently in development. === Fresnel reflectors === Fresnel reflectors are made of many thin, flat mirror strips to concentrate sunlight onto tubes through which working fluid is pumped. Flat mirrors allow more reflective surface in the same amount of space than a parabolic reflector, thus capturing more of the available sunlight, and they are much cheaper than parabolic reflectors. Fresnel reflectors can be used in various size CSPs. Fresnel reflectors are sometimes regarded as a technology with a worse output than other methods. The cost efficiency of this model is what causes some to use this instead of others with higher output ratings. Some new models of Fresnel reflectors with Ray Tracing capabilities have begun to be tested and have initially proved to yield higher output than the standard version. === Dish Stirling === A dish Stirling or dish engine system consists of a stand-alone parabolic reflector that concentrates light onto a receiver positioned at the reflector's focal point. The reflector tracks the Sun along two axes. The working fluid in the receiver is heated to 250–700 °C (482–1,292 °F) and then used by a Stirling engine to generate power. Parabolic-dish systems provide high solar-to-electric efficiency (between 31% and 32%), and their modular nature provides scalability. The Stirling Energy Systems (SES), United Sun Systems (USS) and Science Applications International Corporation (SAIC) dishes at UNLV, and Australian National University's Big Dish in Canberra, Australia are representative of this technology. A world record for solar to electric efficiency was set at 31.25% by SES dishes at the National Solar Thermal Test Facility (NSTTF) in New Mexico on 31 January 2008, a cold, bright day. According to its developer, Ripasso Energy, a Swedish firm, in 2015 its dish Stirling system tested in the Kalahari Desert in South Africa showed 34% efficiency. The SES installation in Maricopa, Phoenix, was the largest Stirling Dish power installation in the world until it was sold to United Sun Systems. Subsequently, larger parts of the installation have been moved to China to satisfy part of the large energy demand. == CSP with thermal energy storage == In a CSP plant that includes storage, the solar energy is first used to heat molten salt or synthetic oil, which is stored providing thermal/heat energy at high temperature in insulated tanks. Later the hot molten salt (or oil) is used in a steam generator to produce steam to generate electricity by steam turbo generator as required. Thus solar energy which is available in daylight only is used to generate electricity round the clock on demand as a load following power plant or solar peaker plant. The thermal storage capacity is indicated in hours of power generation at nameplate capacity. Unlike solar PV or CSP without storage, the power generation from solar thermal storage plants is dispatchable and self-sustainable, similar to coal/gas-fired power plants, but without the pollution. CSP with thermal energy storage plants can also be used as cogeneration plants to supply both electricity and process steam round the clock. As of December 2018, CSP with thermal energy storage plants' generation costs have ranged between 5 c € / kWh and 7 c € / kWh, depending on good to medium solar radiation received at a location. Unlike solar PV plants, CSP with thermal energy storage can also be used economically around the clock to produce process steam, replacing polluting fossil fuels. CSP plants can also be integrated with solar PV for better synergy. CSP with thermal storage systems are also available using Brayton cycle generators with air instead of steam for generating electricity and/or steam round the clock. These CSP plants are equipped with gas turbines to generate electricity. These are also small in capacity (<0.4 MW), with flexibility to install in few acres' area. Waste heat from the power plant can also be used for process steam generation and HVAC needs. In case land availability is not a limitation, any number of these modules can be installed, up to 1000 MW with RAMS and cost advantages since the per MW costs of these units are lower than those of larger size solar thermal stations. Centralized district heating round the clock is also feasible with concentrated solar thermal storage plants. == Deployment around the world == An early plant operated in Sicily at Adrano. The US deployment of CSP plants started by 1984 with the SEGS plants. The last SEGS plant was completed in 1990. From 1991 to 2005, no CSP plants were built anywhere in the world. Global installed CSP-capacity increased nearly tenfold between 2004 and 2013 and grew at an average of 50 percent per year during the last five of those years, as the number of countries with installed CSP was growing.: 51  In 2013, worldwide installed capacity increased by 36% or nearly 0.9 gigawatt (GW) to more than 3.4 GW. The record for capacity installed was reached in 2014, corresponding to 925 MW; however, it was followed by a decline caused by policy changes, the 2008 financial crisis, and the rapid decrease in price of the photovoltaic cells. Nevertheless, total capacity reached 6800 MW in 2021. Spain accounted for almost one third of the world's capacity, at 2,300 MW, despite no new capacity entering commercial operation in the country since 2013. The United States follows with 1,740 MW. Interest is also notable in North Africa and the Middle East, as well as China and India. There is a notable trend towards developing countries and regions with high solar radiation with several large plants under construction in 2017. The global market was initially dominated by parabolic-trough plants, which accounted for 90% of CSP plants at one point. Since about 2010, central power tower CSP has been favored in new plants due to its higher temperature operation – up to 565 °C (1,049 °F) vs. trough's maximum of 400 °C (752 °F) – which promises greater efficiency. Among the larger CSP projects are the Ivanpah Solar Power Facility (392 MW) in the United States, which uses solar power tower technology without thermal energy storage, and the Ouarzazate Solar Power Station in Morocco, which combines trough and tower technologies for a total of 510 MW with several hours of energy storage. == Cost == As early as 2011, the rapid decline of the price of photovoltaic systems led to projections that CSP would no longer be economically viable. As of 2020, the least expensive utility-scale concentrated solar power stations in the United States and worldwide were five times more expensive than utility-scale photovoltaic power stations, with a projected minimum price of 7 cents per kilowatt-hour for the most advanced CSP stations against record lows of 1.32 cents per kWh for utility-scale PV. This five-fold price difference has been maintained since 2018. Some hybrid PV-CSP plants in China have sought to operate profitably on the regional coal tariff of 5 US cents per kWh in 2021. Even though overall deployment of CSP remains limited in the early 2020s, the levelized cost of power from commercial scale plants has decreased since the 2010s. With a learning rate estimated at around 20% cost reduction of every doubling in capacity, the costs were approaching the upper end of the fossil fuel cost range at the beginning of the 2020s, driven by support schemes in several countries, including Spain, the US, Morocco, South Africa, China, and the UAE. === Energy storage === Some researchers expect CSP in combination with Thermal Energy Storage (TES) to become cheaper than PV with lithium batteries for storage durations above 4 hours per day, while others such as NREL expects that by 2030 PV with 10-hour storage lithium batteries will cost the same as PV with 4-hour storage used to cost in 2020, leaving CSP no cost advantage when it comes to energy storage. == Efficiency == The efficiency of a concentrating solar power system depends on the technology used to convert the solar power to electrical energy, the operating temperature of the receiver and the heat rejection, thermal losses in the system, and the presence or absence of other system losses; in addition to the conversion efficiency, the optical system which concentrates the sunlight will also add additional losses. Real-world systems claim a maximum thermal to electrical conversion efficiency of 23-35% for "power tower" type systems, operating at temperatures from 250 to 565 °C, with the higher efficiency number assuming a combined cycle turbine. Dish Stirling systems, operating at temperatures of 550-750 °C, claim an efficiency of about 30%, with the record solar-to-grid conversion efficiency of 31.25%, "the highest recorded efficiency for any field solar technology" set by Sandia in 2008, and a slightly slightly higher record of 31.4% solar-to-electric system efficiency reported by the U.S. Department of Energy. Due to variation in sun incidence during the day, the average conversion efficiency achieved is not equal to these maximum efficiencies, and the net annual solar-to-electricity efficiencies are 7-20% for pilot power tower systems, and 12-25% for demonstration-scale Stirling dish systems. === Theory === The solar energy to electrical power conversion efficiency is the product of several factors: the fraction of solar energy captured (accounting for optical losses in the solar concentration system), the heating efficiency (accounting for thermal losses in the element receiving the solar energy), and the thermal conversion efficiency (the efficiency of converting heat energy to electrical power). The maximum conversion efficiency of any thermal to electrical energy system is given by the Carnot efficiency, which represents a theoretical limit to the efficiency that can be achieved by any system, set by the laws of thermodynamics. Real-world systems do not achieve the Carnot efficiency. The conversion efficiency η {\displaystyle \eta } of the incident solar radiation into mechanical work depends on the thermal radiation properties of the solar receiver and on the heat engine (e.g. steam turbine). Solar irradiation is first concentrated onto the receiver by an optical system and converted into heat by the solar receiver with the efficiency η R e c e i v e r {\displaystyle \eta _{Receiver}} , and subsequently the heat is converted into mechanical energy by the heat engine with the efficiency η m e c h a n i c a l {\displaystyle \eta _{mechanical}} , using Carnot's principle. The mechanical energy is then converted into electrical energy by a generator. For a solar receiver with a mechanical converter (e.g., a turbine), the overall conversion efficiency can be defined as follows: η = η o p t i c s ⋅ η r e c e i v e r ⋅ η m e c h a n i c a l ⋅ η g e n e r a t o r {\displaystyle \eta =\eta _{\mathrm {optics} }\cdot \eta _{\mathrm {receiver} }\cdot \eta _{\mathrm {mechanical} }\cdot \eta _{\mathrm {generator} }} where η o p t i c s {\displaystyle \eta _{\mathrm {optics} }} represents the fraction of incident light concentrated onto the receiver, η r e c e i v e r {\displaystyle \eta _{\mathrm {receiver} }} the fraction of light incident on the receiver that is converted into heat energy, η m e c h a n i c a l {\displaystyle \eta _{\mathrm {mechanical} }} the efficiency of conversion of heat energy into mechanical energy, and η g e n e r a t o r {\displaystyle \eta _{\mathrm {generator} }} the efficiency of converting the mechanical energy into electrical power. η r e c e i v e r {\displaystyle \eta _{\mathrm {receiver} }} is: η r e c e i v e r = Q a b s o r b e d − Q l o s t Q i n c i d e n t {\displaystyle \eta _{\mathrm {receiver} }={\frac {Q_{\mathrm {absorbed} }-Q_{\mathrm {lost} }}{Q_{\mathrm {incident} }}}} with Q i n c i d e n t {\displaystyle Q_{\mathrm {incident} }} , Q a b s o r b e d {\displaystyle Q_{\mathrm {absorbed} }} , Q l o s t {\displaystyle Q_{\mathrm {lost} }} respectively the incoming solar flux and the fluxes absorbed and lost by the system solar receiver. The conversion efficiency η m e c h a n i c a l {\displaystyle \eta _{\mathrm {mechanical} }} is at most the Carnot efficiency, which is determined by the temperature of the receiver T H {\displaystyle T_{H}} and the temperature of the heat rejection ("heat sink temperature") T 0 {\displaystyle T^{0}} , η C a r n o t = 1 − T 0 T H {\displaystyle \eta _{\mathrm {Carnot} }=1-{\frac {T^{0}}{T_{H}}}} The real-world thermal-conversion efficiencies of typical engines achieve 50% to at most 70% of the Carnot efficiency due to losses such as heat loss and windage in the moving parts. === Ideal case === For a solar flux I {\displaystyle I} (e.g. I = 1000 W / m 2 {\displaystyle I=1000\,\mathrm {W/m^{2}} } ) concentrated C {\displaystyle C} times with an efficiency η O p t i c s {\displaystyle \eta _{Optics}} on the system solar receiver with a collecting area A {\displaystyle A} and an absorptivity α {\displaystyle \alpha } : Q s o l a r = I C A {\displaystyle Q_{\mathrm {solar} }=ICA} , Q a b s o r b e d = η o p t i c s α Q s o l a r {\displaystyle Q_{\mathrm {absorbed} }=\eta _{\mathrm {optics} }\alpha Q_{\mathrm {solar} }} , For simplicity's sake, one can assume that the losses are only radiative ones (a fair assumption for high temperatures), thus for a reradiating area A and an emissivity ϵ {\displaystyle \epsilon } applying the Stefan–Boltzmann law yields: Q l o s t = A ϵ σ T H 4 {\displaystyle Q_{\mathrm {lost} }=A\epsilon \sigma T_{H}^{4}} Simplifying these equations by considering perfect optics ( η O p t i c s {\displaystyle \eta _{\mathrm {Optics} }} = 1) and without considering the ultimate conversion step into electricity by a generator, collecting and reradiating areas equal and maximum absorptivity and emissivity ( α {\displaystyle \alpha } = 1, ϵ {\displaystyle \epsilon } = 1) then substituting in the first equation gives η = ( 1 − σ T H 4 I C ) ⋅ ( 1 − T 0 T H ) {\displaystyle \eta =\left(1-{\frac {\sigma T_{H}^{4}}{IC}}\right)\cdot \left(1-{\frac {T^{0}}{T_{H}}}\right)} The graph shows that the overall efficiency does not increase steadily with the receiver's temperature. Although the heat engine's efficiency (Carnot) increases with higher temperature, the receiver's efficiency does not. On the contrary, the receiver's efficiency is decreasing, as the amount of energy it cannot absorb (Qlost) grows by the fourth power as a function of temperature. Hence, there is a maximum reachable temperature. When the receiver efficiency is null (blue curve on the figure below), Tmax is: T m a x = ( I C σ ) 0.25 {\displaystyle T_{\mathrm {max} }=\left({\frac {IC}{\sigma }}\right)^{0.25}} There is a temperature Topt for which the efficiency is maximum, i.e.. when the efficiency derivative relative to the receiver temperature is null: d η d T H ( T o p t ) = 0 {\displaystyle {\frac {d\eta }{dT_{H}}}(T_{\mathrm {opt} })=0} Consequently, this leads us to the following equation: T o p t 5 − ( 0.75 T 0 ) T o p t 4 − T 0 I C 4 σ = 0 {\displaystyle T_{opt}^{5}-(0.75T^{0})T_{\mathrm {opt} }^{4}-{\frac {T^{0}IC}{4\sigma }}=0} Solving this equation numerically allows us to obtain the optimum process temperature according to the solar concentration ratio C {\displaystyle C} (red curve on the figure below) Theoretical efficiencies aside, real-world experience of CSP reveals a 25%–60% shortfall in projected production, a good part of which is due to the practical Carnot cycle losses not included in the above analysis. == Incentives and markets == === Spain === In 2008, Spain launched the first commercial scale CSP market in Europe. Until 2012, solar-thermal electricity generation was initially eligible for feed-in tariff payments (art. 2 RD 661/2007) – leading to the creation of the largest CSP fleet in the world which at 2.3 GW of installed capacity contributes about 5TWh of power to the Spanish grid every year. The initial requirements for plants in the FiT were: Systems registered in the register of systems prior to 29 September 2008: 50 MW for solar-thermal systems. Systems registered after 29 September 2008 (PV only). The capacity limits for the different system types were re-defined during the review of the application conditions every quarter (art. 5 RD 1578/2008, Annex III RD 1578/2008). Prior to the end of an application period, the market caps specified for each system type are published on the website of the Ministry of Industry, Tourism and Trade (art. 5 RD 1578/2008). Because of cost concerns Spain has halted acceptance of new projects for the feed-in-tariff on 27 January 2012 Already accepted projects were affected by a 6% "solar-tax" on feed-in-tariffs, effectively reducing the feed-in-tariff. In this context, the Spanish Government enacted the Royal Decree-Law 9/2013 in 2013, aimed at the adoption of urgent measures to guarantee the economic and financial stability of the electric system, laying the foundations of the new Law 24/2013 of the Spanish electricity sector. This new retroactive legal-economic framework applied to all the renewable energy systems was developed in 2014 by the RD 413/2014, which abolished the former regulatory frameworks set by the RD 661/2007 and the RD 1578/2008 and defined a new remuneration scheme for these assets. After a lost decade for CSP in Europe, Spain announced in its National Energy and Climate Plan with the intention of adding 5GW of CSP capacity between 2021 and 2030. Towards this end bi-annual auctions of 200 MW of CSP capacity starting in October 2022 are expected, but details are not yet known. === Australia === Several CSP dishes have been set up in remote Aboriginal settlements in the Northern Territory: Hermannsburg, Yuendumu and Lajamanu. So far no commercial scale CSP project has been commissioned in Australia, but several projects have been suggested. In 2017, now-bankrupt American CSP developer SolarReserve was awarded a PPA to realize the 150 MW Aurora Solar Thermal Power Project in South Australia at a record low rate of just AUD$ 0.08/kWh, or close to USD$ 0.06/kWh. Unfortunately the company failed to secure financing, and the project was cancelled. Another promising application for CSP in Australia are mines that need 24/7 electricity but often have no grid connection. Vast Solar, a startup company aiming to commercialize a novel modular third generation CSP design, is looking to start construction of a 50 MW combined CSP and PV facility in Mt. Isa of North-West Queensland in 2021. At the federal level, under the Large-scale Renewable Energy Target (LRET), in operation under the Renewable Energy Electricity Act 2000, large-scale solar thermal electricity generation from accredited RET power stations may be entitled to create large-scale generation certificates (LGCs). These certificates can then be sold and transferred to liable entities (usually electricity retailers) to meet their obligations under this tradeable certificates scheme. However, as this legislation is technology neutral in its operation, it tends to favour more established RE technologies with a lower levelised cost of generation, such as large-scale onshore wind, rather than solar thermal and CSP. At state level, renewable energy feed-in laws typically are capped by maximum generation capacity in kWp, and are open only to micro or medium scale generation and in a number of instances are only open to solar photovoltaic (PV) generation. This means that larger scale CSP projects would not be eligible for payment for feed-in incentives in many of the State and Territory jurisdictions. === China === In 2024, China is offering second generation CSP technology to compete with other on-demand electricity generation methods based on renewable or non-renewable fossil fuels without any direct or indirect subsidies. In the current 14th five-year plan CSP projects are developed in several provinces alongside large GW sized solar PV and wind projects. In 2016, China announced its intention to build a batch of 20 technologically diverse CSP demonstration projects in the context of the 13th five-year plan, with the intention of building up an internationally competitive CSP industry. Since the first plants were completed in 2018, the generated electricity from the plants with thermal storage is supported with an administratively set FiT of RMB 1.5 per kWh. At the end of 2020, China operated a total of 545 MW in 12 CSP plants: seven plants (320 MW) are molten-salt towers, another two plants (150 MW) use the proven Eurotrough 150 parabolic trough design, and three plants (75 MW) use linear Fresnel collectors. Plans to build a second batch of demonstration projects were never enacted and further technology specific support for CSP in the upcoming 14th five-year plan is unknown. Federal support projects from the demonstration batch ran out at the end of 2021. === India === In March 2024, SECI announced that a RfQ for 500 MW would be called in the year 2024. == Solar thermal reactors == CSP has other uses than electricity. Researchers are investigating solar thermal reactors for the production of solar fuels, making solar a fully transportable form of energy in the future. These researchers use the solar heat of CSP as a catalyst for thermochemistry to break apart molecules of H2O to create hydrogen (H2) from solar energy with no carbon emissions. By splitting both H2O and CO2, other much-used hydrocarbons – for example, the jet fuel used to fly commercial airplanes – could also be created with solar energy rather than from fossil fuels. Heat from the sun can be used to provide steam used to make heavy oil less viscous and easier to pump. This process is called solar thermal enhanced oil recovery. Solar power towers and parabolic troughs can be used to provide the steam, which is used directly, so no generators are required and no electricity is produced. Solar thermal enhanced oil recovery can extend the life of oilfields with very thick oil which would not otherwise be economical to pump. Carbon neutral synthetic fuel production using concentrated solar thermal energy at nearly 1500 °C temperature is technically feasible and will be commercially viable in the future if the costs of CSP plants decline. Also, carbon-neutral hydrogen can be produced with solar thermal energy (CSP) using the sulfur–iodine cycle, hybrid sulfur cycle, iron oxide cycle, copper–chlorine cycle, zinc–zinc oxide cycle, cerium(IV) oxide–cerium(III) oxide cycle, or an alternative. == Gigawatt-scale solar power plants == Around the turn of the millennium up to about 2010, there have been several proposals for gigawatt-size, very-large-scale solar power plants using CSP. They include the Euro-Mediterranean Desertec proposal and Project Helios in Greece (10 GW), both now canceled. A 2003 study concluded that the world could generate 2,357,840 TWh each year from very large-scale solar power plants using 1% of each of the world's deserts. Total consumption worldwide was 15,223 TWh/year (in 2003). The gigawatt size projects would have been arrays of standard-sized single plants. In 2012, the BLM made available 97,921,069 acres (39,627,251 hectares) of land in the southwestern United States for solar projects, enough for between 10,000 and 20,000 GW. The largest single plant in operation is the 510 MW Noor Solar Power Station. In 2022 the 700 MW CSP 4th phase of the 5GW Mohammed bin Rashid Al Maktoum Solar Park in Dubai will become the largest solar complex featuring CSP. === Suitable sites === The locations with highest direct irradiance are dry, at high altitude, and located in the tropics. These locations have a higher potential for CSP than areas with less sun. Abandoned opencast mines, moderate hill slopes, and crater depressions may be advantageous in the case of power tower CSP, as the power tower can be located on the ground integral with the molten salt storage tank. == Environmental effects == CSP has a number of environmental impacts, particularly by the use of water and land. Water is generally used for cooling and to clean mirrors. Some projects are looking into various approaches to reduce the water and cleaning agents used, including the use of barriers, non-stick coatings on mirrors, water misting systems, and others. === Water use === Concentrating solar power plants with wet-cooling systems have the highest water-consumption intensities of any conventional type of electric power plant; only fossil-fuel plants with carbon-capture and storage may have higher water intensities. A 2013 study comparing various sources of electricity found that the median water consumption during operations of concentrating solar power plants with wet cooling was 3.1 cubic metres per megawatt-hour (810 US gal/MWh) for power tower plants and 3.4 m3/MWh (890 US gal/MWh) for trough plants. This was higher than the operational water consumption (with cooling towers) for nuclear at 2.7 m3/MWh (720 US gal/MWh), coal at 2.0 m3/MWh (530 US gal/MWh), or natural gas at 0.79 m3/MWh (210 US gal/MWh). A 2011 study by the National Renewable Energy Laboratory came to similar conclusions: for power plants with cooling towers, water consumption during operations was 3.27 m3/MWh (865 US gal/MWh) for CSP trough, 2.98 m3/MWh (786 US gal/MWh) for CSP tower, 2.60 m3/MWh (687 US gal/MWh) for coal, 2.54 m3/MWh (672 US gal/MWh) for nuclear, and 0.75 m3/MWh (198 US gal/MWh) for natural gas. The Solar Energy Industries Association noted that the Nevada Solar One trough CSP plant consumes 3.2 m3/MWh (850 US gal/MWh). The issue of water consumption is heightened because CSP plants are often located in arid environments where water is scarce. In 2007, the US Congress directed the Department of Energy to report on ways to reduce water consumption by CSP. The subsequent report noted that dry cooling technology was available that, although more expensive to build and operate, could reduce water consumption by CSP by 91 to 95 percent. A hybrid wet/dry cooling system could reduce water consumption by 32 to 58 percent. A 2015 report by NREL noted that of the 24 operating CSP power plants in the US, 4 used dry cooling systems. The four dry-cooled systems were the three power plants at the Ivanpah Solar Power Facility near Barstow, California, and the Genesis Solar Energy Project in Riverside County, California. Of 15 CSP projects under construction or development in the US as of March 2015, 6 were wet systems, 7 were dry systems, 1 hybrid, and 1 unspecified. Although many older thermoelectric power plants with once-through cooling or cooling ponds use more water than CSP, meaning that more water passes through their systems, most of the cooling water returns to the water body available for other uses, and they consume less water by evaporation. For instance, the median coal power plant in the US with once-through cooling uses 138 m3/MWh (36,350 US gal/MWh), but only 0.95 m3/MWh (250 US gal/MWh) (less than one percent) is lost through evaporation. === Effects on wildlife === Insects can be attracted to the bright light caused by concentrated solar technology, and as a result birds that hunt them can be killed by being burned if they fly near the point where light is being focused. This can also affect raptors that hunt the birds. Federal wildlife officials were quoted by opponents as calling the Ivanpah power towers "mega traps" for wildlife. Some media sources have reported that concentrated solar power plants have injured or killed large numbers of birds due to intense heat from the concentrated sunrays. Some of the claims may have been overstated or exaggerated. According to rigorous reporting, in over six months of its first year of operation, 321 bird fatalities were counted at Ivanpah, of which 133 were related to sunlight being reflected onto the boilers. Over a year, this figure rose to a total count of 415 bird fatalities from known causes, and 288 from unknown causes. Taking into account the search efficiency of the dead bird carcasses, the total avian mortality for the first year was estimated at 1492 for known causes and 2012 from unknown causes. Of the bird deaths due to known causes, 47.4% were burned, 51.9% died of collision effects, and 0.7% died from other causes. Mitigations actions can be taken to reduce these numbers, such as focusing no more than four mirrors on any one place in the air during standby, as was done at Crescent Dunes Solar Energy Project. Over the 2020-2021 period, 288 bird fatalities were directly accounted for at Ivanpah, a figure consistent with the ranges found in previous annual assessments. In more general terms, a 2016 preliminary study assessed that the annual bird mortality per MW of installed power was similar between U.S. concentrated solar power plants and wind power plants, and higher for fossil fuel power plants. == See also == == References == == External links == Concentrating Solar Power Utility NREL Concentrating Solar Power Program Plataforma Solar de Almeria, CSP research center ISFOC (Institute of Concentrating Photovoltaic Systems) Baldizon, Roberto (5 March 2019). "Innovations on Concentrated Solar Thermal Power". Medium. Retrieved 18 January 2020.
Wikipedia/Concentrated_solar_power
Energy supply is the delivery of fuels or transformed fuels to point of consumption. It potentially encompasses the extraction, transmission, generation, distribution and storage of fuels. It is also sometimes called energy flow. This supply of energy can be disrupted by several factors, including imposition of higher energy prices due to action by OPEC or other cartel, war, political disputes, economic disputes, or physical damage to the energy infrastructure due to terrorism. The security of the energy supply is a major concern of national security and energy law. == Other uses == New York Consolidated Laws includes a statutory code called "Energy Law". Article 21 of this code is called "Energy Supply and Production", but rather than a comprehensive code, only consists of one section dealing with renewable energy. == See also == === General energy topics === Energy Energy form Energy conservation Energy density Energy economics Energy law Energy markets and energy derivatives Energy policy Energy price Energy security Energy quality Entropy (energy dispersal) and Introduction to entropy List of energy topics Market transformation World energy consumption Worldwide energy supply === Renewable and alternative energy sources === Clean Tech Nation Effects of 2000s energy crisis Efficient energy use Geothermal power Global warming Intermittent power source Ocean energy Renewable energy Renewable energy commercialization Renewable heat Vehicle-to-grid Wind power === By country === Japan United Kingdom United States == References == == Other sources == Lisa Yount, Energy supply: Library in a book (Infobase Publishing, 2005) ISBN 978-0-8160-5577-7 Found at Google Books. Jon Strand, Energy efficiency and renewable energy supply for the G-7 countries, with emphasis on Germany, Issues 2007–2299, Volumes 7-299 of IMF working paper(International Monetary Fund, 2007) Found at Google Books. Herberg, Mikkal (2014). Energy Security and the Asia-Pacific: Course Reader. United States: The National Bureau of Asian Research. Ewan McLeish, Challenges to Our Energy Supply: Can the Earth Survive? (The Rosen Publishing Group, 2009) ISBN 978-1-4358-5357-7 Found at Google Books.
Wikipedia/Energy_supply
In physics, a conservative force is a force with the property that the total work done by the force in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero. A conservative force depends only on the position of the object. If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points. Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force. Other examples of conservative forces are: force in elastic spring, electrostatic force between two electric charges, and magnetic force between two magnetic poles. The last two forces are called central forces as they act along the line joining the centres of two charged/magnetized bodies. A central force is conservative if and only if it is spherically symmetric. For conservative forces, F c = − dU d s {\displaystyle \mathbf {F_{c}} =-{\frac {\textit {dU}}{d\mathbf {s} }}} where F c {\displaystyle F_{c}} is the conservative force, U {\displaystyle U} is the potential energy, and s {\displaystyle s} is the position. == Informal definition == Informally, a conservative force can be thought of as a force that conserves mechanical energy. Suppose a particle starts at point A, and there is a force F acting on it. Then the particle is moved around by other forces, and eventually ends up at A again. Though the particle may still be moving, at that instant when it passes point A again, it has traveled a closed path. If the net work done by F at this point is 0, then F passes the closed path test. Any force that passes the closed path test for all possible closed paths is classified as a conservative force. The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces. For non-conservative forces, the mechanical energy that is lost (not conserved) has to go somewhere else, by conservation of energy. Usually the energy is turned into heat, for example the heat generated by friction. In addition to heat, friction also often produces some sound energy. The water drag on a moving boat converts the boat's mechanical energy into not only heat and sound energy, but also wave energy at the edges of its wake. These and other energy losses are irreversible because of the second law of thermodynamics. == Path independence == A direct consequence of the closed path test is that the work done by a conservative force on a particle moving between any two points does not depend on the path taken by the particle. This is illustrated in the figure to the right: The work done by the gravitational force on an object depends only on its change in height because the gravitational force is conservative. The work done by a conservative force is equal to the negative of change in potential energy during that process. For a proof, imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2, i.e., the work is independent of the path followed, as long as it goes from A to B. For example, if a child slides down a frictionless slide, the work done by the gravitational force on the child from the start of the slide to the end is independent of the shape of the slide; it only depends on the vertical displacement of the child. == Mathematical description == A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if it meets any of these three equivalent conditions: The curl of F is the zero vector: ∇ × F = 0 . {\displaystyle \mathbf {\nabla } \times \mathbf {F} =\mathbf {0} .} where in two dimensions this reduces to: ∂ F y ∂ x − ∂ F x ∂ y = 0 {\displaystyle {\frac {\partial F_{y}}{\partial x}}-{\frac {\partial F_{x}}{\partial y}}=0} There is zero net work (W) done by the force when moving a particle through a trajectory that starts and ends in the same place: W ≡ ∮ C F ⋅ d r = 0. {\displaystyle W\equiv \oint _{C}\mathbf {F} \cdot \mathrm {d} \mathbf {r} =0.} The force can be written as the negative gradient of a potential, Φ {\displaystyle \Phi } : F = − ∇ Φ . {\displaystyle \mathbf {F} =-\mathbf {\nabla } \Phi .} The term conservative force comes from the fact that when a conservative force exists, it conserves mechanical energy. The most familiar conservative forces are gravity, the electric force (in a time-independent magnetic field, see Faraday's law), and spring force. Many forces (particularly those that depend on velocity) are not force fields. In these cases, the above three conditions are not mathematically equivalent. For example, the magnetic force satisfies condition 2 (since the work done by a magnetic field on a charged particle is always zero), but does not satisfy condition 3, and condition 1 is not even defined (the force is not a vector field, so one cannot evaluate its curl). Accordingly, some authors classify the magnetic force as conservative, while others do not. The magnetic force is an unusual case; most velocity-dependent forces, such as friction, do not satisfy any of the three conditions, and therefore are unambiguously nonconservative. == Non-conservative force == Despite conservation of total energy, non-conservative forces can arise in classical physics due to neglected degrees of freedom or from time-dependent potentials. Many non-conservative forces may be perceived as macroscopic effects of small-scale conservative forces. For instance, friction may be treated without violating conservation of energy by considering the motion of individual molecules; however, that means every molecule's motion must be considered rather than handling it through statistical methods. For macroscopic systems the non-conservative approximation is far easier to deal with than millions of degrees of freedom. Examples of non-conservative forces are friction and non-elastic material stress. Friction has the effect of transferring some of the energy from the large-scale motion of the bodies to small-scale movements in their interior, and therefore appear non-conservative on a large scale. General relativity is non-conservative, as seen in the anomalous precession of Mercury's orbit. However, general relativity does conserve a stress–energy–momentum pseudotensor. == See also == Conservative vector field Conservative system == References ==
Wikipedia/Conservative_force
Electrical energy is the energy transferred as electric charges move between points with different electric potential, that is, as they move across a potential difference. As electric potential is lost or gained, work is done changing the energy of some system. The amount of work in joules is given by the product of the charge that has moved, in coulombs, and the potential difference that has been crossed, in volts. Electrical energy is usually sold by the kilowatt hour (1 kW·h = 3.6 MJ) which is the product of the power in kilowatts multiplied by running time in hours. Electric utilities measure energy using an electricity meter, which keeps a running total of the electrical energy delivered to a customer. Electric heating is an example of converting electrical energy into thermal energy. The simplest and most common type of electric heater uses electrical resistance to convert the energy. There are other ways to use electrical energy. Electric charges moves as a current the heater element which has a potential difference between the ends: energy is transferred from the charges to the element, increasing the element's temperature and thermal energy as the charges lose potential energy. == Electricity generation == Electricity generation is the process of generating electrical energy from other forms of energy. The fundamental principle of electricity generation was discovered during the 1820s and early 1830s by the British scientist Michael Faraday. His basic method is still used today: electric current is generated by the movement of a loop of wire, or disc of copper between the poles of a magnet. For electrical utilities, it is the first step in the delivery of electricity to consumers. The other processes, electricity transmission, distribution, and electrical energy storage and recovery using pumped-storage methods are normally carried out by the electric power industry. Electricity is most often generated at a power station by electromechanical generators, primarily driven by heat engines fueled by chemical combustion or nuclear fission but also by other means such as the kinetic energy of flowing water and wind. There are many other technologies that can be and are used to generate electricity such as solar photovoltaics and geothermal power. == References ==
Wikipedia/Electrical_energy
Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. Separated objects attract and are attracted as if all their mass were concentrated at their centers. The publication of the law has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica (Latin for 'Mathematical Principles of Natural Philosophy' (the Principia)), first published on 5 July 1687. The equation for universal gravitation thus takes the form: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death. Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has charge in place of mass and a different constant. Newton's law was later superseded by Albert Einstein's theory of general relativity, but the universality of the gravitational constant is intact and the law still continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as Mercury's orbit around the Sun). == History == Before Newton's law of gravity, there were many theories explaining gravity. Philosophers made observations about things falling down − and developed theories why they do – as early as Aristotle who thought that rocks fall to the ground because seeking the ground was an essential part of their nature. Around 1600, the scientific method began to take root. René Descartes started over with a more fundamental view, developing ideas of matter and action independent of theology. Galileo Galilei wrote about experimental measurements of falling and rolling objects. Johannes Kepler's laws of planetary motion summarized Tycho Brahe's astronomical observations.: 132  Around 1666 Isaac Newton developed the idea that Kepler's laws must also apply to the orbit of the Moon around the Earth and then to all objects on Earth. The analysis required assuming that the gravitation force acted as if all of the mass of the Earth were concentrated at its center, an unproven conjecture at that time. His calculations of the Moon orbit time was within 16% of the known value. By 1680, new values for the diameter of the Earth improved his orbit time to within 1.6%, but more importantly Newton had found a proof of his earlier conjecture.: 201  In 1687 Newton published his Principia which combined his laws of motion with new mathematical analysis to explain Kepler's empirical results.: 134  His explanation was in the form of a law of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to their separation squared.: 28  Newton's original formula was: F o r c e o f g r a v i t y ∝ m a s s o f o b j e c t 1 × m a s s o f o b j e c t 2 d i s t a n c e f r o m c e n t e r s 2 {\displaystyle {\rm {Force\,of\,gravity}}\propto {\frac {\rm {mass\,of\,object\,1\,\times \,mass\,of\,object\,2}}{\rm {distance\,from\,centers^{2}}}}} where the symbol ∝ {\displaystyle \propto } means "is proportional to". To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them (the gravitational constant). Newton would need an accurate measure of this constant to prove his inverse-square law. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him, ultimately a frivolous accusation.: 204  === Newton's "causes hitherto unknown" === While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" that his equations implied. In 1692, in his third letter to Bentley, he wrote: "That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.": 26  Newton's 1713 General Scholium in the second edition of Principia explains his model of gravity, translated in this case by Samuel Clarke: I have explained the Pharnomena of the Heavens and the Sea, by the Force of Gravity; but the Cause of Gravity I have not yet assigned. It is a Force arising from some Cause, which reaches to the very Centers of the Sun and Planets, without any diminution of its Force: And it acts, not proportionally to the Surfaces of the Particles it acts upon, as Mechanical Causes use to do; but proportionally to the Quantity of Solid Matter: And its Action reaches every way to immense Distances, decreasing always in a duplicate ratio of the Distances. But the Cause of these Properties of Gravity, I have not yet found deducible from Pharnomena: And Hypotheses I make not.: 383  The last sentence is Newton's famous and highly debated Latin phrase Hypotheses non fingo. In other translations it comes out "I feign no hypotheses". == Modern form == In modern language, the law states the following: Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is 6.67430(15)×10−11 m3⋅kg−1⋅s−2. The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G. This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton's Principia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force. == Bodies with spatial extent == If the bodies in question have spatial extent (as opposed to being point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses that constitute the bodies. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies. In this way, it can be shown that an object with a spherically symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its center. (This is not generally true for non-spherically symmetrical bodies.) For points inside a spherically symmetric distribution of matter, Newton's shell theorem can be used to find the gravitational force. The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance r0 from the center of the mass distribution: The portion of the mass that is located at radii r < r0 causes the same force at the radius r0 as if all of the mass enclosed within a sphere of radius r0 was concentrated at the center of the mass distribution (as noted above). The portion of the mass that is located at radii r > r0 exerts no net gravitational force at the radius r0 from the center. That is, the individual gravitational forces exerted on a point at radius r0 by the elements of the mass outside the radius r0 cancel each other. As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere. == Vector form == Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors. F 21 = − G m 1 m 2 | r 21 | 2 r ^ 21 = − G m 1 m 2 | r 21 | 3 r 21 {\displaystyle \mathbf {F} _{21}=-G{m_{1}m_{2} \over {|\mathbf {r} _{21}|}^{2}}{\hat {\mathbf {r} }}_{21}=-G{m_{1}m_{2} \over {|\mathbf {r} _{21}|}^{3}}\mathbf {r} _{21}} where F21 is the force applied on body 2 exerted by body 1, G is the gravitational constant, m1 and m2 are respectively the masses of bodies 1 and 2, r21 = r2 − r1 is the displacement vector between bodies 1 and 2, and r ^ 21 = d e f r 2 − r 1 | r 2 − r 1 | {\displaystyle {\hat {\mathbf {r} }}_{21}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\mathbf {r_{2}-r_{1}} }{|\mathbf {r_{2}-r_{1}} |}}} is the unit vector from body 1 to body 2. It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. Also, it can be seen that F12 = −F21. == Gravity field == The gravitational field is a vector field that describes the gravitational force that would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point. It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write r instead of r12 and m instead of m2 and define the gravitational field g(r) as: g ( r ) = − G m 1 | r | 2 r ^ {\displaystyle \mathbf {g} (\mathbf {r} )=-G{m_{1} \over {{\vert \mathbf {r} \vert }^{2}}}\,\mathbf {\hat {r}} } so that we can write: F ( r ) = m g ( r ) . {\displaystyle \mathbf {F} (\mathbf {r} )=m\mathbf {g} (\mathbf {r} ).} This formulation is dependent on the objects causing the field. The field has units of acceleration; in SI, this is m/s2. Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field V(r) such that g ( r ) = − ∇ V ( r ) . {\displaystyle \mathbf {g} (\mathbf {r} )=-\nabla V(\mathbf {r} ).} If m1 is a point mass or the mass of a sphere with homogeneous mass distribution, the force field g(r) outside the sphere is isotropic, i.e., depends only on the distance r from the center of the sphere. In that case V ( r ) = − G m 1 r . {\displaystyle V(r)=-G{\frac {m_{1}}{r}}.} As per Gauss's law, field in a symmetric body can be found by the mathematical equation: where ∂ V {\displaystyle \partial V} is a closed surface and M enc {\displaystyle M_{\text{enc}}} is the mass enclosed by the surface. Hence, for a hollow sphere of radius R {\displaystyle R} and total mass M {\displaystyle M} , | g ( r ) | = { 0 , if r < R G M r 2 , if r ≥ R {\displaystyle |\mathbf {g(r)} |={\begin{cases}0,&{\text{if }}r<R\\\\{\dfrac {GM}{r^{2}}},&{\text{if }}r\geq R\end{cases}}} For a uniform solid sphere of radius R {\displaystyle R} and total mass M {\displaystyle M} , | g ( r ) | = { G M r R 3 , if r < R G M r 2 , if r ≥ R {\displaystyle |\mathbf {g(r)} |={\begin{cases}{\dfrac {GMr}{R^{3}}},&{\text{if }}r<R\\\\{\dfrac {GM}{r^{2}}},&{\text{if }}r\geq R\end{cases}}} == Limitations == Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities ϕ / c 2 {\displaystyle \phi /c^{2}} and ( v / c ) 2 {\displaystyle (v/c)^{2}} are both much less than one, where ϕ {\displaystyle \phi } is the gravitational potential, v {\displaystyle v} is the velocity of the objects being studied, and c {\displaystyle c} is the speed of light in vacuum. For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since ϕ c 2 = G M s u n r o r b i t c 2 ∼ 10 − 8 , ( v E a r t h c ) 2 = ( 2 π r o r b i t ( 1 y r ) c ) 2 ∼ 10 − 8 , {\displaystyle {\frac {\phi }{c^{2}}}={\frac {GM_{\mathrm {sun} }}{r_{\mathrm {orbit} }c^{2}}}\sim 10^{-8},\quad \left({\frac {v_{\mathrm {Earth} }}{c}}\right)^{2}=\left({\frac {2\pi r_{\mathrm {orbit} }}{(1\ \mathrm {yr} )c}}\right)^{2}\sim 10^{-8},} where r orbit {\displaystyle r_{\text{orbit}}} is the radius of the Earth's orbit around the Sun. In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity. === Observations conflicting with Newton's formula === Newton's theory does not fully explain the precession of the perihelion of the orbits of the planets, especially that of Mercury, which was detected long after the life of Newton. There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th century. The predicted angular deflection of light rays by gravity (treated as particles travelling at the expected speed) that is calculated by using Newton's theory is only one-half of the deflection that is observed by astronomers. Calculations using general relativity are in much closer agreement with the astronomical observations. In spiral galaxies, the orbiting of stars around their centers seems to strongly disobey both Newton's law of universal gravitation and general relativity. Astrophysicists, however, explain this marked phenomenon by assuming the presence of large amounts of dark matter. === Einstein's solution === The first two conflicts with observations above were explained by Einstein's theory of general relativity, in which gravitation is a manifestation of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. This allowed a description of the motions of light and mass that was consistent with all available observations. In general relativity, the gravitational force is a fictitious force resulting from the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime. == Extensions == In recent years, quests for non-inverse square terms in the law of gravity have been carried out by neutron interferometry. == Solutions == The two-body problem has been completely solved, as has the restricted three-body problem. The n-body problem is an ancient, classical problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem – from the time of the Greeks and on – has been motivated by the desire to understand the motions of the Sun, planets and the visible stars. The classical problem can be informally stated as: given the quasi-steady orbital properties (instantaneous position, velocity and time) of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem too. The n-body problem in general relativity is considerably more difficult to solve. == See also == Bentley's paradox – Cosmological paradox involving gravity Gauss's law for gravity – Restatement of Newton's law of universal gravitation Jordan and Einstein frames – different conventions for the metric tensor, in a theory of a dilaton coupled to gravityPages displaying wikidata descriptions as a fallback Kepler orbit – Celestial orbit whose trajectory is a conic section in the orbital plane Newton's cannonball – Thought experiment about gravity Newton's laws of motion – Laws in physics about force and motion Social gravity – Social theory Static forces and virtual-particle exchange – Physical interaction in post-classical physics == Notes == == References == == External links == Media related to Newton's law of universal gravitation at Wikimedia Commons Feather and Hammer Drop on Moon on YouTube Newton's Law of Universal Gravitation Javascript calculator
Wikipedia/Gravitational_force
Energy is defined via work, so the SI unit of energy is the same as the unit of work – the joule (J), named in honour of James Prescott Joule and his experiments on the mechanical equivalent of heat. In slightly more fundamental terms, 1 joule is equal to 1 newton metre and, in terms of SI base units 1 J = 1 k g ( m s ) 2 = 1 k g ⋅ m 2 s 2 {\displaystyle 1\ \mathrm {J} =1\ \mathrm {kg} \left({\frac {\mathrm {m} }{\mathrm {s} }}\right)^{2}=1\ {\frac {\mathrm {kg} \cdot \mathrm {m} ^{2}}{\mathrm {s} ^{2}}}} An energy unit that is used in atomic physics, particle physics, and high energy physics is the electronvolt (eV). One eV is equivalent to 1.602176634×10−19 J. In spectroscopy, the unit cm−1 ≈ 0.0001239842 eV is used to represent energy since energy is inversely proportional to wavelength from the equation E = h ν = h c / λ {\displaystyle E=h\nu =hc/\lambda } . In discussions of energy production and consumption, the units barrel of oil equivalent and ton of oil equivalent are often used. == British imperial / US customary units == The British imperial units and U.S. customary units for both energy and work include the foot-pound force (1.3558 J), the British thermal unit (BTU) which has various values in the region of 1055 J, the horsepower-hour (2.6845 MJ), and the gasoline gallon equivalent (about 120 MJ). The table illustrates the wide range of magnitudes among conventional units of energy. For example, 1 BTU is equivalent to about 1,000 joules, and there are 25 orders-of-magnitude difference between a kilowatt-hour and an electron-volt. == Electricity == A unit of electrical energy, particularly for utility bills, is the kilowatt-hour (kWh); one kilowatt-hour is equivalent to 3.6 megajoules. Electricity usage is often given in units of kilowatt-hours per year or other periods. This is a measurement of average power consumption, meaning the average rate at which energy is transferred. One kilowatt-hour per year is around 0.11 watts. == Natural gas == Natural gas is often sold in units of energy content or by volume. Common units for selling by energy content are joules or therms. One therm is equal to about 1,055 megajoules. Common units for selling by volume are cubic metre or cubic feet. Natural gas in the US is sold in therms or 100 cubic feet (100 ft3). In Australia, natural gas is sold in cubic metres. One cubic metre contains about 38 megajoules. In most of the world, natural gas is sold in gigajoules. == Food industry == The calorie is defined as the amount of thermal energy necessary to raise the temperature of one gram of water by 1 Celsius degree, from a temperature of 14.5 °C, at a pressure of 1 atm. For thermochemistry a calorie of 4.184 J is used, but other calories have also been defined, such as the International Steam Table calorie of 4.1868 J. In many regions, food energy is measured in large calories (a large calory is a kilocalory, equal to 1000 calories), sometimes written capitalized as Calories. In the European Union, food energy labeling in joules is mandatory, often with calories as supplementary information. == Atom physics and chemistry == In physics and chemistry, it is common to measure energy on the atomic scale in the non-SI, but convenient, units electronvolts (eV). One electronvolt (1 eV) is equivalent to the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in a vacuum. It is common to use the SI magnitude prefixes (e.g. milli-, mega- etc) with electronvolts. Because of the relativistic equivalence between mass and energy, the eV is also sometimes used as a unit of mass. The Hartree (the atomic unit of energy) is commonly used in the field of computational chemistry since such units arise directly from the calculation algorithms without any need for conversion. Historically Rydberg units have been used. == Spectroscopy == In spectroscopy and related fields it is common to measure energy levels in units of reciprocal centimetres. These units (cm−1) are strictly speaking not energy units but units proportional to energies, with h c ∼ 2 ⋅ 10 − 23 J c m {\displaystyle \ hc\sim 2\cdot 10^{-23}\ \mathrm {J} \ \mathrm {cm} } being the proportionality constant. == Explosions == A gram of TNT releases 4,100 to 4,600 joules (980 to 1,100 calories) upon explosion. To define the tonne of TNT, this was standardized to 1 kilocalorie (4,184 joules) giving a value of 4.184 gigajoules (1 billion calories) for the tonne of TNT. == See also == Energy consumption Conversion of units of temperature Conversion of units of energy, work, or amount of heat Kilokaiser List of unusual units of measurement Maximum demand indicator Orders of magnitude (energy) erg Foe (unit) == References ==
Wikipedia/Units_of_energy
Quantum chromodynamics binding energy (QCD binding energy), gluon binding energy or chromodynamic binding energy is the energy binding quarks together into hadrons. It is the energy of the field of the strong force, which is mediated by gluons. Motion-energy and interaction-energy contribute most of the hadron's mass. == Source of mass == Most of the mass of hadrons is actually QCD binding energy, through mass–energy equivalence. This phenomenon is related to chiral symmetry breaking. In the case of nucleons —protons and neutrons— QCD binding energy forms about 99% of the nucleon's mass. The kinetic energy of the hadron's constituents, moving at near the speed of light, contributes greatly to the hadron mass; otherwise most of the rest is actual QCD binding energy, which emerges in a complex way from the potential-like terms in the QCD Lagrangian. For protons, the sum of the rest masses of the three valence quarks (two up quarks and one down quark) is approximately 9.4 MeV/c2, while the proton's total mass is about 938.3 MeV/c2. In the standard model, this "quark current mass" can nominally be attributed to the Higgs interaction. For neutrons, the sum of the rest masses of the three valence quarks (two down quarks and one up quark) is approximately 11.9 MeV/c2, while the neutron's total mass is about 939.6 MeV/c2. Considering that nearly all of the atom's mass is concentrated in the nucleons, this means that about 99% of the mass of everyday matter (baryonic matter) is, in fact, chromodynamic binding energy. == Gluon energy == While gluons are massless, they still possess energy — chromodynamic binding energy. In this way, they are similar to photons, which are also massless particles carrying energy — photon energy. The amount of energy per single gluon, or "gluon energy", cannot be directly measured, though a distribution can by inferred from deep inelastic scattering (DIS) experiments (see ref [4] for an old but still valid introduction.) Unlike photon energy, which is quantifiable, described by the Planck–Einstein relation and depends on a single variable (the photon's frequency), no simple formula exists for the quantity of energy carried by each gluon. While the effects of a single photon can be observed, single gluons have not been observed outside of a hadron. A hadron is in totality composed of gluons, valence quarks, sea quarks and other virtual particles. The gluon content of a hadron can be inferred from DIS measurements. Again, not all of the QCD binding energy is gluon interaction energy, but rather, some of it comes from the kinetic energy of the hadron's constituents. Currently, the total QCD binding energy per hadron can be estimated through a combination of the factors mentioned. In the future, studies into quark–gluon plasma will better complement the DIS studies and improve our understanding of the situation. == See also == Gluon Quark Current quark and constituent quark Hadron Strong force Quantum chromodynamics Chiral symmetry breaking Photon energy Invariant mass and relativistic mass Binding energy == References == ° Halzen, Francis and Martin, John, "Quarks and Leptons:An Introductory Course in Modem Particle Physics", John Wiley & Sons (1984).
Wikipedia/Quantum_chromodynamics_binding_energy
Negative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects. == Gravitational energy == Gravitational energy, or gravitational potential energy, is the potential energy a massive object has because it is within a gravitational field. In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. As two objects move apart and the distance between them approaches infinity, the gravitational force between them approaches zero from the positive side of the real number line and the gravitational potential approaches zero from the negative side. Conversely, as two massive objects move towards each other, the motion accelerates under gravity causing an increase in the (positive) kinetic energy of the system and, in order to conserve the total sum of energy, the increase of the same amount in the gravitational potential energy of the object is treated as negative. A universe in which positive energy dominates will eventually collapse in a Big Crunch, while an "open" universe in which negative energy dominates will either expand indefinitely or eventually disintegrate in a Big Rip. In the zero-energy universe model ("flat" or "Euclidean"), the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. It is unclear which, if any, of these models accurately describes the real universe. === Black hole ergosphere === For a classically rotating black hole, the rotation creates an ergosphere outside the event horizon, in which spacetime itself begins to rotate, in a phenomenon known as frame-dragging. Since the ergosphere is outside the event horizon, particles can escape from it. Within the ergosphere, a particle's energy may become negative (via the relativistic rotation of its Killing vector). The negative-energy particle then crosses the event horizon into the black hole, with the law of conservation of energy requiring that an equal amount of positive energy should escape. In the Penrose process, a body divides in two, with one half gaining negative energy and falling in, while the other half gains an equal amount of positive energy and escapes. This is proposed as the mechanism by which the intense radiation emitted by quasars is generated. == Quantum field effects == Negative energies and negative energy density are consistent with quantum field theory. === Virtual particles === In quantum theory, the uncertainty principle allows the vacuum of space to be filled with virtual particle-antiparticle pairs which appear spontaneously and exist for only a short time before, typically, annihilating themselves again. Some of these virtual particles can have negative energy. This behaviour plays a role in several important phenomena, as described below. === Casimir effect === In the Casimir effect, two flat plates placed very close together restrict the wavelengths of quanta which can exist between them. This in turn restricts the types and hence number and density of virtual particle pairs which can form in the intervening vacuum and can result in a negative energy density. Since this restriction does not exist or is much less significant on the opposite sides of the plates, the forces outside the plates are greater than those between the plates. This causes the plates to appear to pull on each other, which has been measured. More accurately, the vacuum energy caused by the virtual particle pairs is pushing the plates together, and the vacuum energy between the plates is too small to negate this effect since fewer virtual particles can exist per unit volume between the plates than can exist outside them. === Squeezed light === It is possible to arrange multiple beams of laser light such that destructive quantum interference suppresses the vacuum fluctuations. Such a squeezed vacuum state involves negative energy. The repetitive waveform of light leads to alternating regions of positive and negative energy. === Dirac sea === According to the theory of the Dirac sea, developed by Paul Dirac in 1930, the vacuum of space is full of negative energy. This theory was developed to explain the anomaly of negative-energy quantum states predicted by the Dirac equation. A year later, after work by Weyl, the negative energy concept was abandoned and replaced by a theory of antimatter.: 9  The following year, 1932, saw the discovery of the positron by Carl Anderson. == Quantum gravity phenomena == The intense gravitational fields around black holes create phenomena which are attributed to both gravitational and quantum effects. In these situations, a particle's Killing vector may be rotated such that its energy becomes negative. === Hawking radiation === Virtual particles can exist for a short period. When a pair of such particles appears next to a black hole's event horizon, one of them may get drawn in. This rotates its Killing vector so that its energy becomes negative and the pair have no net energy. This allows them to become real and the positive particle escapes as Hawking radiation, while the negative-energy particle reduces the black hole's net energy. Thus, a black hole may slowly evaporate. == Speculative suggestions == === Wormholes === Negative energy appears in the speculative theory of wormholes, where it is needed to keep the wormhole open. A wormhole directly connects two locations which may be separated arbitrarily far apart in both space and time, and in principle allows near-instantaneous travel between them. However physicists such as Roger Penrose regard such ideas as unrealistic, more fiction than speculation. === Warp drive === A theoretical principle for a faster-than-light (FTL) warp drive for spaceships has been suggested, using negative energy. The Alcubierre drive is based on a solution to the Einstein field equations of general relativity in which a "bubble" of spacetime is constructed using a hypothetical negative energy. The bubble is then moved by expanding space behind it and shrinking space in front of it. The bubble may travel at arbitrary speeds and is not constrained by the speed of light. This does not contradict general relativity, as the bubble's contents do not actually move through their local spacetime. === Negative-energy particles === Speculative theoretical studies have suggested that particles with negative energies are consistent with Relativistic quantum theory, with some noting interrelationships with negative mass and/or time reversal. == See also == Antimatter Dark energy Dark matter Negative mass Negative pressure == References == === Inline notes === === Bibliography === Lawrence H. Ford and Thomas A. Roman; "Negative energy, wormholes and warp drive", Scientific American January 2000, 282, Pages 46–53. Roger Penrose; The Road to Reality, ppbk, Vintage, 2005. Chapter 30: Gravity's Role in Quantum State Reduction.
Wikipedia/Negative_energy
Energy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include the production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reuse of energy that would otherwise be wasted. Energy conservation and efficiency measures reduce the demand for energy development, and can have benefits to society with improvements to environmental issues. Societies use energy for transportation, manufacturing, illumination, heating and air conditioning, and communication, for industrial, commercial, agricultural and domestic purposes. Energy resources may be classified as primary resources, where the resource can be used in substantially its original form, or as secondary resources, where the energy source must be converted into a more conveniently usable form. Non-renewable resources are significantly depleted by human use, whereas renewable resources are produced by ongoing processes that can sustain indefinite human exploitation. Thousands of people are employed in the energy industry. The conventional industry comprises the petroleum industry, the natural gas industry, the electrical power industry, and the nuclear industry. New energy industries include the renewable energy industry, comprising alternative and sustainable manufacture, distribution, and sale of alternative fuels. == Classification of resources == Energy resources may be classified as primary resources, suitable for end use without conversion to another form, or secondary resources, where the usable form of energy required substantial conversion from a primary source. Examples of primary energy resources are wind power, solar power, wood fuel, fossil fuels such as coal, oil and natural gas, and uranium. Secondary resources are those such as electricity, hydrogen, or other synthetic fuels. Another important classification is based on the time required to regenerate an energy resource. "Renewable resources" are those that recover their capacity in a time significant by human needs. Examples are hydroelectric power or wind power, when the natural phenomena that are the primary source of energy are ongoing and not depleted by human demands. Non-renewable resources are those that are significantly depleted by human usage and that will not recover their potential significantly during human lifetimes. An example of a non-renewable energy source is coal, which does not form naturally at a rate that would support human use. == Fossil fuels == Fossil fuel (primary non-renewable fossil) sources burn coal or hydrocarbon fuels, which are the remains of the decomposition of plants and animals. There are three main types of fossil fuels: coal, petroleum, and natural gas. Another fossil fuel, liquefied petroleum gas (LPG), is principally derived from the production of natural gas. Heat from burning fossil fuel is used either directly for space heating and process heating, or converted to mechanical energy for vehicles, industrial processes, or electrical power generation. These fossil fuels are part of the carbon cycle and allow solar energy stored in the fuel to be released. The use of fossil fuels in the 18th and 19th century set the stage for the Industrial Revolution. Fossil fuels make up the bulk of the world's current primary energy sources. In 2005, 81% of the world's energy needs was met from fossil sources. The technology and infrastructure for the use of fossil fuels already exist. Liquid fuels derived from petroleum deliver much usable energy per unit of weight or volume, which is advantageous when compared with lower energy density sources such as batteries. Fossil fuels are currently economical for decentralized energy use. Energy dependence on imported fossil fuels creates energy security risks for dependent countries. Oil dependence in particular has led to war, funding of radicals, monopolization, and socio-political instability. Fossil fuels are non-renewable resources, which will eventually decline in production and become exhausted. While the processes that created fossil fuels are ongoing, fuels are consumed far more quickly than the natural rate of replenishment. Extracting fuels becomes increasingly costly as society consumes the most accessible fuel deposits. Extraction of fossil fuels results in environmental degradation, such as the strip mining and mountaintop removal for coal. Fuel efficiency is a form of thermal efficiency, meaning the efficiency of a process that converts chemical potential energy contained in a carrier fuel into kinetic energy or work. The fuel economy is the energy efficiency of a particular vehicle, is given as a ratio of distance travelled per unit of fuel consumed. Weight-specific efficiency (efficiency per unit weight) may be stated for freight, and passenger-specific efficiency (vehicle efficiency) per passenger. The inefficient atmospheric combustion (burning) of fossil fuels in vehicles, buildings, and power plants contributes to urban heat islands. Conventional production of oil peaked, conservatively, between 2007 and 2010. In 2010, it was estimated that an investment of $8 trillion in non-renewable resources would be required to maintain current levels of production for 25 years. In 2010, governments subsidized fossil fuels by an estimated $500 billion a year. Fossil fuels are also a source of greenhouse gas emissions, leading to concerns about global warming if consumption is not reduced. The combustion of fossil fuels leads to the release of pollution into the atmosphere. The fossil fuels are mainly carbon compounds. During combustion, carbon dioxide is released, and also nitrogen oxides, soot and other fine particulates. The carbon dioxide is the main contributor to recent climate change. Other emissions from fossil fuel power station include sulphur dioxide, carbon monoxide (CO), hydrocarbons, volatile organic compounds (VOC), mercury, arsenic, lead, cadmium, and other heavy metals including traces of uranium. A typical coal plant generates billions of kilowatt hours of electrical power per year. == Nuclear == === Fission === Nuclear power is the use of nuclear fission to generate useful heat and electricity. Fission of uranium produces nearly all economically significant nuclear power. Radioisotope thermoelectric generators form a very small component of energy generation, mostly in specialized applications such as deep space vehicles. Nuclear power plants, excluding naval reactors, provided about 5.7% of the world's energy and 13% of the world's electricity in 2012. In 2013, the IAEA report that there are 437 operational nuclear power reactors, in 31 countries, although not every reactor is producing electricity. In addition, there are approximately 140 naval vessels using nuclear propulsion in operation, powered by some 180 reactors. As of 2013, attaining a net energy gain from sustained nuclear fusion reactions, excluding natural fusion power sources such as the Sun, remains an ongoing area of international physics and engineering research. More than 60 years after the first attempts, commercial fusion power production remains unlikely before 2050. There is an ongoing debate about nuclear power. Proponents, such as the World Nuclear Association, the IAEA and Environmentalists for Nuclear Energy contend that nuclear power is a safe, sustainable energy source that reduces carbon emissions. Opponents contend that nuclear power poses many threats to people and the environment. Nuclear power plant accidents include the Chernobyl disaster (1986), Fukushima Daiichi nuclear disaster (2011), and the Three Mile Island accident (1979). There have also been some nuclear submarine accidents. In terms of lives lost per unit of energy generated, analysis has determined that nuclear power has caused less fatalities per unit of energy generated than the other major sources of energy generation. Energy production from coal, petroleum, natural gas and hydropower has caused a greater number of fatalities per unit of energy generated due to air pollution and energy accident effects. However, the economic costs of nuclear power accidents is high, and meltdowns can take decades to clean up. The human costs of evacuations of affected populations and lost livelihoods is also significant. Comparing Nuclear's latent cancer deaths, such as cancer with other energy sources immediate deaths per unit of energy generated(GWeyr). This study does not include fossil fuel related cancer and other indirect deaths created by the use of fossil fuel consumption in its "severe accident" classification, which would be an accident with more than 5 fatalities. As of 2012, according to the IAEA, worldwide there were 68 civil nuclear power reactors under construction in 15 countries, approximately 28 of which in the People's Republic of China (PRC), with the most recent nuclear power reactor, as of May 2013, to be connected to the electrical grid, occurring on February 17, 2013, in Hongyanhe Nuclear Power Plant in the PRC. In the United States, two new Generation III reactors are under construction at Vogtle. U.S. nuclear industry officials expect five new reactors to enter service by 2020, all at existing plants. In 2013, four aging, uncompetitive, reactors were permanently closed. Recent experiments in extraction of uranium use polymer ropes that are coated with a substance that selectively absorbs uranium from seawater. This process could make the considerable volume of uranium dissolved in seawater exploitable for energy production. Since ongoing geologic processes carry uranium to the sea in amounts comparable to the amount that would be extracted by this process, in a sense the sea-borne uranium becomes a sustainable resource. Nuclear power is a low carbon power generation method of producing electricity, with an analysis of the literature on its total life cycle emission intensity finding that it is similar to renewable sources in a comparison of greenhouse gas (GHG) emissions per unit of energy generated. Since the 1970s, nuclear fuel has displaced about 64 gigatonnes of carbon dioxide equivalent (GtCO2-eq) greenhouse gases, that would have otherwise resulted from the burning of oil, coal or natural gas in fossil-fuel power stations. ==== Nuclear power phase-out and pull-backs ==== Japan's 2011 Fukushima Daiichi nuclear accident, which occurred in a reactor design from the 1960s, prompted a rethink of nuclear safety and nuclear energy policy in many countries. Germany decided to close all its reactors by 2022, and Italy has banned nuclear power. Following Fukushima, in 2011 the International Energy Agency halved its estimate of additional nuclear generating capacity to be built by 2035. ===== Fukushima ===== Following the 2011 Fukushima Daiichi nuclear disaster – the second worst nuclear incident, that displaced 50,000 households after radioactive material leaked into the air, soil and sea, and with subsequent radiation checks leading to bans on some shipments of vegetables and fish – a global public support survey by Ipsos (2011) for energy sources was published and nuclear fission was found to be the least popular ==== Fission economics ==== The economics of new nuclear power plants is a controversial subject, since there are diverging views on this topic, and multibillion-dollar investments ride on the choice of an energy source. Nuclear power plants typically have high capital costs for building the plant, but low direct fuel costs. In recent years there has been a slowdown of electricity demand growth and financing has become more difficult, which affects large projects such as nuclear reactors, with very large upfront costs and long project cycles which carry a large variety of risks. In Eastern Europe, a number of long-established projects are struggling to find finance, notably Belene in Bulgaria and the additional reactors at Cernavoda in Romania, and some potential backers have pulled out. Where cheap gas is available and its future supply relatively secure, this also poses a major problem for nuclear projects. Analysis of the economics of nuclear power must take into account who bears the risks of future uncertainties. To date all operating nuclear power plants were developed by state-owned or regulated utility monopolies where many of the risks associated with construction costs, operating performance, fuel price, and other factors were borne by consumers rather than suppliers. Many countries have now liberalized the electricity market where these risks, and the risk of cheaper competitors emerging before capital costs are recovered, are borne by plant suppliers and operators rather than consumers, which leads to a significantly different evaluation of the economics of new nuclear power plants. ==== Costs ==== Costs are likely to go up for currently operating and new nuclear power plants, due to increased requirements for on-site spent fuel management and elevated design basis threats. While first of their kind designs, such as the EPRs under construction are behind schedule and over-budget, of the seven South Korean APR-1400s presently under construction worldwide, two are in S.Korea at the Hanul Nuclear Power Plant and four are at the largest nuclear station construction project in the world as of 2016, in the United Arab Emirates at the planned Barakah nuclear power plant. The first reactor, Barakah-1 is 85% completed and on schedule for grid-connection during 2017. Two of the four EPRs under construction (in Finland and France) are significantly behind schedule and substantially over cost. == Renewable sources == Renewable energy is generally defined as energy that comes from resources which are naturally replenished on a human timescale such as sunlight, wind, rain, tides, waves and geothermal heat. Renewable energy replaces conventional fuels in four distinct areas: electricity generation, hot water/space heating, motor fuels, and rural (off-grid) energy services. Including traditional biomass usage, about 19% of global energy consumption is accounted for by renewable resources. Wind powered energy production is being turned to as a prominent renewable energy source, increasing global wind power capacity by 12% in 2021. While not the case for all countries, 58% of sample countries linked renewable energy consumption to have a positive impact on economic growth. At the national level, at least 30 nations around the world already have renewable energy contributing more than 20% of energy supply. National renewable energy markets are projected to continue to grow strongly in the coming decade and beyond.[76] Unlike other energy sources, renewable energy sources are not as restricted by geography. Additionally deployment of renewable energy is resulting in economic benefits as well as combating climate change. Rural electrification has been researched on multiple sites and positive effects on commercial spending, appliance use, and general activities requiring electricity as energy. Renewable energy growth in at least 38 countries has been driven by the high electricity usage rates. International support for promoting renewable sources like solar and wind have continued grow. While many renewable energy projects are large-scale, renewable technologies are also suited to rural and remote areas and developing countries, where energy is often crucial in human development. To ensure human development continues sustainably, governments around the world are beginning to research potential ways to implement renewable sources into their countries and economies. For example, the UK Government’s Department for Energy and Climate Change 2050 Pathways created a mapping technique to educate the public on land competition between energy supply technologies. This tool provides users the ability to understand what the limitations and potential their surrounding land and country has in terms of energy production. === Hydroelectricity === Hydroelectricity is electric power generated by hydropower; the force of falling or flowing water. In 2015 hydropower generated 16.6% of the world's total electricity and 70% of all renewable electricity and was expected to increase about 3.1% each year for the following 25 years. Hydropower is produced in 150 countries, with the Asia-Pacific region generating 32 percent of global hydropower in 2010. China is the largest hydroelectricity producer, with 721 terawatt-hours of production in 2010, representing around 17 percent of domestic electricity use. There are now three hydroelectricity plants larger than 10 GW: the Three Gorges Dam in China, Itaipu Dam across the Brazil/Paraguay border, and Guri Dam in Venezuela. The cost of hydroelectricity is relatively low, making it a competitive source of renewable electricity. The average cost of electricity from a hydro plant larger than 10 megawatts is 3 to 5 U.S. cents per kilowatt-hour. Hydro is also a flexible source of electricity since plants can be ramped up and down very quickly to adapt to changing energy demands. However, damming interrupts the flow of rivers and can harm local ecosystems, and building large dams and reservoirs often involves displacing people and wildlife. Once a hydroelectric complex is constructed, the project produces no direct waste, and has a considerably lower output level of the greenhouse gas carbon dioxide than fossil fuel powered energy plants. === Wind === Wind power harnesses the power of the wind to propel the blades of wind turbines. These turbines cause the rotation of magnets, which creates electricity. Wind towers are usually built together on wind farms. There are offshore and onshore wind farms. Global wind power capacity has expanded rapidly to 336 GW in June 2014, and wind energy production was around 4% of total worldwide electricity usage, and growing rapidly. Wind power is widely used in Europe, Asia, and the United States. Several countries have achieved relatively high levels of wind power penetration, such as 21% of stationary electricity production in Denmark, 18% in Portugal, 16% in Spain, 14% in Ireland, and 9% in Germany in 2010.: 11  By 2011, at times over 50% of electricity in Germany and Spain came from wind and solar power. As of 2011, 83 countries around the world are using wind power on a commercial basis.: 11  Many of the world's largest onshore wind farms are located in the United States, China, and India. Most of the world's largest offshore wind farms are located in Denmark, Germany and the United Kingdom. The two largest offshore wind farm are currently the 630 MW London Array and Gwynt y Môr. === Solar === === Biofuels === A biofuel is a fuel that contains energy from geologically recent carbon fixation. These fuels are produced from living organisms. Examples of this carbon fixation occur in plants and microalgae. These fuels are made by a biomass conversion (biomass refers to recently living organisms, most often referring to plants or plant-derived materials). This biomass can be converted to convenient energy containing substances in three different ways: thermal conversion, chemical conversion, and biochemical conversion. This biomass conversion can result in fuel in solid, liquid, or gas form. This new biomass can be used for biofuels. Biofuels have increased in popularity because of rising oil prices and the need for energy security. Bioethanol is an alcohol made by fermentation, mostly from carbohydrates produced in sugar or starch crops such as corn or sugarcane. Cellulosic biomass, derived from non-food sources, such as trees and grasses, is also being developed as a feedstock for ethanol production. Ethanol can be used as a fuel for vehicles in its pure form, but it is usually used as a gasoline additive to increase octane and improve vehicle emissions. Bioethanol is widely used in the USA and in Brazil. Current plant design does not provide for converting the lignin portion of plant raw materials to fuel components by fermentation. Biodiesel is made from vegetable oils and animal fats. Biodiesel can be used as a fuel for vehicles in its pure form, but it is usually used as a diesel additive to reduce levels of particulates, carbon monoxide, and hydrocarbons from diesel-powered vehicles. Biodiesel is produced from oils or fats using transesterification and is the most common biofuel in Europe. However, research is underway on producing renewable fuels from decarboxylation In 2010, worldwide biofuel production reached 105 billion liters (28 billion gallons US), up 17% from 2009, and biofuels provided 2.7% of the world's fuels for road transport, a contribution largely made up of ethanol and biodiesel. Global ethanol fuel production reached 86 billion liters (23 billion gallons US) in 2010, with the United States and Brazil as the world's top producers, accounting together for 90% of global production. The world's largest biodiesel producer is the European Union, accounting for 53% of all biodiesel production in 2010. As of 2011, mandates for blending biofuels exist in 31 countries at the national level and in 29 states or provinces.: 13–14  The International Energy Agency has a goal for biofuels to meet more than a quarter of world demand for transportation fuels by 2050 to reduce dependence on petroleum and coal. === Geothermal === Geothermal energy is thermal energy generated and stored in the Earth. Thermal energy is the energy that determines the temperature of matter. The geothermal energy of the Earth's crust originates from the original formation of the planet (20%) and from radioactive decay of minerals (80%). The geothermal gradient, which is the difference in temperature between the core of the planet and its surface, drives a continuous conduction of thermal energy in the form of heat from the core to the surface. The adjective geothermal originates from the Greek roots γη (ge), meaning earth, and θερμος (thermos), meaning hot. Earth's internal heat is thermal energy generated from radioactive decay and continual heat loss from Earth's formation. Temperatures at the core-mantle boundary may reach over 4000 °C (7,200 °F). The high temperature and pressure in Earth's interior cause some rock to melt and solid mantle to behave plastically, resulting in portions of mantle convecting upward since it is lighter than the surrounding rock. Rock and water is heated in the crust, sometimes up to 370 °C (700 °F). From hot springs, geothermal energy has been used for bathing since Paleolithic times and for space heating since ancient Roman times, but it is now better known for electricity generation. Worldwide, 11,400 megawatts (MW) of geothermal power is online in 24 countries in 2012. An additional 28 gigawatts of direct geothermal heating capacity is installed for district heating, space heating, spas, industrial processes, desalination and agricultural applications in 2010. Geothermal power is cost effective, reliable, sustainable, and environmentally friendly, but has historically been limited to areas near tectonic plate boundaries. Recent technological advances have dramatically expanded the range and size of viable resources, especially for applications such as home heating, opening a potential for widespread exploitation. Geothermal wells release greenhouse gases trapped deep within the earth, but these emissions are much lower per energy unit than those of fossil fuels. As a result, geothermal power has the potential to help mitigate global warming if widely deployed in place of fossil fuels. The Earth's geothermal resources are theoretically more than adequate to supply humanity's energy needs, but only a very small fraction may be profitably exploited. Drilling and exploration for deep resources is very expensive. Forecasts for the future of geothermal power depend on assumptions about technology, energy prices, subsidies, and interest rates. Pilot programs like EWEB's customer opt in Green Power Program show that customers would be willing to pay a little more for a renewable energy source like geothermal. But as a result of government assisted research and industry experience, the cost of generating geothermal power has decreased by 25% over the past two decades. In 2001, geothermal energy cost between two and ten US cents per kWh. === Oceanic === Marine Renewable Energy (MRE) or marine power (also sometimes referred to as ocean energy, ocean power, or marine and hydrokinetic energy) refers to the energy carried by the mechanical energy of ocean waves, currents, and tides, shifts in salinity gradients, and ocean temperature differences. MRE has the potential to become a reliable and renewable energy source because of the cyclical nature of the oceans. The movement of water in the world's oceans creates a vast store of kinetic energy or energy in motion. This energy can be harnessed to generate electricity to power homes, transport, and industries. The term marine energy encompasses both wave power, i.e. power from surface waves, and tidal power, i.e. obtained from the kinetic energy of large bodies of moving water. Offshore wind power is not a form of marine energy, as wind power is derived from the wind, even if the wind turbines are placed over water. The oceans have a tremendous amount of energy and are close to many if not most concentrated populations. Ocean energy has the potential to provide a substantial amount of new renewable energy around the world. Marine energy technology is in its first stage of development. To be developed, MRE needs efficient methods of storing, transporting, and capturing ocean power, so it can be used where needed. Over the past year, countries around the world have started implementing market strategies for MRE to commercialize. Canada and China introduced incentives, such as feed-in tariffs (FiTs), which are above-market prices for MRE that allow investors and project developers a stable income. Other financial strategies consist of subsidies, grants, and funding from public-private partnerships (PPPs). China alone approved 100 ocean projects in 2019. Portugal and Spain recognize the potential of MRE in accelerating decarbonization, which is fundamental to meeting the goals of the Paris Agreement. Both countries are focusing on solar and offshore wind auctions to attract private investment, ensure cost-effectiveness, and accelerate MRE growth. Ireland sees MRE as a key component to reduce its carbon footprint. The Offshore Renewable Energy Development Plan (OREDP) supports the exploration and development of the country's significant offshore energy potential. Additionally, Ireland has implemented the Renewable Electricity Support Scheme (RESS) which includes auctions designed to provide financial support for communities, increase technology diversity, and guarantee energy security. However, while research is increasing, there have been concerns associated with threats to marine mammals, habitats, and potential changes to ocean currents. MRE can be a renewable energy source for coastal communities helping their transition from fossil fuel, but researchers are calling for a better understanding of its environmental impacts. Because ocean-energy areas are often isolated from both fishing and sea traffic, these zones may provide shelter from humans and predators for some marine species. MRE devices can be an ideal home for many fish, crayfish, mollusks, and barnacles; and may also indirectly affect seabirds, and marine mammals because they feed on those species. Similarly, such areas may create an "artificial reef effect" by boosting biodiversity nearby. Noise pollution generated from the technology is limited, also causing fish and mammals living in the area of the installation to return. In the most recent State of Science Report about MRE, the authors claim that there is no evidence for fish, mammals, or seabirds to be injured by either collision, noise pollution, or the electromagnetic field. The uncertainty of its environmental impact comes from the low quantity of MRE devices in the ocean today where data is collected. === 100% renewable energy === The incentive to use 100% renewable energy, for electricity, transport, or even total primary energy supply globally, has been motivated by global warming and other ecological as well as economic concerns. Renewable energy use has grown much faster than anyone anticipated. The Intergovernmental Panel on Climate Change has said that there are few fundamental technological limits to integrating a portfolio of renewable energy technologies to meet most of total global energy demand. At the national level, at least 30 nations around the world already have renewable energy contributing more than 20% of energy supply. Also, Stephen W. Pacala and Robert H. Socolow have developed a series of "stabilization wedges" that can allow us to maintain our quality of life while avoiding catastrophic climate change, and "renewable energy sources," in aggregate, constitute the largest number of their "wedges." Mark Z. Jacobson says producing all new energy with wind power, solar power, and hydropower by 2030 is feasible and existing energy supply arrangements could be replaced by 2050. Barriers to implementing the renewable energy plan are seen to be "primarily social and political, not technological or economic". Jacobson says that energy costs with a wind, solar, water system should be similar to today's energy costs. Similarly, in the United States, the independent National Research Council has noted that "sufficient domestic renewable resources exist to allow renewable electricity to play a significant role in future electricity generation and thus help confront issues related to climate change, energy security, and the escalation of energy costs ... Renewable energy is an attractive option because renewable resources available in the United States, taken collectively, can supply significantly larger amounts of electricity than the total current or projected domestic demand." . Critics of the "100% renewable energy" approach include Vaclav Smil and James E. Hansen. Smil and Hansen are concerned about the variable output of solar and wind power, but Amory Lovins argues that the electricity grid can cope, just as it routinely backs up nonworking coal-fired and nuclear plants with working ones. Google spent $30 million on their "Renewable Energy Cheaper than Coal" project to develop renewable energy and stave off catastrophic climate change. The project was cancelled after concluding that a best-case scenario for rapid advances in renewable energy could only result in emissions 55 percent below the fossil fuel projections for 2050. == Increased energy efficiency == Although increasing the efficiency of energy use is not energy development per se, it may be considered under the topic of energy development since it makes existing energy sources available to do work.: 22  Efficient energy use reduces the amount of energy required to provide products and services. For example, insulating a home allows a building to use less heating and cooling energy to maintain a comfortable temperature. Installing fluorescent lamps or natural skylights reduces the amount of energy required for illumination compared to incandescent light bulbs. Compact fluorescent lights use two-thirds less energy and may last 6 to 10 times longer than incandescent lights. Improvements in energy efficiency are most often achieved by adopting an efficient technology or production process. Reducing energy use may save consumers money, if the energy savings offsets the cost of an energy efficient technology. Reducing energy use reduces emissions. According to the International Energy Agency, improved energy efficiency in buildings, industrial processes and transportation could reduce the global energy demand in 2050 to around 8% smaller than today, but serving an economy more than twice as big and a population of about 2 billion more people. Energy efficiency and renewable energy are said to be the twin pillars of sustainable energy policy. In many countries energy efficiency is also seen to have a national security benefit because it can be used to reduce the level of energy imports from foreign countries and may slow down the rate at which domestic energy resources are depleted. It's been discovered "that for OECD countries, wind, geothermal, hydro and nuclear have the lowest hazard rates among energy sources in production". == Transmission == While new sources of energy are only rarely discovered or made possible by new technology, distribution technology continually evolves. The use of fuel cells in cars, for example, is an anticipated delivery technology. This section presents the various delivery technologies that have been important to historic energy development. They all rely in way on the energy sources listed in the previous section. === Shipping and pipelines === Coal, petroleum and their derivatives are delivered by boat, rail, or road. Petroleum and natural gas may also be delivered by pipeline, and coal via a Slurry pipeline. Fuels such as gasoline and LPG may also be delivered via aircraft. Natural gas pipelines must maintain a certain minimum pressure to function correctly. The higher costs of ethanol transportation and storage are often prohibitive. === Wired energy transfer === Electricity grids are the networks used to transmit and distribute power from production source to end user, when the two may be hundreds of kilometres away. Sources include electrical generation plants such as a nuclear reactor, coal burning power plant, etc. A combination of sub-stations and transmission lines are used to maintain a constant flow of electricity. Grids may suffer from transient blackouts and brownouts, often due to weather damage. During certain extreme space weather events solar wind can interfere with transmissions. Grids also have a predefined carrying capacity or load that cannot safely be exceeded. When power requirements exceed what's available, failures are inevitable. To prevent problems, power is then rationed. Industrialised countries such as Canada, the US, and Australia are among the highest per capita consumers of electricity in the world, which is possible thanks to a widespread electrical distribution network. The US grid is one of the most advanced, although infrastructure maintenance is becoming a problem. CurrentEnergy provides a realtime overview of the electricity supply and demand for California, Texas, and the Northeast of the US. African countries with small scale electrical grids have a correspondingly low annual per capita usage of electricity. One of the most powerful power grids in the world supplies power to the state of Queensland, Australia. === Wireless energy transfer === Wireless power transfer is a process whereby electrical energy is transmitted from a power source to an electrical load that does not have a built-in power source, without the use of interconnecting wires. Currently available technology is limited to short distances and relatively low power level. Orbiting solar power collectors would require wireless transmission of power to Earth. The proposed method involves creating a large beam of microwave-frequency radio waves, which would be aimed at a collector antenna site on the Earth. Formidable technical challenges exist to ensure the safety and profitability of such a scheme. == Storage == Energy storage is accomplished by devices or physical media that store energy to perform useful operation at a later time. A device that stores energy is sometimes called an accumulator. All forms of energy are either potential energy (e.g. Chemical, gravitational, electrical energy, temperature differential, latent heat, etc.) or kinetic energy (e.g. momentum). Some technologies provide only short-term energy storage, and others can be very long-term such as power to gas using hydrogen or methane and the storage of heat or cold between opposing seasons in deep aquifers or bedrock. A wind-up clock stores potential energy (in this case mechanical, in the spring tension), a battery stores readily convertible chemical energy to operate a mobile phone, and a hydroelectric dam stores energy in a reservoir as gravitational potential energy. Ice storage tanks store ice (thermal energy in the form of latent heat) at night to meet peak demand for cooling. Fossil fuels such as coal and gasoline store ancient energy derived from sunlight by organisms that later died, became buried and over time were then converted into these fuels. Even food (which is made by the same process as fossil fuels) is a form of energy stored in chemical form. == History == Since prehistory, when humanity discovered fire to warm up and roast food, through the Middle Ages in which populations built windmills to grind the wheat, until the modern era in which nations can get electricity splitting the atom. Man has sought endlessly for energy sources. Except nuclear, geothermal and tidal, all other energy sources are from current solar isolation or from fossil remains of plant and animal life that relied upon sunlight. Ultimately, solar energy itself is the result of the Sun's nuclear fusion. Geothermal power from hot, hardened rock above the magma of the Earth's core is the result of the decay of radioactive materials present beneath the Earth's crust, and nuclear fission relies on man-made fission of heavy radioactive elements in the Earth's crust; in both cases these elements were produced in supernova explosions before the formation of the Solar System. Since the beginning of the Industrial Revolution, the question of the future of energy supplies has been of interest. In 1865, William Stanley Jevons published The Coal Question in which he saw that the reserves of coal were being depleted and that oil was an ineffective replacement. In 1914, U.S. Bureau of Mines stated that the total production was 5.7 billion barrels (910,000,000 m3). In 1956, Geophysicist M. King Hubbert deduces that U.S. oil production would peak between 1965 and 1970 and that oil production will peak "within half a century" on the basis of 1956 data. In 1989, predicted peak by Colin Campbell In 2004, OPEC estimated, with substantial investments, it would nearly double oil output by 2025 === Sustainability === The environmental movement has emphasized sustainability of energy use and development. Renewable energy is sustainable in its production; the available supply will not be diminished for the foreseeable future - millions or billions of years. "Sustainability" also refers to the ability of the environment to cope with waste products, especially air pollution. Sources which have no direct waste products (such as wind, solar, and hydropower) are brought up on this point. With global demand for energy growing, the need to adopt various energy sources is growing. Energy conservation is an alternative or complementary process to energy development. It reduces the demand for energy by using it efficiently. === Resilience === Some observers contend that idea of "energy independence" is an unrealistic and opaque concept. The alternative offer of "energy resilience" is a goal aligned with economic, security, and energy realities. The notion of resilience in energy was detailed in the 1982 book Brittle Power: Energy Strategy for National Security. The authors argued that simply switching to domestic energy would not be secure inherently because the true weakness is the often interdependent and vulnerable energy infrastructure of a country. Key aspects such as gas lines and the electrical power grid are often centralized and easily susceptible to disruption. They conclude that a "resilient energy supply" is necessary for both national security and the environment. They recommend a focus on energy efficiency and renewable energy that is decentralized. In 2008, former Intel Corporation Chairman and CEO Andrew Grove looked to energy resilience, arguing that complete independence is unfeasible given the global market for energy. He describes energy resilience as the ability to adjust to interruptions in the supply of energy. To that end, he suggests the U.S. make greater use of electricity. Electricity can be produced from a variety of sources. A diverse energy supply will be less affected by the disruption in supply of any one source. He reasons that another feature of electrification is that electricity is "sticky" – meaning the electricity produced in the U.S. is to stay there because it cannot be transported overseas. According to Grove, a key aspect of advancing electrification and energy resilience will be converting the U.S. automotive fleet from gasoline-powered to electric-powered. This, in turn, will require the modernization and expansion of the electrical power grid. As organizations such as The Reform Institute have pointed out, advancements associated with the developing smart grid would facilitate the ability of the grid to absorb vehicles en masse connecting to it to charge their batteries. === Present and future === Extrapolations from current knowledge to the future offer a choice of energy futures. Predictions parallel the Malthusian catastrophe hypothesis. Numerous are complex models based scenarios as pioneered by Limits to Growth. Modeling approaches offer ways to analyze diverse strategies, and hopefully find a road to rapid and sustainable development of humanity. Short term energy crises are also a concern of energy development. Extrapolations lack plausibility, particularly when they predict a continual increase in oil consumption. Energy production usually requires an energy investment. Drilling for oil or building a wind power plant requires energy. The fossil fuel resources that are left are often increasingly difficult to extract and convert. They may thus require increasingly higher energy investments. If investment is greater than the value of the energy produced by the resource, it is no longer an effective energy source. These resources are no longer an energy source but may be exploited for value as raw materials. New technology may lower the energy investment required to extract and convert the resources, although ultimately basic physics sets limits that cannot be exceeded. Between 1950 and 1984, as the Green Revolution transformed agriculture around the globe, world grain production increased by 250%. The energy for the Green Revolution was provided by fossil fuels in the form of fertilizers (natural gas), pesticides (oil), and hydrocarbon fueled irrigation. The peaking of world hydrocarbon production (peak oil) may lead to significant changes, and require sustainable methods of production. One vision of a sustainable energy future involves all human structures on the earth's surface (i.e., buildings, vehicles and roads) doing artificial photosynthesis (using sunlight to split water as a source of hydrogen and absorbing carbon dioxide to make fertilizer) efficiently than plants. With contemporary space industry's economic activity and the related private spaceflight, with the manufacturing industries, that go into Earth's orbit or beyond, delivering them to those regions will require further energy development. Researchers have contemplated space-based solar power for collecting solar power for use on Earth. Space-based solar power has been in research since the early 1970s. Space-based solar power would require construction of collector structures in space. The advantage over ground-based solar power is higher intensity of light, and no weather to interrupt power collection. == Energy technology == Energy technology is an interdisciplinary engineering science having to do with the efficient, safe, environmentally friendly, and economical extraction, conversion, transportation, storage, and use of energy, targeted towards yielding high efficiency whilst skirting side effects on humans, nature, and the environment. For people, energy is an overwhelming need, and as a scarce resource, it has been an underlying cause of political conflicts and wars. The gathering and use of energy resources can be harmful to local ecosystems and may have global outcomes. Energy is also the capacity to do work. We can get energy from food. Energy can be of different forms such as kinetic, potential, mechanical, heat, light etc. Energy is required for individuals and the whole society for lighting, heating, cooking, running, industries, operating transportation and so forth. Basically there are two types of energy depending on the source s they are; 1.Renewable Energy Sources 2.Non-Renewable Energy Sources === Interdisciplinary fields === As an interdisciplinary science Energy technology is linked with many interdisciplinary fields in sundry, overlapping ways. Physics, for thermodynamics and nuclear physics Chemistry for fuel, combustion, air pollution, flue gas, battery technology and fuel cells. Electrical engineering Engineering, often for fluid energy machines such as combustion engines, turbines, pumps and compressors. Geography, for geothermal energy and exploration for resources. Mining, for petrochemical and fossil fuels. Agriculture and forestry, for sources of renewable energy. Meteorology for wind and solar energy. Water and Waterways, for hydropower. Waste management, for environmental impact. Transportation, for energy-saving transportation systems. Environmental studies, for studying the effect of energy use and production on the environment, nature and climate change. (Lighting Technology), for Interior and Exterior Natural as well as Artificial Lighting Design, Installations, and Energy Savings (Energy Cost/Benefit Analysis), for Simple Payback and Life Cycle Costing of Energy Efficiency/Conservation Measures Recommended === Electrical engineering === Electric power engineering deals with the production and use of electrical energy, which can entail the study of machines such as generators, electric motors and transformers. Infrastructure involves substations and transformer stations, power lines and electrical cable. Load management and power management over networks have meaningful sway on overall energy efficiency. Electric heating is also widely used and researched. === Thermodynamics === Thermodynamics deals with the fundamental laws of energy conversion and is drawn from theoretical Physics. === Thermal and chemical energy === Thermal and chemical energy are intertwined with chemistry and environmental studies. Combustion has to do with burners and chemical engines of all kinds, grates and incinerators along with their energy efficiency, pollution and operational safety. Exhaust gas purification technology aims to lessen air pollution through sundry mechanical, thermal and chemical cleaning methods. Emission control technology is a field of process and chemical engineering. Boiler technology deals with the design, construction and operation of steam boilers and turbines (also used in nuclear power generation, see below), drawn from applied mechanics and materials engineering. Energy conversion has to do with internal combustion engines, turbines, pumps, fans and so on, which are used for transportation, mechanical energy and power generation. High thermal and mechanical loads bring about operational safety worries which are dealt with through many branches of applied engineering science. === Nuclear energy === Nuclear technology deals with nuclear power production from nuclear reactors, along with the processing of nuclear fuel and disposal of radioactive waste, drawing from applied nuclear physics, nuclear chemistry and radiation science. Nuclear power generation has been politically controversial in many countries for several decades but the electrical energy produced through nuclear fission is of worldwide importance. There are high hopes that fusion technologies will one day replace most fission reactors but this is still a research area of nuclear physics. === Renewable energy === Renewable energy has many branches. ==== Wind power ==== Wind turbines convert wind energy into electricity by connecting a spinning rotor to a generator. Wind turbines draw energy from atmospheric currents and are designed using aerodynamics along with knowledge taken from mechanical and electrical engineering. The wind passes across the aerodynamic rotor blades, creating an area of higher pressure and an area of lower pressure on either side of the blade. The forces of lift and drag are formed due to the difference in air pressure. The lift force is stronger than the drag force; therefore the rotor, which is connected to a generator, spins. The energy is then created due to the change from the aerodynamic force to the rotation of the generator. Being recognized as one of the most efficient renewable energy sources, wind power is becoming more and more relevant and used in the world. Wind power does not use any water in the production of energy making it a good source of energy for areas without much water. Wind energy could also be produced even if the climate changes in line with current predictions, as it relies solely on wind. ==== Geothermal ==== Deep within the Earth, is an extreme heat producing layer of molten rock called magma. The very high temperatures from the magma heats nearby groundwater. There are various technologies that have been developed in order to benefit from such heat, such as using different types of power plants (dry, flash or binary), heat pumps, or wells. These processes of harnessing the heat incorporate an infrastructure which has in one form or another a turbine which is spun by either the hot water or the steam produced by it. The spinning turbine, being connected to a generator, produces energy. A more recent innovation involves the use of shallow closed-loop systems that pump heat to and from structures by taking advantage of the constant temperature of soil around 10 feet deep. ==== Hydropower ==== Hydropower draws mechanical energy from rivers, ocean waves and tides. Civil engineering is used to study and build dams, tunnels, waterways and manage coastal resources through hydrology and geology. A low speed water turbine spun by flowing water can power an electrical generator to produce electricity. ==== Bioenergy ==== Bioenergy deals with the gathering, processing and use of biomasses grown in biological manufacturing, agriculture and forestry from which power plants can draw burning fuel. Ethanol, methanol (both controversial) or hydrogen for fuel cells can be had from these technologies and used to generate electricity. ==== Enabling technologies ==== Heat pumps and Thermal energy storage are classes of technologies that can enable the utilization of renewable energy sources that would otherwise be inaccessible due to a temperature that is too low for utilization or a time lag between when the energy is available and when it is needed. While enhancing the temperature of available renewable thermal energy, heat pumps have the additional property of leveraging electrical power (or in some cases mechanical or thermal power) by using it to extract additional energy from a low quality source (such as seawater, lake water, the ground, the air, or waste heat from a process). Thermal storage technologies allow heat or cold to be stored for periods of time ranging from hours or overnight to interseasonal, and can involve storage of sensible energy (i.e. by changing the temperature of a medium) or latent energy (i.e. through phase changes of a medium, such between water and slush or ice). Short-term thermal storages can be used for peak-shaving in district heating or electrical distribution systems. Kinds of renewable or alternative energy sources that can be enabled include natural energy (e.g. collected via solar-thermal collectors, or dry cooling towers used to collect winter's cold), waste energy (e.g. from HVAC equipment, industrial processes or power plants), or surplus energy (e.g. as seasonally from hydropower projects or intermittently from wind farms). The Drake Landing Solar Community (Alberta, Canada) is illustrative. borehole thermal energy storage allows the community to get 97% of its year-round heat from solar collectors on the garage roofs, which most of the heat collected in summer. Types of storages for sensible energy include insulated tanks, borehole clusters in substrates ranging from gravel to bedrock, deep aquifers, or shallow lined pits that are insulated on top. Some types of storage are capable of storing heat or cold between opposing seasons (particularly if very large), and some storage applications require inclusion of a heat pump. Latent heat is typically stored in ice tanks or what are called phase-change materials (PCMs). == See also == World energy supply and consumption Technology Water-energy nexus Policy Energy policy, Energy policy of the United States, Energy policy of China, Energy policy of India, Energy policy of the European Union, Energy policy of the United Kingdom, Energy policy of Russia, Energy policy of Brazil, Energy policy of Canada, Energy policy of the Soviet Union, Energy Industry Liberalization and Privatization (Thailand) General Seasonal thermal energy storage (Interseasonal thermal energy storage), Geomagnetically induced current, Energy harvesting, Timeline of sustainable energy research 2020–present Feedstock Raw material, Biomaterial, Energy consumption, Materials science, Recycling, Upcycling, Downcycling Others Thorium-based nuclear power, List of oil pipelines, List of natural gas pipelines, Ocean thermal energy conversion, Growth of photovoltaics == References == == Sources == Armstrong, Robert C., Catherine Wolfram, Robert Gross, Nathan S. Lewis, and M.V. Ramana et al. The Frontiers of Energy, Nature Energy, Vol 1, 11 January 2016. Serra, J. "Alternative Fuel Resource Development", Clean and Green Fuels Fund, (2006). Bilgen, S. and K. Kaygusuz, Renewable Energy for a Clean and Sustainable Future, Energy Sources 26, 1119 (2004). Energy analysis of Power Systems, UIC Nuclear Issues Briefing Paper 57 (2004). Silvestre B. S., Dalcol P. R. T. (2009). "Geographical proximity and innovation: Evidences from the Campos Basin oil & gas industrial agglomeration — Brazil". Technovation. 29 (8): 546–561. doi:10.1016/j.technovation.2009.01.003. == Journals == Energy Sources, Part A: Recovery, Utilization and Environmental Effects Energy Sources, Part B: Economics, Planning and Policy International Journal of Green Energy == External links == Bureau of Land Management 2012 Renewable Energy Priority Projects Energypedia - a wiki about renewable energies in the context of development cooperation Hidden Health and Environmental Costs Of Energy Production and Consumption In U.S. IEA-ECES - International Energy Agency - Energy Conservation through Energy Conservation programme. IEA HPT TCP - International Energy Agency - Technology Collaboration Programme on Heatpumping Technologies. IEA-SHC - International Energy Agency - Solar Heating and Cooling programme. SDH - Solar District Heating Platform. (European Union)
Wikipedia/Energy_development
An energy transition (or energy system transformation) is a major structural change to energy supply and consumption in an energy system. Currently, a transition to sustainable energy is underway to limit climate change. Most of the sustainable energy is renewable energy. Therefore, another term for energy transition is renewable energy transition. The current transition aims to reduce greenhouse gas emissions from energy quickly and sustainably, mostly by phasing-down fossil fuels and changing as many processes as possible to operate on low carbon electricity. A previous energy transition perhaps took place during the Industrial Revolution from 1760 onwards, from wood and other biomass to coal, followed by oil and later natural gas. Over three-quarters of the world's energy needs are met by burning fossil fuels, but this usage emits greenhouse gases. Energy production and consumption are responsible for most human-caused greenhouse gas emissions. To meet the goals of the 2015 Paris Agreement on climate change, emissions must be reduced as soon as possible and reach net-zero by mid-century. Since the late 2010s, the renewable energy transition has also been driven by the rapidly falling cost of both solar and wind power. After 2024, clean energy is cheaper than ever. Global solar module prices fell 35 percent to less than 9 cents/kWh. EV batteries saw their best price decline in seven years.Another benefit of the energy transition is its potential to reduce the health and environmental impacts of the energy industry. Heating of buildings is being electrified, with heat pumps being the most efficient technology by far. To improve the flexibility of electrical grids, the installation of energy storage and super grids are vital to enable the use of variable, weather-dependent technologies. However fossil-fuel subsidies are slowing the energy transition. == Definition == An energy transition is a broad shift in technologies and behaviours that are needed to replace one source of energy with another.: 202–203  A prime example is the change from a pre-industrial system relying on traditional biomass, wind, water and muscle power to an industrial system characterized by pervasive mechanization, steam power and the use of coal. The IPCC does not define energy transition in the glossary of its Sixth Assessment Report but it does define transition as: "The process of changing from one state or condition to another in a given period of time. Transition can occur in individuals, firms, cities, regions and nations, and can be based on incremental or transformative change." == Development of the term == After the 1973 oil crisis, the term energy transition was coined by politicians and media. It was popularised by US President Jimmy Carter in his 1977 Address on the Nation on Energy, calling to "look back into history to understand our energy problem. Twice in the last several hundred years, there has been a transition in the way people use energy ... Because we are now running out of gas and oil, we must prepare quickly for a third change to strict conservation and to the renewed use of coal and to permanent renewable energy sources like solar power." The term was later globalised after the 1979 second oil shock, during the 1981 United Nations Conference on New and Renewable Sources of Energy. From the 1990s, debates on energy transition have increasingly taken climate change mitigation into account. Parties to the agreement committed "to limit global warming to "well below 2 °C, preferably 1.5 °C compared to pre-industrial levels". This requires a rapid energy transition with a downshift of fossil fuel production to stay within the carbon emissions budget. In this context, the term energy transition encompasses a reorientation of energy policy. This could imply a shift from centralized to distributed generation. It also includes attempts to replace overproduction and avoidable energy consumption with energy-saving measures and increased efficiency. The historical transitions from locally supplied wood, water and wind energies to globally supplied fossil and nuclear fuels has induced growth in end-use demand through the rapid expansion of engineering research, education and standardisation. The mechanisms for the whole-systems changes include new discipline in Transition Engineering amongst all engineering professions, entrepreneurs, researchers and educators. However it has been argued that the term is a mere slogan and that rather than transitioning, as of 2024, use of all forms of primary energy has increased. == Examples of past energy transitions == Historic approaches to past energy transitions are shaped by two main discourses. One argues that humankind experienced several energy transitions in its past, while the other suggests the term "energy additions" as better reflecting the changes in global energy supply in the last three centuries. The chronologically first discourse was most broadly described by Vaclav Smil. It underlines the change in the energy mix of countries and the global economy. By looking at data in percentages of the primary energy source used in a given context, it paints a picture of the world's energy systems as having changed significantly over time, going from biomass to coal, to oil, and now a mix of mostly coal, oil and natural gas. Until the 1950s, the economic mechanism behind energy systems was local rather than global. The second discourse was most broadly described by Jean-Baptiste Fressoz. It emphasises that the term "energy transition" was first used by politicians, not historians, to describe a goal to achieve in the future – not as a concept to analyse past trends. When looking at the sheer amount of energy being used by humankind, the picture is one of ever-increasing consumption of all the main energy sources available to humankind. For instance, the increased use of coal in the 19th century did not replace wood consumption, indeed more wood was burned. Another example is the deployment of passenger cars in the 20th century. This evolution triggered an increase in both oil consumption (to drive the car) and coal consumption (to make the steel needed for the car). In other words, according to this approach, humankind never performed a single energy transition in its history but performed several energy additions. Contemporary energy transitions differ in terms of motivation and objectives, drivers and governance. As development progressed, different national systems became more and more integrated becoming the large, international systems seen today. Historical changes of energy systems have been extensively studied. While historical energy changes were generally protracted affairs, unfolding over many decades, this does not necessarily hold true for the present energy transition, which is unfolding under very different policy and technological conditions. For current energy systems, many lessons can be learned from history. The need for large amounts of firewood in early industrial processes in combination with prohibitive costs for overland transportation led to a scarcity of accessible (e.g. affordable) wood, and eighteenth century glass-works "operated like a forest clearing enterprise". When Britain had to resort to coal after largely having run out of wood, the resulting fuel crisis triggered a chain of events that two centuries later culminated in the Industrial Revolution. Similarly, increased use of peat and coal were vital elements paving the way for the Dutch Golden Age, roughly spanning the entire 17th century. Another example where resource depletion triggered technological innovation and a shift to new energy sources is 19th century whaling: whale oil eventually became replaced by kerosene and other petroleum-derived products. To speed up the energy transition it is also conceivable that there will be government buyouts or bailouts of coal mining regions. == Drivers for current energy transition == === Climate change mitigation and co-benefits === A rapid energy transition to very-low or zero-carbon sources is required to mitigate the effects of climate change.: 66 : 11  Coal, oil and gas combustion account for 89% of CO2 emissions: 20  and still provide 78% of primary energy consumption.: 12  Despite the knowledge about the risks of climate change and the increasing number of climate policies adopted since the 1980s, however, energy transitions have not accelerated towards decarbonization beyond historical trends and remain far off track in achieving climate targets. The deployment of renewable energy can generate co-benefits of climate change mitigation: positive socio-economic effects on employment, industrial development, health and energy access. Depending on the country and the deployment scenario, replacing coal power plants can more than double the number of jobs per average MW capacity. The energy transition could create many green jobs, for example in Africa. The costs for retraining workers for the renewable energy industry was found to be trivial for both coal in the U.S. and oil sands in Canada. The latter of which would only demand 2–6% of federal, provincial, and territorial oil and gas subsidies for a single year to be reallocated to provide oil and gas workers with a new career of approximately equivalent pay. In non-electrified rural areas, the deployment of solar mini-grids can significantly improve electricity access. Employment opportunities by the green transition are associated with the use of renewable energy sources or building activity for infrastructure improvements and renovations. === Energy security === Another important driver is energy security and independence, with increasing importance in Europe and Taiwan because of the 2022 Russian invasion of Ukraine. Unlike Europes 2010s dependence on Russian gas, even if China stops supplying solar panels those already installed continue generating electricity. Militaries are using and developing electric vehicles, particularly for their stealthiness, but not tanks. As of 2023 renewable energy in Taiwan is far too small to help in a blockade. Centralised facilities such as oil refineries and thermal power plants can be put out of action by air attack, whereas although solar can be attacked decentralised power such as solar and wind may be less vulnerable. Solar and batteries reduces risky fuel convoys. However large hydropower plants are vulnerable. Some say that nuclear power plants are unlikely to be military targets, but others conclude that civil NPPs in war zones can be weaponised and exploited by the hostile forces not only for impeding energy supplies (and thus shattering the public morale of the adversary) but also for blackmailing and coercing the decisionmakers of the attacked state and their international allies with a vision of man-made nuclear disaster. === Economic development === For many developing economies, for example in the mineral-rich countries of Sub-Saharan Africa, the transition to renewable energies is predicted to become a driver of sustainable economic development. The International Energy Agency (IEA) has identified 37 minerals as critical for clean energy technologies and estimates that by 2050 global demand for these will increase by 235 per cent. Africa has large reserves of many of these so-called "green minerals, such as bauxite, cobalt, copper, chromium, manganese and graphite. The African Union has outlined a policy framework, the Africa Mining Vision, to leverage the continent's mineral reserves in pursuit of sustainable development and socio-economic transformation. Achieving these goals requires mineral-rich African economies to transition from commodity export to manufacture of higher value-added products. === Cost competitiveness of renewable energies === From 2010 to 2019, the competitiveness of wind and solar power substantially increased. Unit costs of solar energy dropped sharply by 85%, wind energy by 55%, and lithium-ion batteries by 85%.: 11  This has made wind and solar power the cheapest form for new installations in many regions. Levelized costs for combined onshore wind or solar with storage for a few hours are already lower than for gas peaking power plants. In 2021, the new electricity generating capacity of renewables exceeded 80% of all installed power.: 3  == Key technologies and approaches == The emissions reductions necessary to keep global warming below 2 °C will require a system-wide transformation of the way energy is produced, distributed, stored, and consumed.: 46  For a society to replace one form of energy with another, multiple technologies and behaviours in the energy system must change.: 202–203  Many climate change mitigation pathways envision three main aspects of a low-carbon energy system: The use of low-emission energy sources to produce electricity Electrification – that is increased use of electricity instead of directly burning fossil fuels Accelerated adoption of energy efficiency measures: 7.11.3  === Renewable energy === The most important energy sources in the low carbon energy transition are wind power and solar power. They could reduce net emissions by 4 billion tons CO2 equivalent per year each, half of it with lower net lifetime costs than the reference.: 38  Other renewable energy sources include bioenergy, geothermal energy and tidal energy, but they currently have higher net lifetime costs.: 38  By 2022, hydroelectricity is the largest source of renewable electricity in the world, providing 16% of the world's total electricity in 2019. However, because of its heavy dependence on geography and the generally high environmental and social impact of hydroelectric power plants, the growth potential of this technology is limited. Wind and solar power are considered more scalable, but still require vast quantities of land and materials. They have higher potential for growth. These sources have grown nearly exponentially in recent decades thanks to rapidly decreasing costs. In 2019, wind power supplied 5.3% worldwide electricity while solar power supplied 2.6%. While production from most types of hydropower plants can be actively controlled, production from wind and solar power depends on the weather. Electrical grids must be extended and adjusted to avoid wastage. Dammed hydropower is a dispatchable source, while solar and wind are variable renewable energy sources. These sources require dispatchable backup generation or energy storage to provide continuous and reliable electricity. For this reason, storage technologies also play a key role in the renewable energy transition. As of 2020, the largest scale storage technology is pumped storage hydroelectricity, accounting for the great majority of energy storage capacity installed worldwide. Other important forms of energy storage are electric batteries and power to gas. The "Electricity Grids and Secure Energy Transitions" report by the IEA emphasizes the necessity of increasing grid investments to over $600 billion annually by 2030, up from $300 billion, to accommodate the integration of renewable energy. By 2040, the grid must expand by more than 80 million kilometers to manage renewable sources, which are projected to account for over 80% of the global power capacity increase over the next two decades. Failure to enhance grid infrastructure timely could lead to an additional 58 gigatonnes of CO2 emissions by 2050, significantly risking a 2°C global temperature rise. ==== Integration of variable renewable energy sources ==== With the integration of renewable energy, local electricity production is becoming more variable. It has been recommended that "coupling sectors, energy storage, smart grids, demand side management, sustainable biofuels, hydrogen electrolysis and derivatives will ultimately be needed to accommodate large shares of renewables in energy systems".: 28  Fluctuations can be smoothened by combining wind and sun power and by extending electricity grids over large areas. This reduces the dependence on local weather conditions. With highly variable prices, electricity storage and grid extension become more competitive. Researchers have found that "costs for accommodating the integration of variable renewable energy sources in electricity systems are expected to be modest until 2030".: 39  Furthermore, "it will be more challenging to supply the entire energy system with renewable energy".: 28  Fast fluctuations increase with a high integration of wind and solar energy. They can be addressed by operating reserves. Large-scale batteries can react within seconds and are increasingly used to keep the electricity grid stable. ==== 100% renewable energy ==== === Nuclear power === In the 1970s and 1980s, nuclear power gained a large share in some countries. In France and Slovakia more than half of the electrical power is still nuclear. It is a low carbon energy source but comes with risks and increasing costs. Since the late 1990s, deployment has slowed down. Decommissioning increases as many reactors are close to the end of their lifetime or long before because of anti-nuclear sentiments. Germany stopped its last three nuclear power plants by mid April 2023. On the other hand, the China General Nuclear Power Group is aiming for 200 GW by 2035, produced by 150 additional reactors. === Electrification === With the switch to clean energy sources where power is generated via electricity, end uses of energy such as transportation and heating need to be electrified to run on these clean energy sources. Concurrent with this switch is an expansion of the grid to handle larger amounts of generated electricity to supply to these end uses. Two key areas of electrification are electric vehicles and heat pumps. It is easier to sustainably produce electricity than it is to sustainably produce liquid fuels. Therefore, adoption of electric vehicles is a way to make transport more sustainable. While electric vehicle technology is relatively mature in road transport, electric shipping and aviation are still early in their development, hence sustainable liquid fuels may have a larger role to play in these sectors.: 139  A key sustainable solution to heating is electrification (heat pumps, or the less efficient electric heater). The IEA estimates that heat pumps currently provide only 5% of space and water heating requirements globally, but could provide over 90%. Use of ground source heat pumps not only reduces total annual energy loads associated with heating and cooling, it also flattens the electric demand curve by eliminating the extreme summer peak electric supply requirements. However, heat pumps and resistive heating alone will not be sufficient for the electrification of industrial heat. This because in several processes higher temperatures are required which cannot be achieved with these types of equipment. For example, for the production of ethylene via steam cracking temperatures as high as 900 °C are required. Hence, drastically new processes are required. Nevertheless, power-to-heat is expected to be the first step in the electrification of the chemical industry with an expected large-scale implementation by 2025. == Economic and geopolitical aspects == A shift in energy sources has the potential to redefine relations and dependencies between countries, stakeholders and companies. Countries or land owners with resources – fossil or renewable – face massive losses or gains depending on the development of any energy transition. In 2021, energy costs reached 13% of global gross domestic product. Global rivalries have contributed to the driving forces of the economics behind the low carbon energy transition. Technological innovations developed within a country have the potential to become an economic force. === Influences === The energy transition discussion is heavily influenced by contributions from the fossil fuel industries. One way that oil companies are able to continue their work despite growing environmental, social and economic concerns is by lobbying local and national governments. Historically, the fossil fuel lobby has been highly successful in limiting regulations. From 1988 to 2005, Exxon Mobil, one of the largest oil companies in the world, spent nearly $16 million in anti-climate change lobbying and providing misleading information about climate change to the general public. The fossil fuel industry acquires significant support through the existing banking and investment structure. The concept that the industry should no longer be financially supported has led to the social movement known as divestment. Divestment is defined as the removal of investment capital from stocks, bonds or funds in oil, coal and gas companies for both moral and financial reasons. Banks, investing firms, governments, universities, institutions and businesses are all being challenged with this new moral argument against their existing investments in the fossil fuel industry and many; such as Rockefeller Brothers Fund, the University of California, New York City and more; have begun making the shift to more sustainable, eco-friendly investments. In 2024 the International Renewable Energy Agency (IRENA) projected that by 2050, over half of the world's energy will be carried by electricity and over three-quarters of the global energy mix will be from renewables. Although overtaken by both biomass and clean hydrogen, fossil fuels were still projected to supply 12% of energy. The transition is expected to reshape geopolitical power by reducing reliance on long-distance fossil fuel trade and enhancing the importance of regional energy markets. == Social and environmental aspects == === Impacts === A renewable energy transition can present negative social impacts for some people who rely on the existing energy economy or who are affected by mining for minerals required for the transition. This has led to calls for a just transition, which the IPCC defines as, "A set of principles, processes and practices that aim to ensure that no people, workers, places, sectors, countries or regions are left behind in the transition from a high-carbon to a low carbon economy." Use of local energy sources may stabilise and stimulate some local economies, create opportunities for energy trade between communities, states and regions, and increase energy security. Coal mining is economically important in some regions, and a transition to renewables would decrease its viability and could have severe impacts on the communities that rely on this business. Not only do these communities face energy poverty already, but they also face economic collapse when the coal mining businesses move elsewhere or disappear altogether. This broken system perpetuates the poverty and vulnerability that decreases the adaptive capacity of coal mining communities. Potential mitigation could include expanding the program base for vulnerable communities to assist with new training programs, opportunities for economic development and subsidies to assist with the transition. Increasing energy prices resulting from an energy transition may negatively impact developing countries including Vietnam and Indonesia. Increased mining for lithium, cobalt, nickel, copper, and other critical minerals needed for expansion of renewable energy infrastructure has created increased environmental conflict and environmental justice issues for some communities. === Labour === A large portion of the global workforce works directly or indirectly for the fossil fuel economy. Moreover, many other industries are currently dependent on unsustainable energy sources (such as the steel industry or cement and concrete industry). Transitioning these workforces during the rapid period of economic change requires considerable forethought and planning. The international labor movement has advocated for a just transition that addresses these concerns. Recently, an energy crisis is upon the nations of Europe as a result of dependence on Russia's natural gas, which was cut off during the Russia-Ukraine war. This goes to show that humanity is still heavily dependent on fossil fuel energy sources and care should be taken to have a smooth transition, less energy-shortage shocks cripple the very efforts to effectively energise the transition. == Risks and barriers == Amongst the key issues to consider in relation to the pace of the global transition to renewables is how well individual electric companies are able to adapt to the changing reality of the power sector. For example, to date, the uptake of renewables by electric utilities has remained slow, hindered by their continued investment in fossil fuel generation capacity. Incomplete regulations on clean energy uptake and concerns about electricity shortages have been identified as key barriers to the energy transition in coal-dependent, fast developing economies such as Vietnam. Researchers found that social sentiments held by U.S. residents have proven to be barriers for energy transitions. The U.S. Department of Energy plans for wind energy to provide 35% of the electrical grid by 2050 are bringing wind energy projects closer to communities. Sentiments for wind energy opposition in local communities include sound annoyance, perceived health effects, and the reduction of scenic landscapes and views. Anticipated economic aspects are believed to be the most influential variable to perceptions of proposed wind energy developments. Economic barriers to acceptance of renewable energy include local tax increases, increase in electricity rates, decrease in tourism, property value impacts and distributional inequality. However, rural economic development, creation of jobs, investment opportunities, and lower electricity costs stand as possible benefits. == Examples by country == From 2000 to 2012 coal was the source of energy with the total largest growth. The use of oil and natural gas also had considerable growth, followed by hydropower and renewable energy. Renewable energy grew at a rate faster than any other time in history during this period. The demand for nuclear energy decreased, partly in reaction to a number of high profile accidents (Three Mile Island in 1979, Chernobyl in 1986, and Fukushima in 2011) but also due to the rising cost of nuclear energy which has made it more expensive than all utility scale alternatives. More recently, consumption of coal has declined relative to low carbon energy. Coal dropped from about 29% of the global total primary energy consumption in 2015 to 27% in 2017, and non-hydro renewables were up to about 4% from 2%. === Asia === ==== China ==== The Fourteenth Five-Year Plan placed increased emphasis on the green transition as essential to China's pursuit of high-quality and sustainable growth.: 9  ==== India ==== India has set renewable energy goals to transition 50% of its total energy consumption into renewable sources in the Paris climate accords. As of 2022 the Central Electricity Authority are well on track of achieving their goals, producing 160 GW electricity from clean sources like solar, wind, hydro power and nuclear power plants, this is 40% of its total capacity. India is ranked third on Ernst and Young's renewable energy country attractive index behind the US and China. Hydro electric power plants are a major part of India's energy infrastructure since the days of its independence in 1947. Former prime Minister Jawahar Lal Nehru called them the " temples of modern India" and believed them to be key drivers of modernity and industrialism for the nascent republic. Notable examples of hydro power stations include the 2400 MW Tehri hydropower complex, the 1960 MW Koyna hydroelectric project and the 1670 MW Srisailam Dam. Recently, India has given due importance to emerging renewable technologies like solar power plants and wind farms. They house 3 of the world's top 5 solar farms, including world's largest 2255 MW Bhadla Solar Park in and world's second-largest solar park of 2000 MW Pavgada Solar Park and 100 MW Kurnool Ultra mega solar park. While there has been positive change, air pollution from coal still kills many people and India has to cut down its reliance on traditional coal based power production as it still accounts for around 50% of its energy production. India is also moving towards its goal for electrification of the automotive industry, aiming to have at least 30% EV ownership among private vehicles by 2030. ==== Vietnam ==== Vietnam has led the Southeast Asia in solar and wind uptake, achieving about 20 GW in 2022 from almost zero in 2017. Thailand has the highest number of EV registrations, with 218,000 in 2022. The energy transition in Southeast Asia can be summarized as: Challenging, achievable, and interdependent. This implies that while there are obstacles, feasibility largely relies on international support. Public demand for improved local environmental quality and government's aims to promote a green economy are found to be key drivers in Vietnam. Governments ambition to attract international support for green growth initiatives and public demand for a clean environment have been found to be drivers of the energy transition in developing countries, such as Vietnam. Thanks to a relatively more conducive investment environment, Vietnam is poised to a faster energy transition than some other ASEAN members === Europe === ==== European Union ==== The European Green Deal is a set of policy initiatives by the European Commission with the overarching aim of making Europe climate neutral in 2050. An impact assessed plan will also be presented to increase the EU's greenhouse gas emission reductions target for 2030 to at least 50% and towards 55% compared with 1990 levels. The plan is to review each existing law on its climate merits, and also introduce new legislation on the circular economy, building renovation, biodiversity, farming and innovation. The president of the European Commission, Ursula von der Leyen, stated that the European Green Deal would be Europe's "man on the Moon moment", as the plan would make Europe the first climate-neutral continent. A survey found that digitally advanced companies put more money into energy-saving strategies. In the European Union, 59% of companies that have made investments in both basic and advanced technologies have also invested in energy efficiency measures, compared to only 50% of US firms in the same category. Overall, there is a significant disparity between businesses' digital profiles and investments in energy efficiency. ==== Germany ==== Germany has played an outsized role in the transition away from fossil fuels and nuclear power to renewables. The energy transition in Germany is known as die Energiewende (literally, "the energy turn") indicating a turn away from old fuels and technologies to new one. The key policy document outlining the Energiewende was published by the German government in September 2010, some six months before the Fukushima nuclear accident; legislative support was passed in September 2010. The policy has been embraced by the German federal government and has resulted in a huge expansion of renewables, particularly wind power. Germany's share of renewables has increased from around 5% in 1999 to 17% in 2010, reaching close to the OECD average of 18% usage of renewables. In 2022 Germany has a share of 46,2 % and surpassed the OECD average. A large driver for this increase in the shares of renewables energy are decreases in cost of capital. Germany boasts some of the lowest cost of capitals for renewable solar and wind onshore energy worldwide. In 2021 the International Renewable Energy Agency reported capital costs of around 1.1% and 2.4% for solar and wind onshore. This constitutes a significant decrease from previous numbers in the early 2000s, where capital costs hovered around 5.1% and 4.5% respectively. This decrease in capital costs was influenced by a variety of economic and political drivers. Following the 2008 financial crisis, Germany eased the refinancing regulations on banks by giving out cheap loans with low interest rates in order to stimulate the economy again. During this period, the industry around renewable energies also started to experience learning effects in manufacturing, project organisation as well as financing thanks to rising investment and order volumes. This coupled with various forms of subsidies contributed to a large reduction of the capital cost and the levelized cost of electricity (LCOE) for solar and onshore wind power. As the technologies have matured and become integral parts of the existing sociotechnical systems it is to be expected that in the future, experience effects and general interest rates will be key determinants for the cost-competitiveness of these technologies. Producers have been guaranteed a fixed feed-in tariff for 20 years, guaranteeing a fixed income. Energy co-operatives have been created, and efforts were made to decentralize control and profits. The large energy companies have a disproportionately small share of the renewables market. Nuclear power stations were closed, and the existing nine stations will close earlier than necessary, in 2022. The reduction of reliance on nuclear stations has had the consequence of increased reliance on fossil fuels. One factor that has inhibited efficient employment of new renewable energy has been the lack of an accompanying investment in power infrastructure to bring the power to market. It is believed 8300 km of power lines must be built or upgraded. Different Länder have varying attitudes to the construction of new power lines. Industry has had their rates frozen and so the increased costs of the Energiewende have been passed on to consumers, who have had rising electricity bills. Germans in 2013 had some of the highest electricity costs in Europe. Nonetheless, for the first time in more than ten years, electricity prices for household customers fell at the beginning of 2015. ==== Switzerland ==== Due to the high share of hydroelectricity (59.6%) and nuclear power (31.7%) in electricity production, Switzerland's per capita energy-related CO2 emissions are 28% lower than the European Union average and roughly equal to those of France. On 21 May 2017, Swiss voters accepted the new Energy Act establishing the 'energy strategy 2050'. The aims of the energy strategy 2050 are: to reduce energy consumption; to increase energy efficiency; and to promote renewable energies (such as water, solar, wind and geothermal power as well as biomass fuels). The Energy Act of 2006 forbids the construction of new nuclear power plants in Switzerland. ==== United Kingdom ==== By law production of greenhouse gas emissions by the United Kingdom will be reduced to net zero by 2050. To help in reaching this statutory goal national energy policy is mainly focusing on the country's off-shore wind power and delivering new and advanced nuclear power. The increase in national renewable power – particularly from biomass – together with the 20% of electricity generated by nuclear power in the United Kingdom meant that by 2019 low carbon British electricity had overtaken that generated by fossil fuels. In order to meet the net zero target energy networks must be strengthened. Electricity is only a part of energy in the United Kingdom, so natural gas used for industrial and residential heat and petroleum used for transport in the United Kingdom must also be replaced by either electricity or another form of low-carbon energy, such as sustainable bioenergy crops or green hydrogen. Although the need for the energy transition is not disputed by any major political party, in 2020 there is debate about how much of the funding to try and escape the COVID-19 recession should be spent on the transition, and how many jobs could be created, for example in improving energy efficiency in British housing. Some believe that due to post-covid government debt that funding for the transition will be insufficient. Brexit may significantly affect the energy transition, but this is unclear as of 2020. The government is urging UK business to sponsor the climate change conference in 2021, possibly including energy companies but only if they have a credible short-term plan for the energy transition. == See also == == References ==
Wikipedia/Energy_transition
A thermodynamic free entropy is an entropic thermodynamic potential analogous to the free energy. Also known as a Massieu, Planck, or Massieu–Planck potentials (or functions), or (rarely) free information. In statistical mechanics, free entropies frequently appear as the logarithm of a partition function. The Onsager reciprocal relations in particular, are developed in terms of entropic potentials. In mathematics, free entropy means something quite different: it is a generalization of entropy defined in the subject of free probability. A free entropy is generated by a Legendre transformation of the entropy. The different potentials correspond to different constraints to which the system may be subjected. == Examples == The most common examples are: where Note that the use of the terms "Massieu" and "Planck" for explicit Massieu-Planck potentials are somewhat obscure and ambiguous. In particular "Planck potential" has alternative meanings. The most standard notation for an entropic potential is ψ {\displaystyle \psi } , used by both Planck and Schrödinger. (Note that Gibbs used ψ {\displaystyle \psi } to denote the free energy.) Free entropies were invented by French engineer François Massieu in 1869, and actually predate Gibbs's free energy (1875). == Dependence of the potentials on the natural variables == === Entropy === S = S ( U , V , { N i } ) {\displaystyle S=S(U,V,\{N_{i}\})} By the definition of a total differential, d S = ∂ S ∂ U d U + ∂ S ∂ V d V + ∑ i = 1 s ∂ S ∂ N i d N i . {\displaystyle dS={\frac {\partial S}{\partial U}}dU+{\frac {\partial S}{\partial V}}dV+\sum _{i=1}^{s}{\frac {\partial S}{\partial N_{i}}}dN_{i}.} From the equations of state, d S = 1 T d U + P T d V + ∑ i = 1 s ( − μ i T ) d N i . {\displaystyle dS={\frac {1}{T}}dU+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}.} The differentials in the above equation are all of extensive variables, so they may be integrated to yield S = U T + P V T + ∑ i = 1 s ( − μ i N T ) + constant . {\displaystyle S={\frac {U}{T}}+{\frac {PV}{T}}+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}N}{T}}\right)+{\textrm {constant}}.} === Massieu potential / Helmholtz free entropy === Φ = S − U T {\displaystyle \Phi =S-{\frac {U}{T}}} Φ = U T + P V T + ∑ i = 1 s ( − μ i N T ) − U T {\displaystyle \Phi ={\frac {U}{T}}+{\frac {PV}{T}}+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}N}{T}}\right)-{\frac {U}{T}}} Φ = P V T + ∑ i = 1 s ( − μ i N T ) {\displaystyle \Phi ={\frac {PV}{T}}+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}N}{T}}\right)} Starting over at the definition of Φ {\displaystyle \Phi } and taking the total differential, we have via a Legendre transform (and the chain rule) d Φ = d S − 1 T d U − U d 1 T , {\displaystyle d\Phi =dS-{\frac {1}{T}}dU-Ud{\frac {1}{T}},} d Φ = 1 T d U + P T d V + ∑ i = 1 s ( − μ i T ) d N i − 1 T d U − U d 1 T , {\displaystyle d\Phi ={\frac {1}{T}}dU+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}-{\frac {1}{T}}dU-Ud{\frac {1}{T}},} d Φ = − U d 1 T + P T d V + ∑ i = 1 s ( − μ i T ) d N i . {\displaystyle d\Phi =-Ud{\frac {1}{T}}+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}.} The above differentials are not all of extensive variables, so the equation may not be directly integrated. From d Φ {\displaystyle d\Phi } we see that Φ = Φ ( 1 T , V , { N i } ) . {\displaystyle \Phi =\Phi ({\frac {1}{T}},V,\{N_{i}\}).} If reciprocal variables are not desired,: 222  d Φ = d S − T d U − U d T T 2 , {\displaystyle d\Phi =dS-{\frac {TdU-UdT}{T^{2}}},} d Φ = d S − 1 T d U + U T 2 d T , {\displaystyle d\Phi =dS-{\frac {1}{T}}dU+{\frac {U}{T^{2}}}dT,} d Φ = 1 T d U + P T d V + ∑ i = 1 s ( − μ i T ) d N i − 1 T d U + U T 2 d T , {\displaystyle d\Phi ={\frac {1}{T}}dU+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}-{\frac {1}{T}}dU+{\frac {U}{T^{2}}}dT,} d Φ = U T 2 d T + P T d V + ∑ i = 1 s ( − μ i T ) d N i , {\displaystyle d\Phi ={\frac {U}{T^{2}}}dT+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i},} Φ = Φ ( T , V , { N i } ) . {\displaystyle \Phi =\Phi (T,V,\{N_{i}\}).} === Planck potential / Gibbs free entropy === Ξ = Φ − P V T {\displaystyle \Xi =\Phi -{\frac {PV}{T}}} Ξ = P V T + ∑ i = 1 s ( − μ i N T ) − P V T {\displaystyle \Xi ={\frac {PV}{T}}+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}N}{T}}\right)-{\frac {PV}{T}}} Ξ = ∑ i = 1 s ( − μ i N T ) {\displaystyle \Xi =\sum _{i=1}^{s}\left(-{\frac {\mu _{i}N}{T}}\right)} Starting over at the definition of Ξ {\displaystyle \Xi } and taking the total differential, we have via a Legendre transform (and the chain rule) d Ξ = d Φ − P T d V − V d P T {\displaystyle d\Xi =d\Phi -{\frac {P}{T}}dV-Vd{\frac {P}{T}}} d Ξ = − U d 2 T + P T d V + ∑ i = 1 s ( − μ i T ) d N i − P T d V − V d P T {\displaystyle d\Xi =-Ud{\frac {2}{T}}+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}-{\frac {P}{T}}dV-Vd{\frac {P}{T}}} d Ξ = − U d 1 T − V d P T + ∑ i = 1 s ( − μ i T ) d N i . {\displaystyle d\Xi =-Ud{\frac {1}{T}}-Vd{\frac {P}{T}}+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}.} The above differentials are not all of extensive variables, so the equation may not be directly integrated. From d Ξ {\displaystyle d\Xi } we see that Ξ = Ξ ( 1 T , P T , { N i } ) . {\displaystyle \Xi =\Xi \left({\frac {1}{T}},{\frac {P}{T}},\{N_{i}\}\right).} If reciprocal variables are not desired,: 222  d Ξ = d Φ − T ( P d V + V d P ) − P V d T T 2 , {\displaystyle d\Xi =d\Phi -{\frac {T(PdV+VdP)-PVdT}{T^{2}}},} d Ξ = d Φ − P T d V − V T d P + P V T 2 d T , {\displaystyle d\Xi =d\Phi -{\frac {P}{T}}dV-{\frac {V}{T}}dP+{\frac {PV}{T^{2}}}dT,} d Ξ = U T 2 d T + P T d V + ∑ i = 1 s ( − μ i T ) d N i − P T d V − V T d P + P V T 2 d T , {\displaystyle d\Xi ={\frac {U}{T^{2}}}dT+{\frac {P}{T}}dV+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i}-{\frac {P}{T}}dV-{\frac {V}{T}}dP+{\frac {PV}{T^{2}}}dT,} d Ξ = U + P V T 2 d T − V T d P + ∑ i = 1 s ( − μ i T ) d N i , {\displaystyle d\Xi ={\frac {U+PV}{T^{2}}}dT-{\frac {V}{T}}dP+\sum _{i=1}^{s}\left(-{\frac {\mu _{i}}{T}}\right)dN_{i},} Ξ = Ξ ( T , P , { N i } ) . {\displaystyle \Xi =\Xi (T,P,\{N_{i}\}).} == References == == Bibliography == Massieu, M.F. (1869). "Compt. Rend". 69 (858): 1057. {{cite journal}}: Cite journal requires |journal= (help) Callen, Herbert B. (1985). Thermodynamics and an Introduction to Thermostatistics (2nd ed.). New York: John Wiley & Sons. ISBN 0-471-86256-8.
Wikipedia/Free_entropy
Energy recycling is the energy recovery process of using energy that would normally be wasted, usually by converting it into electricity or thermal energy. Undertaken at manufacturing facilities, power plants, and large institutions such as hospitals and universities, it significantly increases efficiency, thereby reducing energy costs and greenhouse gas pollution simultaneously. The process is noted for its potential to mitigate global warming profitably. This work is usually done in the form of combined heat and power (also called cogeneration) or waste heat recovery. == Forms of energy recycling == === Waste heat recovery === Waste heat recovery is a process that captures excess heat that would normally be discharged at manufacturing facilities and converts it into electricity and steam, or returns energy to the manufacturing process in the form of heated air, water, glycol, or oil. A "waste heat recovery boiler" contains a series of water-filled tubes placed throughout the area where heat is released. When high-temperature heat meets the boiler, steam is produced, which in turn powers a turbine that creates electricity. This process is similar to that of other fired boilers, but in this case, waste heat replaces a traditional flame. No fossil fuels are used in this process. Metals, glass, pulp and paper, silicon and other production plants are typical locations where waste heat recovery can be effective. === Combined heat and power (CHP) === Combined heat and power (CHP), also called cogeneration, is, according to the U.S. Environmental Protection Agency, “an efficient, clean, and reliable approach to generating electricity and heat energy from a single fuel source. By installing a CHP system designed to meet the thermal and electrical base loads of a facility, CHP can greatly increase the facility's operational efficiency and decrease energy costs. At the same time, CHP reduces the emission of greenhouse gases, which contribute to global climate change.” When electricity is produced on-site with a CHP plant, excess heat is recycled to produce both processed heat and additional power. === Waste heat recovery from air conditioning === Waste heat recovery from air conditioning is also used as an alternative to wasting heat to the atmosphere from chiller plants. Heat recovered in summer from chiller plants is stored in Thermalbanks in the ground and recycled back to the same building in winter via a heat pump to provide heating without burning fossil fuels. This elegant approach saves energy - and carbon - in both seasons by recycling summer heat for winter use. Some companies offer products to install on the HVAC Condenser Unit, to collect waste heat that the condenser is supposed to evacuate in the air, to heat up heat-producing devices like water heaters. Those devices are called heat recovery units (HRU). For residential applications, some units available are : HotSpot Energy Heat Recovery Unit or LG Heat Recovery Units For industrial applications, these units are usually called waste heat recovery unit (WHRU). === Heat pumps === Heat pumps and thermal energy storage are classes of technologies that can enable the recycling of energy that would otherwise be inaccessible due to a temperature that is too low for use or a time lag between when the energy is available and when it is needed. While enhancing the temperature of available renewable thermal energy, heat pumps have the additional property of leveraging electrical power (or in some cases mechanical or thermal power) by using it to extract additional energy from a low quality source (such as seawater, lake water, the ground, the air, or waste heat from a process). Innovation efforts are underway now for full electrification of industry, including with Industry Heat Pumps at levels of efficiency between COP 5 & 9 using multi-stage thermal recycling via refrigerant tuned Heat Pump Modules. === Thermal storage === Thermal storage technologies allow heat or cold to be stored for periods of time ranging from hours or overnight to interseasonal, and can involve storage of sensible energy (i.e. by changing the temperature of a medium) or latent energy (i.e. through phase changes of a medium, such between water and slush or ice). Short-term thermal storages can be used for peak-shaving in district heating or electrical distribution systems. Kinds of renewable or alternative energy sources that can be enabled include natural energy (e.g. collected via solar-thermal collectors, or dry cooling towers used to collect winter's cold), waste energy (e.g. from HVAC equipment, industrial processes or power plants), or surplus energy (e.g. as seasonally from hydropower projects or intermittently from wind farms). The Drake Landing Solar Community (Alberta, Canada) is illustrative. Borehole thermal energy storage allows the community to get 97% of its year-round heat from solar collectors on the garage roofs, with most of the heat collected in summer. Types of storages for sensible energy include insulated tanks, borehole clusters in substrates ranging from gravel to bedrock, deep aquifers, or shallow lined pits that are insulated on top. Some types of storage are capable of storing heat or cold between opposing seasons (particularly if very large), and some storage applications require inclusion of a heat pump. Latent heat is typically stored in ice tanks or what are called phase-change materials (PCMs). == Current system == Both waste heat recovery and CHP constitute "decentralized" energy production, which is in contrast to traditional "centralized" power generated at large power plants run by regional utilities. The “centralized” system has an average efficiency of 34 percent, requiring about three units of fuel to produce one unit of power. By capturing both heat and power, CHP and waste heat recovery projects have higher efficiencies. A 2007 Department of Energy study found the potential for 135,000 megawatts of CHP in the U.S., and a Lawrence Berkley National Laboratory study identified about 64,000 megawatts that could be obtained from industrial waste energy, not counting CHP. These studies suggest about 200,000 megawatts—or 20% -- of total power capacity that could come from energy recycling in the U.S. Widespread use of energy recycling could therefore reduce global warming emissions by an estimated 20 percent. Indeed, as of 2005, about 42 percent of U.S. greenhouse gas pollution came from the production of electricity and 27 percent from the production of heat. Advocates contend that recycled energy costs less and has lower emissions than most other energy options in current use. Currently RecyclingEnergy Int. Corp. takes advantage of recycling energy in heat recovery ventilation and latent heat pump and CHCP. == History == Perhaps the first modern use of energy recycling was done by Thomas Edison. His 1882 Pearl Street Station, the world's first commercial power plant, was a CHP plant, producing both electricity and thermal energy while using waste heat to warm neighboring buildings. Recycling allowed Edison's plant to achieve approximately 50 percent efficiency. By the early 1900s, regulations emerged to promote rural electrification through the construction of centralized plants managed by regional utilities. These regulations not only promoted electrification throughout the countryside, but they also discouraged decentralized power generation, such as CHP. They even went so far as to make it illegal for non-utilities to sell power. By 1978, Congress recognized that efficiency at central power plants had stagnated and sought to encourage improved efficiency with the Public Utility Regulatory Policies Act (PURPA), which encouraged utilities to buy power from other energy producers. CHP plants proliferated, soon producing about 8 percent of all energy in the U.S. However, the bill left implementation and enforcement up to individual states, resulting in little or nothing being done in many parts of the country. In 2008 Tom Casten, chairman of Recycled Energy Development, said that "We think we could make about 19 to 20 percent of U.S. electricity with heat that is currently thrown away by industry." Outside the U.S., energy recycling is more common. Denmark is probably the most active energy recycler, obtaining about 55% of its energy from CHP and waste heat recovery. Other large countries, including Germany, Russia, and India, also obtain a much higher share of their energy from decentralized sources. == See also == Energy conservation – Reducing energy consumption Renewable energy – Energy collected from renewable resources Sustainable energy – Energy that responsibly meets social, economic, and environmental needs Waste heat recovery unit – Energy recovery heat exchanger Water heat recycling – Use of a heat exchanger to recover energy and reuse heat from drain water == References ==
Wikipedia/Energy_recycling
The second season of the American television series The Flash, which is based on the DC Comics character Barry Allen / Flash, sees Barry recognized as a hero in Central City after saving the city, only to face a new threat from a parallel universe in the form of the speedster Zoom, who seeks to eliminate everyone connected to the Speed Force throughout the multiverse. It is set in the Arrowverse, sharing continuity with the other television series of the universe, and is a spin-off of Arrow. The season was produced by Berlanti Productions, Warner Bros. Television, and DC Entertainment, with Andrew Kreisberg, Gabrielle Stanton, Aaron Helbing, and Todd Helbing serving as showrunners. The season was ordered in January 2015, and filmed from that July to the following April in Vancouver. Grant Gustin stars as Barry, alongside principal cast members Candice Patton, Danielle Panabaker, Carlos Valdes, Tom Cavanagh, and Jesse L. Martin also returning from the first season, and are joined by Keiynan Lonsdale. This season also introduces characters from Legends of Tomorrow, which was being developed as a spin-off. The season ran for 23 episodes and premiered on October 6, 2015, airing on The CW until May 24, 2016. The premiere was watched by 3.58 million viewers, down from the first-season premiere but average for the series. The second season of The Flash received universal acclaim from critics, being viewed as an improvement over the first season, and finished as the 112th ranked show, slightly up from season one, with an average viewership of 4.25 million. The series was renewed for a third season on March 11, 2016. == Episodes == == Cast and characters == === Guest === == Production == === Development === On January 11, 2015, The Flash was renewed for a second season. With the commencement of production on the season, former Arrow and Ugly Betty writer Gabrielle Stanton was promoted to executive producer and showrunner; after having served as consulting producer and writer on the first season's finale "Fast Enough". However, it was later reported that series co-creator Andrew Kreisberg would be returning to sole showrunner duties at an unspecified time. That time was later proved to be at the start of 2016, "Potential Energy", when Stanton was no longer credited as being involved with the show. Aaron and Todd Helbing also served as the season's showrunners. === Casting === Main cast members Grant Gustin, Candice Patton, Danielle Panabaker, Carlos Valdes and Jesse L. Martin return from the first season as Barry Allen / The Flash, Iris West, Caitlin Snow, Cisco Ramon / Vibe and Joe West, respectively. Tom Cavanagh, who portrayed Eobard Thawne impersonating Harrison Wells in season one, also returned as a regular, playing Wells' Earth-2 doppelgänger. Rick Cosnett, a main cast member from season one, did not return as a regular because his character, Eddie Thawne, died in the season one finale. He instead returned as a guest star in the season premiere "The Man Who Saved Central City" in a dream sequence, and later in the episode "Flash Back", where Barry travels back to a time when Eddie was still alive. In August 2015, Keiynan Lonsdale was cast as Wally West, the unknown son of Joe, and Iris' brother. Gustin, Patton, Panabaker, Valdes and Martin also portray the Earth-2 versions of their characters in the episode "Welcome to Earth-2", while Cavanagh portrays Thawne impersonating the Earth-1 Wells in "The Man Who Saved Central City" and "Flash Back". Discussing the casting of Lonsdale, Kreisberg stated, "Just like when we met Grant [Gustin] for the first time, we instantly knew Keiynan embodied all the heart and courage of a hero. We are so excited to be bringing this much-beloved character onto the show." It was always intended for Wally to be the son of Joe and brother of Iris, which differs from the character's comic history, as the producers disliked second seasons of television series that would introduce cousins of characters that were never previously mentioned, feeling it was "weird". Lonsdale originally auditioned for Legends of Tomorrow to portray Jefferson "Jax" Jackson. Shantel VanSanten appeared in a recurring role as Barry's love interest Patty Spivot. VanSanten's character departed after the mid season premiere. The reason was initially reported as being due to scheduling conflicts with Shooter; VanSanten later revealed in an interview that she was set to return but "one of the showrunners at the time took a personal disliking to her". In July 2015, it was announced that Teddy Sears would recur in the role of Jay Garrick, the Flash of Earth-2. However, later in the season it was revealed that his character was actually Hunter Zolomon / Zoom posing as Jay. Ryan Handley portrayed Zoom in costume prior to this revelation, while Tony Todd voiced Zoom. === Design === Maya Mani replaced Colleen Atwood as the costume designer for the second season and made slight changes to the Flash costume, such as changing the color of his chest emblem from red to white, being faithful to the Flash costume from the comics. Gustin stated that, around the time of filming the season's ninth episode, "we stopped gluing the mask to my face and switched to a mask that just slipped on and off with a zipper". While Zoom's costume in the comics is a verbatim replica of Eobard Thawne's yellow-and-red Reverse-Flash costume, the costume seen in the TV series is entirely in black. Kreisberg compared Zoom's appearance to that of the Marvel Comics character Venom, saying, "The Zoom outfit is much more organic than the Reverse-Flash suit. In a way, it's hard to tell if it is a suit or alive... There's no skin showing, for all you know there's a robot underneath, or dark energy." === Filming === Production on the season began on July 7, 2015, in Vancouver, British Columbia, and concluded on April 18, 2016. === Music === Composer Blake Neely returned as the primary composer for the second season. The soundtrack for the second season was released digitally on July 22, 2016 and in CD format on July 26, 2016. Neely also composed a theme when Gustin as Barry appeared on the eighteenth episode of Supergirl, "Worlds Finest". The theme was titled "World's Finest" when it was released on the Supergirl: Season 1 soundtrack. All music composed by Blake Neely. === Arrowverse tie-ins === In October 2015, Arrow showrunner Wendy Mericle revealed that the producers of the Arrowverse had begun having someone track all the characters and plots used by each series, in order to make sure everything lines up, though Aaron Helbing noted in April 2016 that "sometimes the schedules don't line up exactly...and that stuff is out of our control", such as when Barry is shown using his abilities on Arrow that month, while not having them the same week on The Flash. The second season of The Flash began to explore the concept of the multiverse, by introducing Earth-2, which features doppelgängers of the inhabitants in the Arrowverse (or Earth-1). In "Welcome to Earth-2" of The Flash, glimpses of the multiverse are seen, including an image of Supergirl star Melissa Benoist as Supergirl and an image of John Wesley Shipp as the Flash from the 1990 television series, implying that those two television series exist on alternate Earths to the Arrowverse. The second annual two-way crossover with Arrow aired on December 1 and 2, 2015, where the Flash and the Green Arrow team up to take on Vandal Savage, who is looking for Kendra Saunders and Carter Hall, the reincarnations of Hawkgirl and Hawkman. Though Legends of Tomorrow did not have an episode as part of the 2015–16 crossover, the Arrow and The Flash episodes from this event did set up a number of characters who star and recur in that series. Casper Crump, Falk Hentschel and Peter Francis James debut in the crossover, as Vandal Savage, Carter Hall / Hawkman, and Dr. Aldus Boardman, respectively. Screen Rant's Alice Walker discussed how the annual Arrow/The Flash crossover suffered from also trying to set up Legends, which was "too much to ask from the already crowded storylines and ended up feeling like an exercise in synchronicity, with producers planting more seeds than they could reap. The crossover event was no longer a fun way to contrast the two shows; it now had to serve the much larger purpose of setting up an entirely new world." ==== Crossover with Supergirl ==== In February 2016, it was announced that Gustin would appear on the eighteenth episode of Supergirl, with Berlanti and Kreisberg, also Supergirl executive producers, thanking "the fans and journalists who have kept asking for this to happen. It is our pleasure and hope to create an episode worthy of everyone's enthusiasm and support." While no plot details on the episodes were released at the time, Ross A. Lincoln of Deadline Hollywood noted that "the in-universe reason" for the crossover was due to Barry's ability to travel to various dimensions, thus implying that Supergirl exists on an alternate Earth to the Arrowverse in a multiverse. "Welcome to Earth-2" confirmed this, showing an image of Benoist as Supergirl during a sequence where characters travel through that multiverse. The Earth that the series inhabits has been informally referred to as "Earth-CBS" by Marc Guggenheim, one of the creators of Arrow. In "Worlds Finest", which aired on CBS on March 28, 2016, Supergirl is established as being in an alternate universe where the Flash helps Kara fight the Silver Banshee and Livewire in exchange for her help in returning home. The episode title was inspired by the World's Finest Comics series, in which Superman would team up with various other DC superheroes, including the Flash. The events of this episode take place between two moments in the eighteenth episode of The Flash season two, "Versus Zoom", which aired on April 19, 2016, in which Barry enters and exits a breach while wearing the tachyon device seen in this episode. The crossover required "a lot more logistical trickery" than the usual Arrowverse crossovers due to Gustin filming The Flash in Vancouver alongside Arrow and Legends of Tomorrow, while Supergirl is produced in Los Angeles. The producers chose to use the Flash as the character to crossover, due to his ability to travel between various Earths, and because it was "a little more fun at first to bring the veteran from that show to the chemistry of a new show." Berlanti stated that "in a perfect world", the crossover would have featured both Gustin and Amell's Green Arrow, "but logistically that would have been a nightmare to try and do both shows. We had to facilitate one." Gustin was optimistic that the crossover in 2016 would allow another crossover the following year with the rest of the Arrowverse shows. The crossover episode received excellent reviews. Cliff Wheatley of IGN gave the episode an 8.6/10, stating "After the grim 'n' gritty Batman v Superman, Supergirl's "Worlds Finest" offered a fun, upbeat palette cleanser and one of the series' strongest episodes to date. Instead of the usual "beatdown" introduction, Supergirl and the Flash went straight to being superfriends, which was refreshing. Not only did Barry Allen fit perfectly in Kara's world, but actors Grant Gustin and Melissa Benoist had fantastic chemistry together onscreen. While the city's turnaround on Supergirl's Red K incident was a little sudden, overall, "Worlds Finest" was delightful." Stacy Glanzman of TV Fanatic gave the episode a 5.0 out of 5 stars. == Marketing == The Flash surged 1,378% in buzz (highest year over year growth in conversation) from last year for its second season. == Release == === Broadcast === The season premiered on The CW on October 6, 2015, and ran until May 24, 2016. === Home media === The season began streaming on Netflix on October 4, 2016, and was released on Blu-ray and DVD in Region 1 on September 6, 2016. === Copyright infringement === The second season of The Flash was the fourth most-torrented television show of 2016. == Reception == === Ratings === The second season finished as the 112th ranked show, with an average viewership of 4.25 million. === Critical response === The review aggregator website Rotten Tomatoes reported a 94% approval rating for the second season with an average rating of 7.84/10, based on 24 reviews. The website's consensus reads, "With distinctive visuals and a terrific cast, The Flash remains one of the strongest comic book shows on television." Metacritic, which uses a weighted average, assigned the season a score of 81 out of 100, based on 4 reviews, indicating "universal acclaim". Reviewing for Collider, Dave Trumbore gave the season premiere a rating of 4 stars out of 5, saying, "All in all, a very good way to start season two after the strong run of season one." Mike Cecchini of Den of Geek! meanwhile rated the episode 3.5 stars out of 5, criticizing the episode's "unsettled" and "rushed" nature. He felt that the episode "seems so focused on getting this season off to a running start that it [...] doesn't give events time to breathe." Erik Kain of Forbes noted a "very big piece" missing in the absence of Harrison Wells, but felt that the episode was "an excellent start to the sophomore season of the CW's best super hero show." Although Henry Allen's abrupt exit was a common point of criticism amongst reviewers, Trumbore nevertheless felt that it was "a small price to pay for an otherwise cohesive, entertaining, and emotionally satisfying episode." The episode "Welcome to Earth-2" received a number of positive reviews. Erik Kain said that it was "The Flash at its best. An engaging, funny, scary episode that hits all the right notes from start to finish." IGN's Jesse Schedeen rated it 9.7 out of 10, praising the concept of Earth-2, Barry's dramatic moments, the depiction of Deathstorm, Killer Frost, and Reverb, but criticized the need to kill off Reverb so soon. He concluded, "The Flash delivered one of its best episodes yet as Barry and friends took a hilarious but emotional trip to Earth-2." Angelica Jade Bastién of Vulture said the episode "marries incredible action sequences, amazing direction by Millicent Shelton, some of the cast's best acting (particularly from Candice Patton and Grant Gustin), lots of heart, and just the right number of nods to the comics. It is undoubtedly the best episode of the season, and just may be the best episode of The Flash yet." Dave Trumbore rated the episode 4 stars out of 5, saying, "This was an absolutely insane episode of The Flash, and that's saying something since this show is normally fast-paced and full of Easter eggs even on a relatively slow week." Entertainment Weekly's Jonathon Dornbush praised the scene where Barry talks to his Earth-2 doppelgänger's mother over phone, saying Gustin "has proved mightily adept at tackling Barry's grief, hope, and the many other emotions swirling around in regard to his mother and her death." Scott Von Doviak of The A.V. Club said, "Since its return from hiatus, The Flash has been sluggish and morose, and the Zoom arc has fizzled. 'Welcome to Earth-2' jump-starts both the storyline and the season as a whole [...and] is just about as good as The Flash gets." Reviewing the season finale, Allison Keene of Collider directed specific praise to Gustin's performance, saying "Sometimes a great TV performer can come out of an already fantastic episode, but occasionally an actor can rise above the material, proving that even though the writers have let them down, the actor is going to make the most of what they've been given. That's exactly where we find ourselves with The Flash's head-scratching finale, which capped off a largely enjoyable but ultimately uneven second season. What has never been in doubt, though, is star Grant Gustin's ability to convince viewers that this all makes sense in an emotional, earnest, and often light-hearted way." In his review for Nerdist, Joseph McCabe concluded, "For all this season's faults, most of which came from repeating the major villain arc of season one, [...] there were moments in the last handful of episodes where Barry demonstrated more independent thought than the show often allows him. Coming up with his own ideas, for example, to defeat the villain of the week rather than relying on his friends at S.T.A.R. Labs. That's the Barry I want to see more of in season three. A number of critics felt that the season as a whole suffered from the standards set by its predecessor, calling it "uneven" and criticizing the handling of the season's main villain. Collider's Kayti Burt gave the season 3 stars out of 5, saying, "The Flash finished off an uneven season with an uneven finale that couldn't overcome the burden of an underdeveloped, illogical villain. With Zoom, The Flash fell victim to a common drama mistake of a contemporary TV era: it prioritized the plot twist over the well-developed character arc." Jeff Jensen of Entertainment Weekly gave the season a "B−" grade, calling it "certifiably slumptacular" and said that the "bold" introduction of the multiverse did not meet his expectations. Jensen praised Barry's onscreen rapport with Joe but felt it was underutilized due to the introduction of Joe's biological son Wally, and criticized Barry's romantic fixation for Iris. He also criticized Zoom, saying, "He began as an alluring mystery but lost zip over time" and once his identity was revealed, "became a weak embodiment of generic villainy". Jesse Schedeen gave the entire season a rating of 8.6 out of 10, explaining, "This season met and occasionally even exceeded the heights of its predecessor. But it was also a more uneven and ultimately more flawed experience in the end." === Accolades === The Flash was included on multiple Best/Top TV Shows of 2015 lists, ranking on The Salt Lake Tribune's (4th), Omaha World-Herald's (7th), and IndieWire's (10th), as well as on un-ranked lists of Criticwire and Variety. In its second season, The Flash was nominated for 20 awards, winning five. The series was nominated for three Saturn Awards, winning Best Superhero Adaption Television Series for the second year in a row. The show was also nominated for three Leo Awards, winning again for Best Visual Effects in a Dramatic Series for the episode "Gorilla Warfare". At the 2016 Teen Choice Awards, the show gained six nominations with Gustin winning for Choice TV Actor: Fantasy/Sci-Fi. == Notes == == References == === General references === == External links == Official website The Flash at IMDb
Wikipedia/Potential_Energy_(The_Flash)
In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calculated by integrating radiant flux (or power) with respect to time. The symbol Qe is often used throughout literature to denote radiant energy ("e" for "energetic", to avoid confusion with photometric quantities). In branches of physics other than radiometry, electromagnetic energy is referred to using E or W. The term is used particularly when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be visible or invisible to the human eye. == Terminology use and history == The term "radiant energy" is most commonly used in the fields of radiometry, solar energy, heating and lighting, but is also sometimes used in other fields (such as telecommunications). In modern applications involving transmission of power from one location to another, "radiant energy" is sometimes used to refer to the electromagnetic waves themselves, rather than their energy (a property of the waves). In the past, the term "electro-radiant energy" has also been used. The term "radiant energy" also applies to gravitational radiation. For example, the first gravitational waves ever observed were produced by a black hole collision that emitted about 5.3×1047 joules of gravitational-wave energy. == Analysis == Because electromagnetic (EM) radiation can be conceptualized as a stream of photons, radiant energy can be viewed as photon energy – the energy carried by these photons. Alternatively, EM radiation can be viewed as an electromagnetic wave, which carries energy in its oscillating electric and magnetic fields. These two views are completely equivalent and are reconciled to one another in quantum field theory (see wave-particle duality). EM radiation can have various frequencies. The bands of frequency present in a given EM signal may be sharply defined, as is seen in atomic spectra, or may be broad, as in blackbody radiation. In the particle picture, the energy carried by each photon is proportional to its frequency. In the wave picture, the energy of a monochromatic wave is proportional to its intensity. This implies that if two EM waves have the same intensity, but different frequencies, the one with the higher frequency "contains" fewer photons, since each photon is more energetic. When EM waves are absorbed by an object, the energy of the waves is converted to heat (or converted to electricity in case of a photoelectric material). This is a very familiar effect, since sunlight warms surfaces that it irradiates. Often this phenomenon is associated particularly with infrared radiation, but any kind of electromagnetic radiation will warm an object that absorbs it. EM waves can also be reflected or scattered, in which case their energy is redirected or redistributed as well. === Open systems === Radiant energy is one of the mechanisms by which energy can enter or leave an open system. Such a system can be man-made, such as a solar energy collector, or natural, such as the Earth's atmosphere. In geophysics, most atmospheric gases, including the greenhouse gases, allow the Sun's short-wavelength radiant energy to pass through to the Earth's surface, heating the ground and oceans. The absorbed solar energy is partly re-emitted as longer wavelength radiation (chiefly infrared radiation), some of which is absorbed by the atmospheric greenhouse gases. Radiant energy is produced in the sun as a result of nuclear fusion. == Applications == Radiant energy is used for radiant heating. It can be generated electrically by infrared lamps, or can be absorbed from sunlight and used to heat water. The heat energy is emitted from a warm element (floor, wall, overhead panel) and warms people and other objects in rooms rather than directly heating the air. Because of this, the air temperature may be lower than in a conventionally heated building, even though the room appears just as comfortable. Various other applications of radiant energy have been devised. These include treatment and inspection, separating and sorting, medium of control, and medium of communication. Many of these applications involve a source of radiant energy and a detector that responds to that radiation and provides a signal representing some characteristic of the radiation. Radiant energy detectors produce responses to incident radiant energy either as an increase or decrease in electric potential or current flow or some other perceivable change, such as exposure of photographic film. == SI radiometry units == == See also == == Notes and references == == Further reading ==
Wikipedia/Electromagnetic_energy
In continuum mechanics, stress is a physical quantity that describes forces present during deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to tensile stress and may undergo elongation. An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has dimension of force per area, with SI units of newtons per square meter (N/m2) or pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the relative deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface (such as a piston) push against them in (Newtonian) reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma (σ). Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the bulk material (like gravity) or to its surface (like contact forces, external pressure, or friction). Any strain (deformation) of a solid material generates an internal elastic stress, analogous to the reaction force of a spring, that tends to restore the material to its original non-deformed state. In liquids and gases, only deformations that change the volume generate persistent elastic stress. If the deformation changes gradually with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the name mechanical stress. Significant stress may exist even when deformation is negligible or non-existent (a common assumption when modeling the flow of water). Stress may exist in the absence of external forces; such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, or by external electromagnetic fields (as in piezoelectric and magnetostrictive materials). The relation between mechanical stress, strain, and the strain rate can be quite complicated, although a linear approximation may be adequate in practice if the quantities are sufficiently small. Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow, fracture, cavitation) or even change its crystal structure and chemical composition. == History == Humans have known about stress inside materials since ancient times. Until the 17th century, this understanding was largely intuitive and empirical, though this did not prevent the development of relatively advanced technologies like the composite bow and glass blowing. Over several millennia, architects and builders in particular, learned how to put together carefully shaped wood beams and stone blocks to withstand, transmit, and distribute stress in the most effective manner, with ingenious devices such as the capitals, arches, cupolas, trusses and the flying buttresses of Gothic cathedrals. Ancient and medieval architects did develop some geometrical methods and simple formulas to compute the proper sizes of pillars and beams, but the scientific understanding of stress became possible only after the necessary tools were invented in the 17th and 18th centuries: Galileo Galilei's rigorous experimental method, René Descartes's coordinates and analytic geometry, and Newton's laws of motion and equilibrium and calculus of infinitesimals. With those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model of a deformed elastic body by introducing the notions of stress and strain. Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and, moreover, that it must be a symmetric function (with zero total momentum). The understanding of stress in liquids started with Newton, who provided a differential formula for friction forces (shear stress) in parallel laminar flow. == Definition == Stress is defined as the force across a small boundary per unit area of that boundary, for all orientations of the boundary. Derived from a physical quantity (force) and a purely geometrical quantity (area), stress is also a physical quantity, like velocity, torque or energy, that can be quantified and analyzed without explicit consideration of the nature of the material or of its physical causes. Following the basic premises of continuum mechanics, stress is a macroscopic concept. Namely, the particles considered in its definition and analysis should be just small enough to be treated as homogeneous in composition and state, but still large enough to ignore quantum effects and the detailed motions of molecules. Thus, the force between two particles is actually the average of a very large number of atomic forces between their molecules; and physical quantities like mass, velocity, and forces that act through the bulk of three-dimensional bodies, like gravity, are assumed to be smoothly distributed over them.: 90–106  Depending on the context, one may also assume that the particles are large enough to allow the averaging out of other microscopic features, like the grains of a metal rod or the fibers of a piece of wood. Quantitatively, the stress is expressed by the Cauchy traction vector T defined as the traction force F between adjacent parts of the material across an imaginary separating surface S, divided by the area of S.: 41–50  In a fluid at rest the force is perpendicular to the surface, and is the familiar pressure. In a solid, or in a flow of viscous liquid, the force F may not be perpendicular to S; hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude generally depend on the orientation of S. Thus the stress state of the material must be described by a tensor, called the (Cauchy) stress tensor; which is a linear function that relates the normal vector n of a surface S to the traction vector T across S. With respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers. Even within a homogeneous body, the stress tensor may vary from place to place, and may change over time; therefore, the stress within a material is, in general, a time-varying tensor field. === Normal and shear === In general, the stress T that a particle P applies on another particle Q across a surface S can have any direction relative to S. The vector T may be regarded as the sum of two components: the normal stress (compression or tension) perpendicular to the surface, and the shear stress that is parallel to the surface. If the normal unit vector n of the surface (pointing from Q towards P) is assumed fixed, the normal component can be expressed by a single number, the dot product T · n. This number will be positive if P is "pulling" on Q (tensile stress), and negative if P is "pushing" against Q (compressive stress). The shear component is then the vector T − (T · n)n. == Units == The dimension of stress is that of pressure, and therefore its coordinates are measured in the same units as pressure: namely, pascals (Pa, that is, newtons per square metre) in the International System, or pounds per square inch (psi) in the Imperial system. Because mechanical stresses easily exceed a million Pascals, MPa, which stands for megapascal, is a common unit of stress. == Causes and effects == Stress in a material body may be due to multiple physical causes, including external influences and internal physical processes. Some of these agents (like gravity, changes in temperature and phase, and electromagnetic fields) act on the bulk of the material, varying continuously with position and time. Other agents (like external loads and friction, ambient pressure, and contact forces) may create stresses and forces that are concentrated on certain surfaces, lines or points; and possibly also on very short time intervals (as in the impulses due to collisions). In active matter, self-propulsion of microscopic particles generates macroscopic stress profiles. In general, the stress distribution in a body is expressed as a piecewise continuous function of space and time. Conversely, stress is usually correlated with various effects on the material, possibly including changes in physical properties like birefringence, polarization, and permeability. The imposition of stress by an external agent usually creates some strain (deformation) in the material, even if it is too small to be detected. In a solid material, such strain will in turn generate an internal elastic stress, analogous to the reaction force of a stretched spring, tending to restore the material to its original undeformed state. Fluid materials (liquids, gases and plasmas) by definition can only oppose deformations that would change their volume. If the deformation changes with time, even in fluids there will usually be some viscous stress, opposing that change. Such stresses can be either shear or normal in nature. Molecular origin of shear stresses in fluids is given in the article on viscosity. The same for normal viscous stresses can be found in Sharma (2019). The relation between stress and its effects and causes, including deformation and rate of change of deformation, can be quite complicated (although a linear approximation may be adequate in practice if the quantities are small enough). Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow, fracture, cavitation) or even change its crystal structure and chemical composition. == Simple types == In some situations, the stress within a body may adequately be described by a single number, or by a single vector (a number and a direction). Three such simple stress situations, that are often encountered in engineering design, are the uniaxial normal stress, the simple shear stress, and the isotropic normal stress. === Uniaxial normal === A common situation with a simple stress pattern is when a straight rod, with uniform material and cross section, is subjected to tension by opposite forces of magnitude F {\displaystyle F} along its axis. If the system is in equilibrium and not changing with time, and the weight of the bar can be neglected, then through each transversal section of the bar the top part must pull on the bottom part with the same force, F with continuity through the full cross-sectional area, A. Therefore, the stress σ throughout the bar, across any horizontal surface, can be expressed simply by the single number σ, calculated simply with the magnitude of those forces, F, and cross sectional area, A. σ = F A {\displaystyle \sigma ={\frac {F}{A}}} On the other hand, if one imagines the bar being cut along its length, parallel to the axis, there will be no force (hence no stress) between the two halves across the cut. This type of stress may be called (simple) normal stress or uniaxial stress; specifically, (uniaxial, simple, etc.) tensile stress. If the load is compression on the bar, rather than stretching it, the analysis is the same except that the force F and the stress σ {\displaystyle \sigma } change sign, and the stress is called compressive stress. This analysis assumes the stress is evenly distributed over the entire cross-section. In practice, depending on how the bar is attached at the ends and how it was manufactured, this assumption may not be valid. In that case, the value σ {\displaystyle \sigma } = F/A will be only the average stress, called engineering stress or nominal stress. If the bar's length L is many times its diameter D, and it has no gross defects or built-in stress, then the stress can be assumed to be uniformly distributed over any cross-section that is more than a few times D from both ends. (This observation is known as the Saint-Venant's principle). Normal stress occurs in many other situations besides axial tension and compression. If an elastic bar with uniform and symmetric cross-section is bent in one of its planes of symmetry, the resulting bending stress will still be normal (perpendicular to the cross-section), but will vary over the cross section: the outer part will be under tensile stress, while the inner part will be compressed. Another variant of normal stress is the hoop stress that occurs on the walls of a cylindrical pipe or vessel filled with pressurized fluid. === Shear === Another simple type of stress occurs when a uniformly thick layer of elastic material like glue or rubber is firmly attached to two stiff bodies that are pulled in opposite directions by forces parallel to the layer; or a section of a soft metal bar that is being cut by the jaws of a scissors-like tool. Let F be the magnitude of those forces, and M be the midplane of that layer. Just as in the normal stress case, the part of the layer on one side of M must pull the other part with the same force F. Assuming that the direction of the forces is known, the stress across M can be expressed simply by the single number τ {\displaystyle \tau } , calculated simply with the magnitude of those forces, F and the cross sectional area, A. τ = F A {\displaystyle \tau ={\frac {F}{A}}} Unlike normal stress, this simple shear stress is directed parallel to the cross-section considered, rather than perpendicular to it. For any plane S that is perpendicular to the layer, the net internal force across S, and hence the stress, will be zero. As in the case of an axially loaded bar, in practice the shear stress may not be uniformly distributed over the layer; so, as before, the ratio F/A will only be an average ("nominal", "engineering") stress. That average is often sufficient for practical purposes.: 292  Shear stress is observed also when a cylindrical bar such as a shaft is subjected to opposite torques at its ends. In that case, the shear stress on each cross-section is parallel to the cross-section, but oriented tangentially relative to the axis, and increases with distance from the axis. Significant shear stress occurs in the middle plate (the "web") of I-beams under bending loads, due to the web constraining the end plates ("flanges"). === Isotropic === Another simple type of stress occurs when the material body is under equal compression or tension in all directions. This is the case, for example, in a portion of liquid or gas at rest, whether enclosed in some container or as part of a larger mass of fluid; or inside a cube of elastic material that is being pressed or pulled on all six faces by equal perpendicular forces — provided, in both cases, that the material is homogeneous, without built-in stress, and that the effect of gravity and other external forces can be neglected. In these situations, the stress across any imaginary internal surface turns out to be equal in magnitude and always directed perpendicularly to the surface independently of the surface's orientation. This type of stress may be called isotropic normal or just isotropic; if it is compressive, it is called hydrostatic pressure or just pressure. Gases by definition cannot withstand tensile stresses, but some liquids may withstand very large amounts of isotropic tensile stress under some circumstances. see Z-tube. === Cylinder === Parts with rotational symmetry, such as wheels, axles, pipes, and pillars, are very common in engineering. Often the stress patterns that occur in such parts have rotational or even cylindrical symmetry. The analysis of such cylinder stresses can take advantage of the symmetry to reduce the dimension of the domain and/or of the stress tensor. == General types == Often, mechanical bodies experience more than one type of stress at the same time; this is called combined stress. In normal and shear stress, the magnitude of the stress is maximum for surfaces that are perpendicular to a certain direction d {\displaystyle d} , and zero across any surfaces that are parallel to d {\displaystyle d} . When the shear stress is zero only across surfaces that are perpendicular to one particular direction, the stress is called biaxial, and can be viewed as the sum of two normal or shear stresses. In the most general case, called triaxial stress, the stress is nonzero across every surface element. == Cauchy tensor == Combined stresses cannot be described by a single vector. Even if the material is stressed in the same way throughout the volume of the body, the stress across any imaginary surface will depend on the orientation of that surface, in a non-trivial way. Cauchy observed that the stress vector T {\displaystyle T} across a surface will always be a linear function of the surface's normal vector n {\displaystyle n} , the unit-length vector that is perpendicular to it. That is, T = σ ( n ) {\displaystyle T={\boldsymbol {\sigma }}(n)} , where the function σ {\displaystyle {\boldsymbol {\sigma }}} satisfies σ ( α u + β v ) = α σ ( u ) + β σ ( v ) {\displaystyle {\boldsymbol {\sigma }}(\alpha u+\beta v)=\alpha {\boldsymbol {\sigma }}(u)+\beta {\boldsymbol {\sigma }}(v)} for any vectors u , v {\displaystyle u,v} and any real numbers α , β {\displaystyle \alpha ,\beta } . The function σ {\displaystyle {\boldsymbol {\sigma }}} , now called the (Cauchy) stress tensor, completely describes the stress state of a uniformly stressed body. (Today, any linear connection between two physical vector quantities is called a tensor, reflecting Cauchy's original use to describe the "tensions" (stresses) in a material.) In tensor calculus, σ {\displaystyle {\boldsymbol {\sigma }}} is classified as a second-order tensor of type (0,2) or (1,1) depending on convention. Like any linear map between vectors, the stress tensor can be represented in any chosen Cartesian coordinate system by a 3×3 matrix of real numbers. Depending on whether the coordinates are numbered x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} or named x , y , z {\displaystyle x,y,z} , the matrix may be written as [ σ 11 σ 12 σ 13 σ 21 σ 22 σ 23 σ 31 σ 32 σ 33 ] {\displaystyle {\begin{bmatrix}\sigma _{11}&\sigma _{12}&\sigma _{13}\\\sigma _{21}&\sigma _{22}&\sigma _{23}\\\sigma _{31}&\sigma _{32}&\sigma _{33}\end{bmatrix}}} or [ σ x x σ x y σ x z σ y x σ y y σ y z σ z x σ z y σ z z ] {\displaystyle {\begin{bmatrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{yx}&\sigma _{yy}&\sigma _{yz}\\\sigma _{zx}&\sigma _{zy}&\sigma _{zz}\\\end{bmatrix}}} The stress vector T = σ ( n ) {\displaystyle T={\boldsymbol {\sigma }}(n)} across a surface with normal vector n {\displaystyle n} (which is covariant - "row; horizontal" - vector) with coordinates n 1 , n 2 , n 3 {\displaystyle n_{1},n_{2},n_{3}} is then a matrix product T = n ⋅ σ {\displaystyle T=n\cdot {\boldsymbol {\sigma }}} (where T in upper index is transposition, and as a result we get covariant (row) vector) (look on Cauchy stress tensor), that is [ T 1 T 2 T 3 ] = [ n 1 n 2 n 3 ] ⋅ [ σ 11 σ 21 σ 31 σ 12 σ 22 σ 32 σ 13 σ 23 σ 33 ] {\displaystyle {\begin{bmatrix}T_{1}&T_{2}&T_{3}\end{bmatrix}}={\begin{bmatrix}n_{1}&n_{2}&n_{3}\end{bmatrix}}\cdot {\begin{bmatrix}\sigma _{11}&\sigma _{21}&\sigma _{31}\\\sigma _{12}&\sigma _{22}&\sigma _{32}\\\sigma _{13}&\sigma _{23}&\sigma _{33}\end{bmatrix}}} The linear relation between T {\displaystyle T} and n {\displaystyle n} follows from the fundamental laws of conservation of linear momentum and static equilibrium of forces, and is therefore mathematically exact, for any material and any stress situation. The components of the Cauchy stress tensor at every point in a material satisfy the equilibrium equations (Cauchy's equations of motion for zero acceleration). Moreover, the principle of conservation of angular momentum implies that the stress tensor is symmetric, that is σ 12 = σ 21 {\displaystyle \sigma _{12}=\sigma _{21}} , σ 13 = σ 31 {\displaystyle \sigma _{13}=\sigma _{31}} , and σ 23 = σ 32 {\displaystyle \sigma _{23}=\sigma _{32}} . Therefore, the stress state of the medium at any point and instant can be specified by only six independent parameters, rather than nine. These may be written [ σ x τ x y τ x z τ x y σ y τ y z τ x z τ y z σ z ] {\displaystyle {\begin{bmatrix}\sigma _{x}&\tau _{xy}&\tau _{xz}\\\tau _{xy}&\sigma _{y}&\tau _{yz}\\\tau _{xz}&\tau _{yz}&\sigma _{z}\end{bmatrix}}} where the elements σ x , σ y , σ z {\displaystyle \sigma _{x},\sigma _{y},\sigma _{z}} are called the orthogonal normal stresses (relative to the chosen coordinate system), and τ x y , τ x z , τ y z {\displaystyle \tau _{xy},\tau _{xz},\tau _{yz}} the orthogonal shear stresses. === Change of coordinates === The Cauchy stress tensor obeys the tensor transformation law under a change in the system of coordinates. A graphical representation of this transformation law is the Mohr's circle of stress distribution. As a symmetric 3×3 real matrix, the stress tensor σ {\displaystyle {\boldsymbol {\sigma }}} has three mutually orthogonal unit-length eigenvectors e 1 , e 2 , e 3 {\displaystyle e_{1},e_{2},e_{3}} and three real eigenvalues λ 1 , λ 2 , λ 3 {\displaystyle \lambda _{1},\lambda _{2},\lambda _{3}} , such that σ e i = λ i e i {\displaystyle {\boldsymbol {\sigma }}e_{i}=\lambda _{i}e_{i}} . Therefore, in a coordinate system with axes e 1 , e 2 , e 3 {\displaystyle e_{1},e_{2},e_{3}} , the stress tensor is a diagonal matrix, and has only the three normal components λ 1 , λ 2 , λ 3 {\displaystyle \lambda _{1},\lambda _{2},\lambda _{3}} the principal stresses. If the three eigenvalues are equal, the stress is an isotropic compression or tension, always perpendicular to any surface, there is no shear stress, and the tensor is a diagonal matrix in any coordinate frame. === Tensor field === In general, stress is not uniformly distributed over a material body, and may vary with time. Therefore, the stress tensor must be defined for each point and each moment, by considering an infinitesimal particle of the medium surrounding that point, and taking the average stresses in that particle as being the stresses at the point. === Thin plates === Human-made objects are often made from stock plates of various materials by operations that do not change their essentially two-dimensional character, like cutting, drilling, gentle bending and welding along the edges. The description of stress in such bodies can be simplified by modeling those parts as two-dimensional surfaces rather than three-dimensional bodies. In that view, one redefines a "particle" as being an infinitesimal patch of the plate's surface, so that the boundary between adjacent particles becomes an infinitesimal line element; both are implicitly extended in the third dimension, normal to (straight through) the plate. "Stress" is then redefined as being a measure of the internal forces between two adjacent "particles" across their common line element, divided by the length of that line. Some components of the stress tensor can be ignored, but since particles are not infinitesimal in the third dimension one can no longer ignore the torque that a particle applies on its neighbors. That torque is modeled as a bending stress that tends to change the curvature of the plate. These simplifications may not hold at welds, at sharp bends and creases (where the radius of curvature is comparable to the thickness of the plate). === Thin beams === The analysis of stress can be considerably simplified also for thin bars, beams or wires of uniform (or smoothly varying) composition and cross-section that are subjected to moderate bending and twisting. For those bodies, one may consider only cross-sections that are perpendicular to the bar's axis, and redefine a "particle" as being a piece of wire with infinitesimal length between two such cross sections. The ordinary stress is then reduced to a scalar (tension or compression of the bar), but one must take into account also a bending stress (that tries to change the bar's curvature, in some direction perpendicular to the axis) and a torsional stress (that tries to twist or un-twist it about its axis). == Analysis == Stress analysis is a branch of applied physics that covers the determination of the internal distribution of internal forces in solid objects. It is an essential tool in engineering for the study and design of structures such as tunnels, dams, mechanical parts, and structural frames, under prescribed or expected loads. It is also important in many other disciplines; for example, in geology, to study phenomena like plate tectonics, vulcanism and avalanches; and in biology, to understand the anatomy of living beings. === Goals and assumptions === Stress analysis is generally concerned with objects and structures that can be assumed to be in macroscopic static equilibrium. By Newton's laws of motion, any external forces being applied to such a system must be balanced by internal reaction forces,: 97  which are almost always surface contact forces between adjacent particles — that is, as stress. Since every particle needs to be in equilibrium, this reaction stress will generally propagate from particle to particle, creating a stress distribution throughout the body. The typical problem in stress analysis is to determine these internal stresses, given the external forces that are acting on the system. The latter may be body forces (such as gravity or magnetic attraction), that act throughout the volume of a material;: 42–81  or concentrated loads (such as friction between an axle and a bearing, or the weight of a train wheel on a rail), that are imagined to act over a two-dimensional area, or along a line, or at single point. In stress analysis one normally disregards the physical causes of the forces or the precise nature of the materials. Instead, one assumes that the stresses are related to deformation (and, in non-static problems, to the rate of deformation) of the material by known constitutive equations. === Methods === Stress analysis may be carried out experimentally, by applying loads to the actual artifact or to scale model, and measuring the resulting stresses, by any of several available methods. This approach is often used for safety certification and monitoring. Most stress is analysed by mathematical methods, especially during design. The basic stress analysis problem can be formulated by Euler's equations of motion for continuous bodies (which are consequences of Newton's laws for conservation of linear momentum and angular momentum) and the Euler-Cauchy stress principle, together with the appropriate constitutive equations. Thus one obtains a system of partial differential equations involving the stress tensor field and the strain tensor field, as unknown functions to be determined. The external body forces appear as the independent ("right-hand side") term in the differential equations, while the concentrated forces appear as boundary conditions. The basic stress analysis problem is therefore a boundary-value problem. Stress analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation, one must use more complicated constitutive equations, that can account for the physical processes involved (plastic flow, fracture, phase change, etc.). Engineered structures are usually designed so the maximum expected stresses are well within the range of linear elasticity (the generalization of Hooke's law for continuous media); that is, the deformations caused by internal stresses are linearly related to them. In this case the differential equations that define the stress tensor are linear, and the problem becomes much easier. For one thing, the stress at any point will be a linear function of the loads, too. For small enough stresses, even non-linear systems can usually be assumed to be linear. Stress analysis is simplified when the physical dimensions and the distribution of loads allow the structure to be treated as one- or two-dimensional. In the analysis of trusses, for example, the stress field may be assumed to be uniform and uniaxial over each member. Then the differential equations reduce to a finite set of equations (usually linear) with finitely many unknowns. In other contexts one may be able to reduce the three-dimensional problem to a two-dimensional one, and/or replace the general stress and strain tensors by simpler models like uniaxial tension/compression, simple shear, etc. Still, for two- or three-dimensional cases one must solve a partial differential equation problem. Analytical or closed-form solutions to the differential equations can be obtained when the geometry, constitutive relations, and boundary conditions are simple enough. Otherwise one must generally resort to numerical approximations such as the finite element method, the finite difference method, and the boundary element method. == Measures == Other useful stress measures include the first and second Piola–Kirchhoff stress tensors, the Biot stress tensor, and the Kirchhoff stress tensor. == See also == == References == == Further reading ==
Wikipedia/Stress_(physics)
The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e., the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. Without a thermodynamic process, the internal energy of an isolated system cannot change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics. The notion has been introduced to describe the systems characterized by temperature variations, temperature being added to the set of state parameters, the position variables known in mechanics (and their conjugated generalized force parameters), in a similar way to potential energy of the conservative fields of force, gravitational and electrostatic. Its author is Rudolf Clausius. Without transfer of matter, internal energy changes equal the algebraic sum of the heat transferred and the work done. In systems without temperature changes, internal energy changes equal the work done by/on the system. The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of substance, or of energy, as heat, or by thermodynamic work. These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property. Thermodynamics defines internal energy macroscopically, for the body as a whole. In statistical mechanics, the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energies associated with microscopic forces, including chemical bonds. The unit of energy in the International System of Units (SI) is the joule (J). The internal energy relative to the mass with unit J/kg is the specific internal energy. The corresponding quantity relative to the amount of substance with unit J/mol is the molar internal energy. == Cardinal functions == The internal energy of a system depends on its entropy S, its volume V and its number of massive particles: U(S,V,{Nj}). It expresses the thermodynamics of a system in the energy representation. As a function of state, its arguments are exclusively extensive variables of state. Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy, as a function, S(U,V,{Nj}), of the same list of extensive variables of state, except that the entropy, S, is replaced in the list by the internal energy, U. It expresses the entropy representation. Each cardinal function is a monotonic function of each of its natural or canonical variables. Each provides its characteristic or fundamental equation, for example U = U(S,V,{Nj}), that by itself contains all thermodynamic information about the system. The fundamental equations for the two cardinal functions can in principle be interconverted by solving, for example, U = U(S,V,{Nj}) for S, to get S = S(U,V,{Nj}). In contrast, Legendre transformations are necessary to derive fundamental equations for other thermodynamic potentials and Massieu functions. The entropy as a function only of extensive state variables is the one and only cardinal function of state for the generation of Massieu functions. It is not itself customarily designated a 'Massieu function', though rationally it might be thought of as such, corresponding to the term 'thermodynamic potential', which includes the internal energy. For real and practical systems, explicit expressions of the fundamental equations are almost always unavailable, but the functional relations exist in principle. Formal, in principle, manipulations of them are valuable for the understanding of thermodynamics. == Description and definition == The internal energy U {\displaystyle U} of a given state of the system is determined relative to that of a standard state of the system, by adding up the macroscopic transfers of energy that accompany a change of state from the reference state to the given state: Δ U = ∑ i E i , {\displaystyle \Delta U=\sum _{i}E_{i},} where Δ U {\displaystyle \Delta U} denotes the difference between the internal energy of the given state and that of the reference state, and the E i {\displaystyle E_{i}} are the various energies transferred to the system in the steps from the reference state to the given state. It is the energy needed to create the given state of the system from the reference state. From a non-relativistic microscopic point of view, it may be divided into microscopic potential energy, U micro,pot {\displaystyle U_{\text{micro,pot}}} , and microscopic kinetic energy, U micro,kin {\displaystyle U_{\text{micro,kin}}} , components: U = U micro,pot + U micro,kin . {\displaystyle U=U_{\text{micro,pot}}+U_{\text{micro,kin}}.} The microscopic kinetic energy of a system arises as the sum of the motions of all the system's particles with respect to the center-of-mass frame, whether it be the motion of atoms, molecules, atomic nuclei, electrons, or other particles. The microscopic potential energy algebraic summative components are those of the chemical and nuclear particle bonds, and the physical force fields within the system, such as due to internal induced electric or magnetic dipole moment, as well as the energy of deformation of solids (stress-strain). Usually, the split into microscopic kinetic and potential energies is outside the scope of macroscopic thermodynamics. Internal energy does not include the energy due to motion or location of a system as a whole. That is to say, it excludes any kinetic or potential energy the body may have because of its motion or location in external gravitational, electrostatic, or electromagnetic fields. It does, however, include the contribution of such a field to the energy due to the coupling of the internal degrees of freedom of the system with the field. In such a case, the field is included in the thermodynamic description of the object in the form of an additional external parameter. For practical considerations in thermodynamics or engineering, it is rarely necessary, convenient, nor even possible, to consider all energies belonging to the total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Indeed, in most systems under consideration, especially through thermodynamics, it is impossible to calculate the total internal energy. Therefore, a convenient null reference point may be chosen for the internal energy. The internal energy is an extensive property: it depends on the size of the system, or on the amount of substance it contains. At any temperature greater than absolute zero, microscopic potential energy and kinetic energy are constantly converted into one another, but the sum remains constant in an isolated system (cf. table). In the classical picture of thermodynamics, kinetic energy vanishes at zero temperature and the internal energy is purely potential energy. However, quantum mechanics has demonstrated that even at zero temperature particles maintain a residual energy of motion, the zero point energy. A system at absolute zero is merely in its quantum-mechanical ground state, the lowest energy state available. At absolute zero a system of given composition has attained its minimum attainable entropy. The microscopic kinetic energy portion of the internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore, it relates the mean microscopic kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system. While temperature is an intensive measure, this energy expresses the concept as an extensive property of the system, often referred to as the thermal energy, The scaling property between temperature and thermal energy is the entropy change of the system. Statistical mechanics considers any system to be statistically distributed across an ensemble of N {\displaystyle N} microstates. In a system that is in thermodynamic contact equilibrium with a heat reservoir, each microstate has an energy E i {\displaystyle E_{i}} and is associated with a probability p i {\displaystyle p_{i}} . The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by its probability of occurrence: U = ∑ i = 1 N p i E i . {\displaystyle U=\sum _{i=1}^{N}p_{i}\,E_{i}.} This is the statistical expression of the law of conservation of energy. === Internal energy changes === Thermodynamics is chiefly concerned with the changes in internal energy Δ U {\displaystyle \Delta U} . For a closed system, with mass transfer excluded, the changes in internal energy are due to heat transfer Q {\displaystyle Q} and due to thermodynamic work W {\displaystyle W} done by the system on its surroundings. Accordingly, the internal energy change Δ U {\displaystyle \Delta U} for a process may be written Δ U = Q − W (closed system, no transfer of substance) . {\displaystyle \Delta U=Q-W\quad {\text{(closed system, no transfer of substance)}}.} When a closed system receives energy as heat, this energy increases the internal energy. It is distributed between microscopic kinetic and microscopic potential energies. In general, thermodynamics does not trace this distribution. In an ideal gas all of the extra energy results in a temperature increase, as it is stored solely as microscopic kinetic energy; such heating is said to be sensible. A second kind of mechanism of change in the internal energy of a closed system changed is in its doing of work on its surroundings. Such work may be simply mechanical, as when the system expands to drive a piston, or, for example, when the system changes its electric polarization so as to drive a change in the electric field in the surroundings. If the system is not closed, the third mechanism that can increase the internal energy is transfer of substance into the system. This increase, Δ U m a t t e r {\displaystyle \Delta U_{\mathrm {matter} }} cannot be split into heat and work components. If the system is so set up physically that heat transfer and work that it does are by pathways separate from and independent of matter transfer, then the transfers of energy add to change the internal energy: Δ U = Q − W + Δ U matter (matter transfer pathway separate from heat and work transfer pathways) . {\displaystyle \Delta U=Q-W+\Delta U_{\text{matter}}\quad {\text{(matter transfer pathway separate from heat and work transfer pathways)}}.} If a system undergoes certain phase transformations while being heated, such as melting and vaporization, it may be observed that the temperature of the system does not change until the entire sample has completed the transformation. The energy introduced into the system while the temperature does not change is called latent energy or latent heat, in contrast to sensible heat, which is associated with temperature change. == Internal energy of the ideal gas == Thermodynamics often uses the concept of the ideal gas for teaching purposes, and as an approximation for working systems. The ideal gas consists of particles considered as point objects that interact only by elastic collisions and fill a volume such that their mean free path between collisions is much larger than their diameter. Such systems approximate monatomic gases such as helium and other noble gases. For an ideal gas the kinetic energy consists only of the translational energy of the individual atoms. Monatomic particles do not possess rotational or vibrational degrees of freedom, and are not electronically excited to higher energies except at very high temperatures. Therefore, the internal energy of an ideal gas depends solely on its temperature (and the number of gas particles): U = U ( N , T ) {\displaystyle U=U(N,T)} . It is not dependent on other thermodynamic quantities such as pressure or density. The internal energy of an ideal gas is proportional to its amount of substance (number of moles) N {\displaystyle N} and to its temperature T {\displaystyle T} U = c V N T , {\displaystyle U=c_{V}NT,} where c V {\displaystyle c_{V}} is the isochoric (at constant volume) molar heat capacity of the gas; c V {\displaystyle c_{V}} is constant for an ideal gas. The internal energy of any gas (ideal or not) may be written as a function of the three extensive properties S {\displaystyle S} , V {\displaystyle V} , N {\displaystyle N} (entropy, volume, number of moles). In case of the ideal gas it is in the following way U ( S , V , N ) = c o n s t ⋅ e S c V N V − R c V N R + c V c V , {\displaystyle U(S,V,N)=\mathrm {const} \cdot e^{\frac {S}{c_{V}N}}V^{\frac {-R}{c_{V}}}N^{\frac {R+c_{V}}{c_{V}}},} where c o n s t {\displaystyle \mathrm {const} } is an arbitrary positive constant and where R {\displaystyle R} is the universal gas constant. It is easily seen that U {\displaystyle U} is a linearly homogeneous function of the three variables (that is, it is extensive in these variables), and that it is weakly convex. Knowing temperature and pressure to be the derivatives T = ∂ U ∂ S , {\displaystyle T={\frac {\partial U}{\partial S}},} P = − ∂ U ∂ V , {\displaystyle P=-{\frac {\partial U}{\partial V}},} the ideal gas law P V = N R T {\displaystyle PV=NRT} immediately follows as below: T = ∂ U ∂ S = U c V N {\displaystyle T={\frac {\partial U}{\partial S}}={\frac {U}{c_{V}N}}} P = − ∂ U ∂ V = U R c V V {\displaystyle P=-{\frac {\partial U}{\partial V}}=U{\frac {R}{c_{V}V}}} P T = U R c V V U c V N = N R V {\displaystyle {\frac {P}{T}}={\frac {\frac {UR}{c_{V}V}}{\frac {U}{c_{V}N}}}={\frac {NR}{V}}} P V = N R T {\displaystyle PV=NRT} == Internal energy of a closed thermodynamic system == The above summation of all components of change in internal energy assumes that a positive energy denotes heat added to the system or the negative of work done by the system on its surroundings. This relationship may be expressed in infinitesimal terms using the differentials of each term, though only the internal energy is an exact differential.: 33  For a closed system, with transfers only as heat and work, the change in the internal energy is d U = δ Q − δ W , {\displaystyle \mathrm {d} U=\delta Q-\delta W,} expressing the first law of thermodynamics. It may be expressed in terms of other thermodynamic parameters. Each term is composed of an intensive variable (a generalized force) and its conjugate infinitesimal extensive variable (a generalized displacement). For example, the mechanical work done by the system may be related to the pressure P {\displaystyle P} and volume change d V {\displaystyle \mathrm {d} V} . The pressure is the intensive generalized force, while the volume change is the extensive generalized displacement: δ W = P d V . {\displaystyle \delta W=P\,\mathrm {d} V.} This defines the direction of work, W {\displaystyle W} , to be energy transfer from the working system to the surroundings, indicated by a positive term. Taking the direction of heat transfer Q {\displaystyle Q} to be into the working fluid and assuming a reversible process, the heat is δ Q = T d S , {\displaystyle \delta Q=T\mathrm {d} S,} where T {\displaystyle T} denotes the temperature, and S {\displaystyle S} denotes the entropy. The change in internal energy becomes d U = T d S − P d V . {\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V.} === Changes due to temperature and volume === The expression relating changes in internal energy to changes in temperature and volume is This is useful if the equation of state is known. In case of an ideal gas, we can derive that d U = C V d T {\displaystyle dU=C_{V}\,dT} , i.e. the internal energy of an ideal gas can be written as a function that depends only on the temperature. === Changes due to temperature and pressure === When considering fluids or solids, an expression in terms of the temperature and pressure is usually more useful: d ⁡ U = ( C P − α P V ) d ⁡ T + ( β T P − α T ) V d ⁡ P , {\displaystyle \operatorname {d} U=\left(C_{P}-\alpha PV\right)\operatorname {d} T+\left(\beta _{T}P-\alpha T\right)V\operatorname {d} P,} where it is assumed that the heat capacity at constant pressure is related to the heat capacity at constant volume according to C P = C V + V T α 2 β T . {\displaystyle C_{P}=C_{V}+VT{\frac {\alpha ^{2}}{\beta _{T}}}.} === Changes due to volume at constant temperature === The internal pressure is defined as a partial derivative of the internal energy with respect to the volume at constant temperature: π T = ( ∂ U ∂ V ) T . {\displaystyle \pi _{T}=\left({\frac {\partial U}{\partial V}}\right)_{T}.} == Internal energy of multi-component systems == In addition to including the entropy S {\displaystyle S} and volume V {\displaystyle V} terms in the internal energy, a system is often described also in terms of the number of particles or chemical species it contains: U = U ( S , V , N 1 , … , N n ) , {\displaystyle U=U(S,V,N_{1},\ldots ,N_{n}),} where N j {\displaystyle N_{j}} are the molar amounts of constituents of type j {\displaystyle j} in the system. The internal energy is an extensive function of the extensive variables S {\displaystyle S} , V {\displaystyle V} , and the amounts N j {\displaystyle N_{j}} , the internal energy may be written as a linearly homogeneous function of first degree: U ( α S , α V , α N 1 , α N 2 , … ) = α U ( S , V , N 1 , N 2 , … ) , {\displaystyle U(\alpha S,\alpha V,\alpha N_{1},\alpha N_{2},\ldots )=\alpha U(S,V,N_{1},N_{2},\ldots ),} where α {\displaystyle \alpha } is a factor describing the growth of the system. The differential internal energy may be written as d U = ∂ U ∂ S d S + ∂ U ∂ V d V + ∑ i ∂ U ∂ N i d N i = T d S − P d V + ∑ i μ i d N i , {\displaystyle \mathrm {d} U={\frac {\partial U}{\partial S}}\mathrm {d} S+{\frac {\partial U}{\partial V}}\mathrm {d} V+\sum _{i}\ {\frac {\partial U}{\partial N_{i}}}\mathrm {d} N_{i}\ =T\,\mathrm {d} S-P\,\mathrm {d} V+\sum _{i}\mu _{i}\mathrm {d} N_{i},} which shows (or defines) temperature T {\displaystyle T} to be the partial derivative of U {\displaystyle U} with respect to entropy S {\displaystyle S} and pressure P {\displaystyle P} to be the negative of the similar derivative with respect to volume V {\displaystyle V} , T = ∂ U ∂ S , {\displaystyle T={\frac {\partial U}{\partial S}},} P = − ∂ U ∂ V , {\displaystyle P=-{\frac {\partial U}{\partial V}},} and where the coefficients μ i {\displaystyle \mu _{i}} are the chemical potentials for the components of type i {\displaystyle i} in the system. The chemical potentials are defined as the partial derivatives of the internal energy with respect to the variations in composition: μ i = ( ∂ U ∂ N i ) S , V , N j ≠ i . {\displaystyle \mu _{i}=\left({\frac {\partial U}{\partial N_{i}}}\right)_{S,V,N_{j\neq i}}.} As conjugate variables to the composition { N j } {\displaystyle \lbrace N_{j}\rbrace } , the chemical potentials are intensive properties, intrinsically characteristic of the qualitative nature of the system, and not proportional to its extent. Under conditions of constant T {\displaystyle T} and P {\displaystyle P} , because of the extensive nature of U {\displaystyle U} and its independent variables, using Euler's homogeneous function theorem, the differential d U {\displaystyle \mathrm {d} U} may be integrated and yields an expression for the internal energy: U = T S − P V + ∑ i μ i N i . {\displaystyle U=TS-PV+\sum _{i}\mu _{i}N_{i}.} The sum over the composition of the system is the Gibbs free energy: G = ∑ i μ i N i {\displaystyle G=\sum _{i}\mu _{i}N_{i}} that arises from changing the composition of the system at constant temperature and pressure. For a single component system, the chemical potential equals the Gibbs energy per amount of substance, i.e. particles or moles according to the original definition of the unit for { N j } {\displaystyle \lbrace N_{j}\rbrace } . == Internal energy in an elastic medium == For an elastic medium the potential energy component of the internal energy has an elastic nature expressed in terms of the stress σ i j {\displaystyle \sigma _{ij}} and strain ε i j {\displaystyle \varepsilon _{ij}} involved in elastic processes. In Einstein notation for tensors, with summation over repeated indices, for unit volume, the infinitesimal statement is d U = T d S + σ i j d ε i j . {\displaystyle \mathrm {d} U=T\mathrm {d} S+\sigma _{ij}\mathrm {d} \varepsilon _{ij}.} Euler's theorem yields for the internal energy: U = T S + 1 2 σ i j ε i j . {\displaystyle U=TS+{\frac {1}{2}}\sigma _{ij}\varepsilon _{ij}.} For a linearly elastic material, the stress is related to the strain by σ i j = C i j k l ε k l , {\displaystyle \sigma _{ij}=C_{ijkl}\varepsilon _{kl},} where the C i j k l {\displaystyle C_{ijkl}} are the components of the 4th-rank elastic constant tensor of the medium. Elastic deformations, such as sound, passing through a body, or other forms of macroscopic internal agitation or turbulent motion create states when the system is not in thermodynamic equilibrium. While such energies of motion continue, they contribute to the total energy of the system; thermodynamic internal energy pertains only when such motions have ceased. == History == James Joule studied the relationship between heat, work, and temperature. He observed that friction in a liquid, such as caused by its agitation with work by a paddle wheel, caused an increase in its temperature, which he described as producing a quantity of heat. Expressed in modern units, he found that c. 4186 joules of energy were needed to raise the temperature of one kilogram of water by one degree Celsius. == Notes == == See also == Calorimetry Enthalpy Exergy Thermodynamic equations Thermodynamic potentials Gibbs free energy Helmholtz free energy == References == === Bibliography of cited references === Adkins, C. J. (1968/1975). Equilibrium Thermodynamics, second edition, McGraw-Hill, London, ISBN 0-07-084057-1. Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3. Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London. Callen, H. B. (1960/1985), Thermodynamics and an Introduction to Thermostatistics, (first edition 1960), second edition 1985, John Wiley & Sons, New York, ISBN 0-471-86256-8. Crawford, F. H. (1963). Heat, Thermodynamics, and Statistical Physics, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc. Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081. Thomas W. Leland Jr., G. A. Mansoori (ed.), Basic Principles of Classical and Statistical Thermodynamics (PDF). Landau, L. D.; Lifshitz, E. M. (1986). Theory of Elasticity (Course of Theoretical Physics Volume 7). (Translated from Russian by J. B. Sykes and W. H. Reid) (Third ed.). Boston, MA: Butterworth Heinemann. ISBN 978-0-7506-2633-0. Münster, A. (1970), Classical Thermodynamics, translated by E. S. Halberstadt, Wiley–Interscience, London, ISBN 0-471-62430-6. Planck, M., (1923/1927). Treatise on Thermodynamics, translated by A. Ogg, third English edition, Longmans, Green and Co., London. Tschoegl, N. W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics, Elsevier, Amsterdam, ISBN 0-444-50426-5. == Bibliography == Alberty, R. A. (2001). "Use of Legendre transforms in chemical thermodynamics" (PDF). Pure Appl. Chem. 73 (8): 1349–1380. doi:10.1351/pac200173081349. S2CID 98264934. Lewis, Gilbert Newton; Randall, Merle: Revised by Pitzer, Kenneth S. & Brewer, Leo (1961). Thermodynamics (2nd ed.). New York, NY USA: McGraw-Hill Book Co. ISBN 978-0-07-113809-3. {{cite book}}: ISBN / Date incompatibility (help)CS1 maint: multiple names: authors list (link)
Wikipedia/Internal_energy
In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calculated by integrating radiant flux (or power) with respect to time. The symbol Qe is often used throughout literature to denote radiant energy ("e" for "energetic", to avoid confusion with photometric quantities). In branches of physics other than radiometry, electromagnetic energy is referred to using E or W. The term is used particularly when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be visible or invisible to the human eye. == Terminology use and history == The term "radiant energy" is most commonly used in the fields of radiometry, solar energy, heating and lighting, but is also sometimes used in other fields (such as telecommunications). In modern applications involving transmission of power from one location to another, "radiant energy" is sometimes used to refer to the electromagnetic waves themselves, rather than their energy (a property of the waves). In the past, the term "electro-radiant energy" has also been used. The term "radiant energy" also applies to gravitational radiation. For example, the first gravitational waves ever observed were produced by a black hole collision that emitted about 5.3×1047 joules of gravitational-wave energy. == Analysis == Because electromagnetic (EM) radiation can be conceptualized as a stream of photons, radiant energy can be viewed as photon energy – the energy carried by these photons. Alternatively, EM radiation can be viewed as an electromagnetic wave, which carries energy in its oscillating electric and magnetic fields. These two views are completely equivalent and are reconciled to one another in quantum field theory (see wave-particle duality). EM radiation can have various frequencies. The bands of frequency present in a given EM signal may be sharply defined, as is seen in atomic spectra, or may be broad, as in blackbody radiation. In the particle picture, the energy carried by each photon is proportional to its frequency. In the wave picture, the energy of a monochromatic wave is proportional to its intensity. This implies that if two EM waves have the same intensity, but different frequencies, the one with the higher frequency "contains" fewer photons, since each photon is more energetic. When EM waves are absorbed by an object, the energy of the waves is converted to heat (or converted to electricity in case of a photoelectric material). This is a very familiar effect, since sunlight warms surfaces that it irradiates. Often this phenomenon is associated particularly with infrared radiation, but any kind of electromagnetic radiation will warm an object that absorbs it. EM waves can also be reflected or scattered, in which case their energy is redirected or redistributed as well. === Open systems === Radiant energy is one of the mechanisms by which energy can enter or leave an open system. Such a system can be man-made, such as a solar energy collector, or natural, such as the Earth's atmosphere. In geophysics, most atmospheric gases, including the greenhouse gases, allow the Sun's short-wavelength radiant energy to pass through to the Earth's surface, heating the ground and oceans. The absorbed solar energy is partly re-emitted as longer wavelength radiation (chiefly infrared radiation), some of which is absorbed by the atmospheric greenhouse gases. Radiant energy is produced in the sun as a result of nuclear fusion. == Applications == Radiant energy is used for radiant heating. It can be generated electrically by infrared lamps, or can be absorbed from sunlight and used to heat water. The heat energy is emitted from a warm element (floor, wall, overhead panel) and warms people and other objects in rooms rather than directly heating the air. Because of this, the air temperature may be lower than in a conventionally heated building, even though the room appears just as comfortable. Various other applications of radiant energy have been devised. These include treatment and inspection, separating and sorting, medium of control, and medium of communication. Many of these applications involve a source of radiant energy and a detector that responds to that radiation and provides a signal representing some characteristic of the radiation. Radiant energy detectors produce responses to incident radiant energy either as an increase or decrease in electric potential or current flow or some other perceivable change, such as exposure of photographic film. == SI radiometry units == == See also == == Notes and references == == Further reading ==
Wikipedia/Radiant_energy
An integrated gasification combined cycle (IGCC) is a technology using a high pressure gasifier to turn coal and other carbon based fuels into pressurized synthesis gas. This enables removal of impurities from the fuel prior to generating electricity, reducing emissions of sulfur dioxide, particulates, mercury, and in some cases carbon dioxide. Some of these impurities, such as sulfur, can be turned into re-usable byproducts through the Claus process. With additional process equipment, carbon monoxide can be converted to carbon dioxide via water-gas shift reaction, enabling it to be sequestered and increasing gasification efficiency. Excess heat from the primary combustion and syngas fired generation is then passed to a steam cycle, producing additional electricity. This process results in improved thermodynamic efficiency, compared to conventional pulverized coal combustion. == Significance == Coal can be found in abundance in the USA and many other countries and its price has remained relatively constant in recent years. Of the traditional hydrocarbon fuels - oil, coal, and natural gas - coal is used as a feedstock for 40% of global electricity generation. Fossil fuel consumption and its contribution to large-scale CO2 emissions is becoming a pressing issue because of the adverse effects of climate change. In particular, coal contains more CO2 per BTU than oil or natural gas and is responsible for 43% of CO2 emissions from fuel combustion. Thus, the lower emissions that IGCC technology allows through gasification and pre-combustion carbon capture is discussed as a way to addressing aforementioned concerns. == Operations == Below is a schematic flow diagram of an IGCC plant: The gasification process can produce syngas from a wide variety of carbon-containing feedstocks, such as high-sulfur coal, heavy petroleum residues, and biomass. The plant is called integrated because (1) the syngas produced in the gasification section is used as fuel for the gas turbine in the combined cycle and (2) the steam produced by the syngas coolers in the gasification section is used by the steam turbine in the combined cycle. In this example the syngas produced is used as fuel in a gas turbine which produces electrical power. In a normal combined cycle, so-called "waste heat" from the gas turbine exhaust is used in a Heat Recovery Steam Generator (HRSG) to make steam for the steam turbine cycle. An IGCC plant improves the overall process efficiency by adding the higher-temperature steam produced by the gasification process to the steam turbine cycle. This steam is then used in steam turbines to produce additional electrical power. IGCC plants are advantageous in comparison to conventional coal power plants due to their high thermal efficiency, low non-carbon greenhouse gas emissions, and capability to process low grade coal. The disadvantages include higher capital and maintenance costs, and the amount of CO2 released without pre-combustion capture. == Process overview == The solid coal is gasified to produce syngas, or synthetic gas. Syngas is synthesized by gasifying coal in a closed pressurized reactor with a shortage of oxygen. The shortage of oxygen ensures that coal is broken down by the heat and pressure as opposed to burning completely. The chemical reaction between coal and oxygen produces a product that is a mixture of carbon and hydrogen, or syngas. CxHy + (x/2)O2 → (x)CO + (y/2)H2 The heat from the production of syngas is used to produce steam from cooling water which is then used for steam turbine electricity production. The syngas must go through a pre-combustion separation process to remove CO2 and other impurities to produce a more purified fuel. Three steps are necessary for the separation of impurities: Water-gas-shift reaction. The reaction that occurs in a water-gas-shift reactor is CO + H2O ⇌ {\displaystyle \rightleftharpoons } CO2 + H2. This produces a syngas with a higher composition of hydrogen fuel which is more efficient for burning later in combustion. Physical separation process. This can be done through various mechanisms such as absorption, adsorption or membrane separation. Drying, compression and storage/shipping. The resulting syngas fuels a combustion turbine that produces electricity. At this stage the syngas is fairly pure H2. == Benefits and drawbacks == A major drawback of using coal as a fuel source is the emission of carbon dioxide and pollutants, including sulfur dioxide, nitrogen oxide, mercury, and particulates. Almost all coal-fired power plants use pulverized coal combustion, which grinds the coal to increase the surface area, burns it to make steam, and runs the steam through a turbine to generate electricity. Pulverized coal plants can only capture carbon dioxide after combustion when it is diluted and harder to separate. In comparison, gasification in IGCC allows for separation and capture of the concentrated and pressurized carbon dioxide before combustion. Syngas cleanup includes filters to remove bulk particulates, scrubbing to remove fine particulates, and solid adsorbents for mercury removal. Additionally, hydrogen gas is used as fuel, which produces no pollutants under combustion. IGCC also consumes less water than traditional pulverized coal plants. In a pulverized coal plant, coal is burned to produce steam, which is then used to create electricity using a steam turbine. Then steam exhaust must then be condensed with cooling water, and water is lost by evaporation. In IGCC, water consumption is reduced by combustion in a gas turbine, which uses the generated heat to expand air and drive the turbine. Steam is only used to capture the heat from the combustion turbine exhaust for use in a secondary steam turbine. Currently, the major drawback is the high capital cost compared to other forms of power production. == Installations == The DOE Clean Coal Demonstration Project helped construct 3 IGCC plants: Edwarsport Power Station in Edwardsport, Indiana, Polk Power Station in Tampa, Florida (online 1996), and Pinon Pine in Reno, Nevada. In the Reno demonstration project, researchers found that then-current IGCC technology would not work more than 300 feet (100m) above sea level. The DOE report in reference 3 however makes no mention of any altitude effect, and most of the problems were associated with the solid waste extraction system. The Polk Power station is currently operating, following resolution of demonstration start-up problems, but the Piñon Pine project encountered significant problems and was abandoned. The US DOE's Clean Coal Power Initiative (CCPI Phase 2) selected the Kemper Project as one of two projects to demonstrate the feasibility of low emission coal-fired power plants. Mississippi Power began construction on the Kemper Project in Kemper County, Mississippi, in 2010 and is poised to begin operation in 2016, though there have been many delays. In March, the projected date was further pushed back from early 2016 to August 31, 2016, adding $110 million to the total and putting the project 3 years behind schedule. The electrical plant is a flagship Carbon Capture and Storage (CCS) project that burns lignite coal and utilizes pre-combustion IGCC technology with a projected 65% emission capture rate. The first generation of IGCC plants polluted less than contemporary coal-based technology, but also polluted water; for example, the Wabash Gasification Facility, located in Vigo County, Indiana, was out of compliance with its water permit during 1998–2001 because it emitted arsenic, selenium and cyanide. Wabash operated commercially until 2016, and was being converted to a low carbon hydrogen and ammonia facility as of 2025. IGCC is now touted as capture ready and could potentially be used to capture and store carbon dioxide. (See FutureGen)Poland's Kędzierzyn will soon host a Zero-Emission Power & Chemical Plant that combines coal gasification technology with Carbon Capture & Storage (CCS). This installation had been planned, but there has been no information about it since 2009. Other operating IGCC plants in existence around the world are the Alexander (formerly Buggenum) in the Netherlands, Puertollano in Spain, and JGC in Japan. The Texas Clean Energy project planned to build a 400 MW IGCC facility that would incorporate carbon capture, utilization and storage (CCUS) technology. The project would have been the first coal power plant in the United States to combine IGCC and 90% carbon capture and storage. The sponsor Summit Power filed for bankruptcy in 2017. There are several advantages and disadvantages when compared to conventional post combustion carbon capture and various variations == Cost and reliability == A key issue in implementing IGCC is its high capital cost, which prevents it from competing with other power plant technologies. Currently, ordinary pulverized coal plants are the lowest cost power plant option. The advantage of IGCC comes from the ease of retrofitting existing power plants that could offset the high capital cost. In a 2007 model, IGCC with CCS is the lowest-cost system in all cases. This model compared estimations of levelized cost of electricity, showing IGCC with CCS to cost 71.9 $US2005/MWh, pulverized coal with CCS to cost 88 $US2005/MWh, and natural gas combined cycle with CCS to cost 80.6 $US2005/MWh. The levelized cost of electricity was noticeably sensitive to the price of natural gas and the inclusion of carbon storage and transport costs. The potential benefit of retrofitting has so far, not offset the cost of IGCC with carbon capture technology. A 2013 report by the U.S. Energy Information Administration demonstrates that the overnight cost of IGCC with CCS has increased 19% since 2010. Amongst the three power plant types, pulverized coal with CCS has an overnight capital cost of $5,227 (2012 dollars)/kW, IGCC with CCS has an overnight capital cost of $6,599 (2012 dollars)/kW, and natural gas combined cycle with CCS has an overnight capital cost of $2,095 (2012 dollars)/kW. Pulverized coal and NGCC costs did not change significantly since 2010. The report further relates that the 19% increase in IGCC cost is due to recent information from IGCC projects that have gone over budget and cost more than expected. Recent testimony in regulatory proceedings show the cost of IGCC to be twice that predicted by Goddell, from $96 to 104/MWh. That's before addition of carbon capture and sequestration (sequestration has been a mature technology at both Weyburn in Canada (for enhanced oil recovery) and Sleipner in the North Sea at a commercial scale for the past ten years)—capture at a 90% rate is expected to have a $30/MWh additional cost. Wabash was down repeatedly for long stretches due to gasifier problems. Subsequent projects, such as Excelsior's Mesaba Project, have a third gasifier and train built in. The Polk County IGCC has design problems. First, the project was initially shut down because of corrosion in the slurry pipeline that fed slurried coal from the rail cars into the gasifier. A new coating for the pipe was developed. Second, the thermocoupler was replaced in less than two years; an indication that the gasifier had problems with a variety of feedstocks; from bituminous to sub-bituminous coal. The gasifier was designed to also handle lower rank lignites. Third, unplanned down time on the gasifier because of refractory liner problems, and those problems were expensive to repair. The gasifier was originally designed in Italy to be half the size of what was built at Polk. Newer ceramic materials may assist in improving gasifier performance and longevity. Understanding the operating problems of the current IGCC plant is necessary to improve the design for the IGCC plant of the future. (Polk IGCC Power Plant, https://web.archive.org/web/20151228085513/http://www.clean-energy.us/projects/polk_florida.html.) Keim, K., 2009, IGCC A Project on Sustainability Management Systems for Plant Re-Design and Re-Image. This is an unpublished paper from Harvard University) General Electric is currently designing an IGCC model plant that should introduce greater reliability. GE's model features advanced turbines optimized for the coal syngas. Eastman's industrial gasification plant in Kingsport, TN uses a GE Energy solid-fed gasifier. Eastman, a fortune 500 company, built the facility in 1983 without any state or federal subsidies and turns a profit. There are several refinery-based IGCC plants in Europe that have demonstrated good availability (90-95%) after initial shakedown periods. Several factors help this performance: None of these facilities use advanced technology (F type) gas turbines. All refinery-based plants use refinery residues, rather than coal, as the feedstock. This eliminates coal handling and coal preparation equipment and its problems. Also, there is a much lower level of ash produced in the gasifier, which reduces cleanup and downtime in its gas cooling and cleaning stages. These non-utility plants have recognized the need to treat the gasification system as an up-front chemical processing plant, and have reorganized their operating staff accordingly. Another IGCC success story has been the 250 MW Buggenum plant in The Netherlands, which was commissioned in 1994 and closed in 2013, had good availability. This coal-based IGCC plant was originally designed to use up to 30% biomass as a supplemental feedstock. The owner, NUON, was paid an incentive fee by the government to use the biomass. NUON has constructed a 1,311 MW IGCC plant in the Netherlands, comprising three 437 MW CCGT units. The Nuon Magnum IGCC power plant was commissioned in 2011, and was officially opened in June 2013. Mitsubishi Heavy Industries has been awarded to construct the power plant. Following a deal with environmental organizations, NUON has been prohibited from using the Magnum plant to burn coal and biomass, until 2020. Because of high gas prices in the Netherlands, two of the three units are currently offline, whilst the third unit sees only low usage levels. The relatively low 59% efficiency of the Magnum plant means that more efficient CCGT plants (such as the Hemweg 9 plant) are preferred to provide (backup) power. A new generation of IGCC-based coal-fired power plants has been proposed, although none is yet under construction. Projects are being developed by AEP, Duke Energy, and Southern Company in the US, and in Europe by ZAK/PKE, Centrica (UK), E.ON and RWE (both Germany) and NUON (Netherlands). In Minnesota, the state's Dept. of Commerce analysis found IGCC to have the highest cost, with an emissions profile not significantly better than pulverized coal. In Delaware, the Delmarva and state consultant analysis had essentially the same results. The high cost of IGCC is the biggest obstacle to its integration in the power market; however, most energy executives recognize that carbon regulation is coming soon. Bills requiring carbon reduction are being proposed again both the House and the Senate, and with the Democratic majority it seems likely that with the next President there will be a greater push for carbon regulation. The Supreme Court decision requiring the EPA to regulate carbon (Commonwealth of Massachusetts et al. v. Environmental Protection Agency et al.)[20] also speaks to the likelihood of future carbon regulations coming sooner, rather than later. With carbon capture, the cost of electricity from an IGCC plant would increase approximately 33%. For a natural gas CC, the increase is approximately 46%. For a pulverized coal plant, the increase is approximately 57%. This potential for less expensive carbon capture makes IGCC an attractive choice for keeping low cost coal an available fuel source in a carbon constrained world. However, the industry needs a lot more experience to reduce the risk premium. IGCC with CCS requires some sort of mandate, higher carbon market price, or regulatory framework to properly incentivize the industry. In Japan, electric power companies, in conjunction with Mitsubishi Heavy Industries has been operating a 200 t/d IGCC pilot plant since the early '90s. In September 2007, they started up a 250 MW demo plant in Nakoso. It runs on air-blown (not oxygen) dry feed coal only. It burns PRB coal with an unburned carbon content ratio of <0.1% and no detected leaching of trace elements. It employs not only F type turbines but G type as well. (see gasification.org link below) Next generation IGCC plants with CO2 capture technology will be expected to have higher thermal efficiency and to hold the cost down because of simplified systems compared to conventional IGCC. The main feature is that instead of using oxygen and nitrogen to gasify coal, they use oxygen and CO2. The main advantage is that it is possible to improve the performance of cold gas efficiency and to reduce the unburned carbon (char). As a reference for powerplant efficiency: With Frame E gas turbine, 30bar quench gas cooling, Cold Temperature Gas Cleaning and 2 level HRSC it is possible to achieve around 38% energy efficiency. With Frame F gas turbine, 60 bar quench gasifier, Cold Temperature Gas Cleaning and 3 level+RH HRSC it is possible to achieve around 45% energy efficiency. Latest development of Frame G gas turbines, ASU air integration, High temperature desulfurization may shift up performance even further. The CO2 extracted from gas turbine exhaust gas is utilized in this system. Using a closed gas turbine system capable of capturing the CO2 by direct compression and liquefication obviates the need for a separation and capture system. == CO2 capture in IGCC == Pre-combustion CO2 removal is much easier than CO2 removal from flue gas in post-combustion capture due to the high concentration of CO2 after the water-gas-shift reaction and the high pressure of the syngas. During pre-combustion in IGCC, the partial pressure of CO2 is nearly 1000 times higher than in post-combustion flue gas. Due to the high concentration of CO2 pre-combustion, physical solvents, such as Selexol and Rectisol, are preferred for the removal of CO2 vs that of chemical solvents. Physical solvents work by absorbing the acid gases without the need of a chemical reaction as in traditional amine based solvents. The solvent can then be regenerated, and the CO2 desorbed, by reducing the pressure. The biggest obstacle with physical solvents is the need to cool the syngas before separation, then reheat it afterwards for combustion, consuming energy and decreasing overall plant efficiency. == Testing == National and international test codes are used to standardize the procedures and definitions used to test IGCC Power Plants. Selection of the test code to be used is an agreement between the purchaser and the manufacturer, and has some significance to the design of the plant and associated systems. In the United States, The American Society of Mechanical Engineers published the Performance Test Code for IGCC Power Generation Plants (PTC 47) in 2006 which provides procedures for the determination of quantity and quality of fuel gas by its flow rate, temperature, pressure, composition, heating value, and its content of contaminants. == IGCC emission controversy == In 2007, the New York State Attorney General's office demanded full disclosure of "financial risks from greenhouse gases" to the shareholders of electric power companies proposing the development of IGCC coal-fired power plants. "Any one of the several new or likely regulatory initiatives for CO2 emissions from power plants - including state carbon controls, EPA's regulations under the Clean Air Act, or the enactment of federal global warming legislation - would add a significant cost to carbon-intensive coal generation"; U.S. Senator Hillary Clinton from New York has proposed that this full risk disclosure be required of all publicly traded power companies nationwide. This honest disclosure has begun to reduce investor interest in all types of existing-technology coal-fired power plant development, including IGCC. Senator Harry Reid (Majority Leader of the 2007/2008 U.S. Senate) told the 2007 Clean Energy Summit that he will do everything he can to stop construction of proposed new IGCC coal-fired electric power plants in Nevada. Reid wants Nevada utility companies to invest in solar energy, wind energy and geothermal energy instead of coal technologies. Reid stated that global warming is a reality, and just one proposed coal-fired plant would contribute to it by burning seven million tons of coal a year. The long-term healthcare costs would be far too high, he claimed (no source attributed). "I'm going to do everything I can to stop these plants.", he said. "There is no clean coal technology. There is cleaner coal technology, but there is no clean coal technology." One of the most efficient ways to treat the H2S gas from an IGCC plant is by converting it into sulphuric acid in a wet gas sulphuric acid process WSA process. However, the majority of the H2S treating plants utilize the modified Claus process, as the sulphur market infrastructure and the transportation costs of sulphuric acid versus sulphur are in favour of sulphur production. == See also == Relative cost of electricity generated by different sources Environmental impact of the coal industry Integrated Gasification Fuel Cell Cycle == References == == External links == Huntstown: Ireland's most efficient power plant @ Siemens Power Generation website Natural Gas Combined-cycle Gas Turbine Power Plants Northwest Power Planning Council, New Resource Characterization for the Fifth Power Plan, August 2002 Combined cycle solar power
Wikipedia/Integrated_gasification_combined_cycle
Quantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905, Albert Einstein argued that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized, obtaining the relation E = h ν {\displaystyle E=h\nu } . This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. Currently quantum thermodynamics addresses the emergence of thermodynamic laws from quantum mechanics. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition, there is a quest for the theory to be relevant for a single individual quantum system. == Dynamical view == There is an intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts dynamics into thermodynamics, giving a sound foundation to finite-time-thermodynamics. The main assumption is that the entire world is a large closed system, and therefore, time evolution is governed by a unitary transformation generated by a global Hamiltonian. For the combined system bath scenario, the global Hamiltonian can be decomposed into: H = H S + H B + H SB {\displaystyle H=H_{\text{S}}+H_{\text{B}}+H_{\text{SB}}} where H S {\displaystyle H_{\text{S}}} is the system Hamiltonian, H B {\displaystyle H_{\text{B}}} is the bath Hamiltonian and H SB {\displaystyle H_{\text{SB}}} is the system-bath interaction. The state of the system is obtained from a partial trace over the combined system and bath: ρ S ( t ) = Tr B ⁡ ( ρ SB ( t ) ) . {\displaystyle \rho _{\text{S}}(t)=\operatorname {Tr} _{\text{B}}(\rho _{\text{SB}}(t)).} Reduced dynamics is an equivalent description of the system dynamics utilizing only system operators. Assuming Markov property for the dynamics the basic equation of motion for an open quantum system is the Lindblad equation (GKLS): ρ ˙ S = − i ℏ [ H S , ρ S ] + L D ( ρ S ) {\displaystyle {\dot {\rho }}_{\text{S}}=-{i \over \hbar }[H_{\text{S}},\rho _{\text{S}}]+L_{\text{D}}(\rho _{\text{S}})} H S {\displaystyle H_{\text{S}}} is a (Hermitian) Hamiltonian part and L D {\displaystyle L_{\text{D}}} : L D ( ρ S ) = ∑ n [ V n ρ S V n † − 1 2 ( ρ S V n † V n + V n † V n ρ S ) ] {\displaystyle L_{\text{D}}(\rho _{\text{S}})=\sum _{n}\left[V_{n}\rho _{\text{S}}V_{n}^{\dagger }-{\tfrac {1}{2}}\left(\rho _{\text{S}}V_{n}^{\dagger }V_{n}+V_{n}^{\dagger }V_{n}\rho _{\text{S}}\right)\right]} is the dissipative part describing implicitly through system operators V n {\displaystyle V_{n}} the influence of the bath on the system. The Markov property imposes that the system and bath are uncorrelated at all times ρ SB = ρ s ⊗ ρ B {\displaystyle \rho _{\text{SB}}=\rho _{s}\otimes \rho _{\text{B}}} . The L-GKS equation is unidirectional and leads any initial state ρ S {\displaystyle \rho _{\text{S}}} to a steady state solution which is an invariant of the equation of motion ρ ˙ S ( t → ∞ ) = 0 {\displaystyle {\dot {\rho }}_{\text{S}}(t\to \infty )=0} . The Heisenberg picture supplies a direct link to quantum thermodynamic observables. The dynamics of a system observable represented by the operator, O {\displaystyle O} , has the form: d O d t = i ℏ [ H S , O ] + L D ∗ ( O ) + ∂ O ∂ t {\displaystyle {\frac {dO}{dt}}={\frac {i}{\hbar }}[H_{\text{S}},O]+L_{\text{D}}^{*}(O)+{\frac {\partial O}{\partial t}}} where the possibility that the operator, O {\displaystyle O} is explicitly time-dependent, is included. === Emergence of time derivative of first law of thermodynamics === When O = H S {\displaystyle O=H_{\text{S}}} the first law of thermodynamics emerges: d E d t = ⟨ ∂ H S ∂ t ⟩ + ⟨ L D ∗ ( H S ) ⟩ {\displaystyle {\frac {dE}{dt}}=\left\langle {\frac {\partial H_{\text{S}}}{\partial t}}\right\rangle +\langle L_{\text{D}}^{*}(H_{\text{S}})\rangle } where power is interpreted as P = ⟨ ∂ H S ∂ t ⟩ {\displaystyle P=\left\langle {\frac {\partial H_{\text{S}}}{\partial t}}\right\rangle } and the heat current J = ⟨ L D ∗ ( H S ) ⟩ . {\displaystyle J=\left\langle L_{\text{D}}^{*}(H_{\text{S}})\right\rangle .} Additional conditions have to be imposed on the dissipator L D {\displaystyle L_{\text{D}}} to be consistent with thermodynamics. First the invariant ρ S ( ∞ ) {\displaystyle \rho _{\text{S}}(\infty )} should become an equilibrium Gibbs state. This implies that the dissipator L D {\displaystyle L_{\text{D}}} should commute with the unitary part generated by H S {\displaystyle H_{\text{S}}} . In addition an equilibrium state is stationary and stable. This assumption is used to derive the Kubo-Martin-Schwinger stability criterion for thermal equilibrium i.e. KMS state. A unique and consistent approach is obtained by deriving the generator, L D {\displaystyle L_{\text{D}}} , in the weak system bath coupling limit. In this limit, the interaction energy can be neglected. This approach represents a thermodynamic idealization: it allows energy transfer, while keeping a tensor product separation between the system and bath, i.e., a quantum version of an isothermal partition. Markovian behavior involves a rather complicated cooperation between system and bath dynamics. This means that in phenomenological treatments, one cannot combine arbitrary system Hamiltonians, H S {\displaystyle H_{\text{S}}} , with a given L-GKS generator. This observation is particularly important in the context of quantum thermodynamics, where it is tempting to study Markovian dynamics with an arbitrary control Hamiltonian. Erroneous derivations of the quantum master equation can easily lead to a violation of the laws of thermodynamics. An external perturbation modifying the Hamiltonian of the system will also modify the heat flow. As a result, the L-GKS generator has to be renormalized. For a slow change, one can adopt the adiabatic approach and use the instantaneous system’s Hamiltonian to derive L D {\displaystyle L_{\text{D}}} . An important class of problems in quantum thermodynamics is periodically driven systems. Periodic quantum heat engines and power-driven refrigerators fall into this class. A reexamination of the time-dependent heat current expression using quantum transport techniques has been proposed. A derivation of consistent dynamics beyond the weak coupling limit has been suggested. Phenomenological formulations of irreversible quantum dynamics consistent with the second law and implementing the geometric idea of "steepest entropy ascent" or "gradient flow" have been suggested to model relaxation and strong coupling. === Emergence of the second law === The second law of thermodynamics is a statement on the irreversibility of dynamics or, the breakup of time reversal symmetry (T-symmetry). This should be consistent with the empirical direct definition: heat will flow spontaneously from a hot source to a cold sink. From a static viewpoint, for a closed quantum system, the 2nd law of thermodynamics is a consequence of the unitary evolution. In this approach, one accounts for the entropy change before and after a change in the entire system. A dynamical viewpoint is based on local accounting for the entropy changes in the subsystems and the entropy generated in the baths. ==== Entropy ==== In thermodynamics, entropy is related to the amount of energy of a system that can be converted into mechanical work in a concrete process. In quantum mechanics, this translates to the ability to measure and manipulate the system based on the information gathered by measurement. An example is the case of Maxwell’s demon, which has been resolved by Leó Szilárd. The entropy of an observable is associated with the complete projective measurement of an observable, ⟨ A ⟩ {\displaystyle \langle A\rangle } , where the operator A {\displaystyle A} has a spectral decomposition: A = ∑ j α j P j , {\displaystyle A=\sum _{j}\alpha _{j}P_{j},} where P j {\displaystyle P_{j}} are the projection operators of the eigenvalue α j . {\displaystyle \alpha _{j}.} The probability of outcome j {\displaystyle j} is p j = Tr ⁡ ( ρ P j ) . {\displaystyle p_{j}=\operatorname {Tr} (\rho P_{j}).} The entropy associated with the observable ⟨ A ⟩ {\displaystyle \langle A\rangle } is the Shannon entropy with respect to the possible outcomes: S A = − ∑ j p j ln ⁡ p j {\displaystyle S_{A}=-\sum _{j}p_{j}\ln p_{j}} The most significant observable in thermodynamics is the energy represented by the Hamiltonian operator H , {\displaystyle H,} and its associated energy entropy, S E . {\displaystyle S_{E}.} John von Neumann suggested to single out the most informative observable to characterize the entropy of the system. This invariant is obtained by minimizing the entropy with respect to all possible observables. The most informative observable operator commutes with the state of the system. The entropy of this observable is termed the Von Neumann entropy and is equal to S vn = − Tr ⁡ ( ρ ln ⁡ ρ ) . {\displaystyle S_{\text{vn}}=-\operatorname {Tr} (\rho \ln \rho ).} As a consequence, S A ≥ S vn {\displaystyle S_{A}\geq S_{\text{vn}}} for all observables. At thermal equilibrium the energy entropy is equal to the von Neumann entropy: S E = S vn . {\displaystyle S_{E}=S_{\text{vn}}.} S vn {\displaystyle S_{\text{vn}}} is invariant to a unitary transformation changing the state. The Von Neumann entropy S vn {\displaystyle S_{\text{vn}}} is additive only for a system state that is composed of a tensor product of its subsystems: ρ = Π j ⊗ ρ j {\displaystyle \rho =\Pi _{j}\otimes \rho _{j}} ==== Clausius version of the II-law ==== No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature. This statement for N-coupled heat baths in steady state becomes ∑ n J n T n ≥ 0 {\displaystyle \sum _{n}{\frac {J_{n}}{T_{n}}}\geq 0} A dynamical version of the II-law can be proven, based on Spohn's inequality: Tr ⁡ ( L D ρ [ ln ⁡ ρ ( ∞ ) − ln ⁡ ρ ] ) ≥ 0 , {\displaystyle \operatorname {Tr} \left(L_{\text{D}}\rho \left[\ln \rho (\infty )-\ln \rho \right]\right)\geq 0,} which is valid for any L-GKS generator, with a stationary state, ρ ( ∞ ) {\displaystyle \rho (\infty )} . Consistency with thermodynamics can be employed to verify quantum dynamical models of transport. For example, local models for networks where local L-GKS equations are connected through weak links have been thought to violate the second law of thermodynamics. In 2018 has been shown that, by correctly taking into account all work and energy contributions in the full system, local master equations are fully coherent with the second law of thermodynamics. === Quantum and thermodynamic adiabatic conditions and quantum friction === Thermodynamic adiabatic processes have no entropy change. Typically, an external control modifies the state. A quantum version of an adiabatic process can be modeled by an externally controlled time dependent Hamiltonian H ( t ) {\displaystyle H(t)} . If the system is isolated, the dynamics are unitary, and therefore, S vn {\displaystyle S_{\text{vn}}} is a constant. A quantum adiabatic process is defined by the energy entropy S E {\displaystyle S_{E}} being constant. The quantum adiabatic condition is therefore equivalent to no net change in the population of the instantaneous energy levels. This implies that the Hamiltonian should commute with itself at different times: [ H ( t ) , H ( t ′ ) ] = 0 {\displaystyle [H(t),H(t')]=0} . When the adiabatic conditions are not fulfilled, additional work is required to reach the final control value. For an isolated system, this work is recoverable, since the dynamics is unitary and can be reversed. In this case, quantum friction can be suppressed using shortcuts to adiabaticity as demonstrated in the laboratory using a unitary Fermi gas in a time-dependent trap. The coherence stored in the off-diagonal elements of the density operator carry the required information to recover the extra energy cost and reverse the dynamics. Typically, this energy is not recoverable, due to interaction with a bath that causes energy dephasing. The bath, in this case, acts like a measuring apparatus of energy. This lost energy is the quantum version of friction. === Emergence of the dynamical version of the third law of thermodynamics === There are seemingly two independent formulations of the third law of thermodynamics. Both were originally stated by Walther Nernst. The first formulation is known as the Nernst heat theorem, and can be phrased as: The entropy of any pure substance in thermodynamic equilibrium approaches zero as the temperature approaches zero. The second formulation is dynamical, known as the unattainability principle It is impossible by any procedure, no matter how idealized, to reduce any assembly to absolute zero temperature in a finite number of operations. At steady state the second law of thermodynamics implies that the total entropy production is non-negative. When the cold bath approaches the absolute zero temperature, it is necessary to eliminate the entropy production divergence at the cold side when T c → 0 {\displaystyle T_{\text{c}}\rightarrow 0} , therefore S ˙ c ∝ − T c α , α ≥ 0 . {\displaystyle {\dot {S}}_{\text{c}}\propto -T_{\text{c}}^{\alpha }~~~,~~~~\alpha \geq 0~~.} For α = 0 {\displaystyle \alpha =0} the fulfillment of the second law depends on the entropy production of the other baths, which should compensate for the negative entropy production of the cold bath. The first formulation of the third law modifies this restriction. Instead of α ≥ 0 {\displaystyle \alpha \geq 0} the third law imposes α > 0 {\displaystyle \alpha >0} , guaranteeing that at absolute zero the entropy production at the cold bath is zero: S ˙ c = 0 {\displaystyle {\dot {S}}_{\text{c}}=0} . This requirement leads to the scaling condition of the heat current J c ∝ T c α + 1 {\displaystyle {J}_{\text{c}}\propto T_{\text{c}}^{\alpha +1}} . The second formulation, known as the unattainability principle can be rephrased as; No refrigerator can cool a system to absolute zero temperature at finite time. The dynamics of the cooling process is governed by the equation: J c ( T c ( t ) ) = − c V ( T c ( t ) ) d T c ( t ) d t . {\displaystyle {J}_{\text{c}}(T_{\text{c}}(t))=-c_{V}(T_{\text{c}}(t)){\frac {dT_{\text{c}}(t)}{dt}}~~.} where c V ( T c ) {\displaystyle c_{V}(T_{\text{c}})} is the heat capacity of the bath. Taking J c ∝ T c α + 1 {\displaystyle {J}_{\text{c}}\propto T_{\text{c}}^{\alpha +1}} and c V ∼ T c η {\displaystyle c_{V}\sim T_{\text{c}}^{\eta }} with η ≥ 0 {\displaystyle {\eta }\geq 0} , we can quantify this formulation by evaluating the characteristic exponent ζ {\displaystyle \zeta } of the cooling process, d T c ( t ) d t ∝ − T c ζ , T c → 0 , ζ = α − η + 1 {\displaystyle {\frac {dT_{\text{c}}(t)}{dt}}\propto -T_{\text{c}}^{\zeta },~~~~~T_{\text{c}}\to 0,\;\;\quad {\zeta =\alpha -\eta +1}} This equation introduces the relation between the characteristic exponents ζ {\displaystyle \zeta } and α {\displaystyle \alpha } . When ζ < 0 {\displaystyle \zeta <0} then the bath is cooled to zero temperature in a finite time, which implies a violation of the third law. It is apparent from the last equation, that the unattainability principle is more restrictive than the Nernst heat theorem. == Typicality as a source of emergence of thermodynamic phenomena == The basic idea of quantum typicality is that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schrödinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Quantum ergodic theorem originated by John von Neumann is a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of termed normal typicality, i.e. the statement that, for typical large systems, every initial wave function ψ 0 {\displaystyle \psi _{0}} from an energy shell is ‘normal’: it evolves in such a way that ψ t {\displaystyle \psi _{t}} for most t, is macroscopically equivalent to the micro-canonical density matrix. == Resource theory == The second law of thermodynamics can be interpreted as quantifying state transformations which are statistically unlikely so that they become effectively forbidden. The second law typically applies to systems composed of many particles interacting; Quantum thermodynamics resource theory is a formulation of thermodynamics in the regime where it can be applied to a small number of particles interacting with a heat bath. For processes which are cyclic or very close to cyclic, the second law for microscopic systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on what state transformations are possible, but an entire family of constraints. These second laws are not only relevant for small systems, but also apply to individual macroscopic systems interacting via long-range interactions, which only satisfy the ordinary second law on average. By making precise the definition of thermal operations, the laws of thermodynamics take on a form with the first law defining the class of thermal operations, the zeroth law emerging as a unique condition ensuring the theory is nontrivial, and the remaining laws being a monotonicity property of generalised free energies. == Noncommuting conserved charges == Thermodynamic systems typically conserve quantities—known as charges—such as energy and particle number. These charges are often implicitly assumed to commute. This assumption underlies, for example, the derivation of thermal state forms, the Eigenstate Thermalization Hypothesis, and transport coefficients. However, key quantum phenomena, including uncertainty relations, arise precisely from the noncommutation of observables. How does this noncommutation affect thermodynamic behaviour? The noncommutation of conserved charges has been shown to challenge standard assumptions: it can invalidate conventional derivations of the thermal state, increase entanglement, induce critical dynamics, alter entropy production, and conflict with the eigenstate thermalization hypothesis, among other effects. A central open question remains: evidence suggests that noncommuting charges can both hinder and enhance thermalization, revealing a conceptual tension at the heart of this growing field. == Engineered reservoirs == Nanoscale allows for the preparation of quantum systems in physical states without classical analogs. There, complex out-of-equilibrium scenarios may be produced by the initial preparation of either the working substance or the reservoirs of quantum particles, the latter dubbed as "engineered reservoirs". There are different forms of engineered reservoirs. Some of them involve subtle quantum coherence or correlation effects, while others rely solely on nonthermal classical probability distribution functions. Interesting phenomena may emerge from the use of engineered reservoirs such as efficiencies greater than the Otto limit, violations of Clausius inequalities, or simultaneous extraction of heat and work from the reservoirs. == See also == Quantum statistical mechanics Thermal quantum field theory == References == == Further reading == Deffner, Sebastian; Campbell, Steve (2019). Quantum Thermodynamics: An introduction to the thermodynamics of quantum information. Morgan & Claypool Publishers. Bibcode:2019qtit.book.....D. doi:10.1088/2053-2571/ab21c6. ISBN 978-1-64327-658-8. S2CID 195791624. F. Binder, L. A. Correa, C. Gogolin, J. Anders, G. Adesso (eds.) (2018). Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions. Springer, ISBN 978-3-319-99045-3. Jochen Gemmer, M. Michel, Günter Mahler (2009). Quantum thermodynamics: Emergence of Thermodynamic Behavior Within Composite Quantum Systems. 2nd edition, Springer, ISBN 978-3-540-70509-3. Heinz-Peter Breuer, Francesco Petruccione (2007). The Theory of Open Quantum Systems. Oxford University Press, ISBN 978-0-19-921390-0. == External links == Go to "Concerning an Heuristic Point of View Toward the Emission and Transformation of Light" to read an English translation of Einstein's 1905 paper. (Retrieved: 2014 Apr 11)
Wikipedia/Quantum_thermodynamics
Energy consumption is the amount of energy used. == Biology == In the body, energy consumption is part of energy homeostasis. It derived from food energy. Energy consumption in the body is a product of the basal metabolic rate and the physical activity level. The physical activity level are defined for a non-pregnant, non-lactating adult as that person's total energy expenditure (TEE) in a 24-hour period, divided by his or her basal metabolic rate (BMR): PAL = TEE/24h BMR {\displaystyle {\text{PAL}}={\frac {\text{TEE/24h}}{\text{BMR}}}} == Demographics == Topics related to energy consumption in a demographic sense are: World energy supply and consumption Domestic energy consumption Electric energy consumption === Effects of energy consumption === Environmental impact of the energy industry Climate change White's law === Reduction of energy consumption === Energy conservation, the practice of decreasing the quantity of energy used Efficient energy use == See also == Energy efficiency – Methods for higher energy efficiency Energy efficiency in transport – Discussing what form of transport is the most fuel efficient and economical Electricity generation – Process of generating electrical power Energy mix – Primary energy sources from which secondary energy for direct use is produced Energy policy – How a government or business deals with energy Energy transformation – Process of changing energy Fuel consumption – Form of thermal efficiencyPages displaying short descriptions of redirect targets == References == == External links == Media related to Energy consumption at Wikimedia Commons World energy consumption per capita per country
Wikipedia/Energy_consumption
Solar energy is the radiant energy from the Sun's light and heat, which can be harnessed using a range of technologies such as solar electricity, solar thermal energy (including solar water heating) and solar architecture. It is an essential source of renewable energy, and its technologies are broadly characterized as either passive solar or active solar depending on how they capture and distribute solar energy or convert it into solar power. Active solar techniques include the use of photovoltaic systems, concentrated solar power, and solar water heating to harness the energy. Passive solar techniques include designing a building for better daylighting, selecting materials with favorable thermal mass or light-dispersing properties, and organizing spaces that naturally circulate air. In 2011, the International Energy Agency said that "the development of affordable, inexhaustible and clean solar energy technologies will have huge longer-term benefits. It will increase countries' energy security through reliance on an indigenous, inexhaustible, and mostly import-independent resource, enhance sustainability, reduce pollution, lower the costs of mitigating global warming .... these advantages are global". == Potential == The Earth receives 174 petawatts (PW) of incoming solar radiation (insolation) at the upper atmosphere. Approximately 30% is reflected back to space while the rest, 122 PW, is absorbed by clouds, oceans and land masses. The spectrum of solar light at the Earth's surface is mostly spread across the visible and near-infrared ranges with a small part in the near-ultraviolet. Most of the world's population live in areas with insolation levels of 150–300 watts/m2, or 3.5–7.0 kWh/m2 per day. Solar radiation is absorbed by the Earth's land surface, oceans – which cover about 71% of the globe – and atmosphere. Warm air containing evaporated water from the oceans rises, causing atmospheric circulation or convection. When the air reaches a high altitude, where the temperature is low, water vapor condenses into clouds, which rain onto the Earth's surface, completing the water cycle. The latent heat of water condensation amplifies convection, producing atmospheric phenomena such as wind, cyclones and anticyclones. Sunlight absorbed by the oceans and land masses keeps the surface at an average temperature of 14 °C. By photosynthesis, green plants convert solar energy into chemically stored energy, which produces food, wood and the biomass from which fossil fuels are derived. The total solar energy absorbed by Earth's atmosphere, oceans and land masses is approximately 122 PW·year = 3,850,000 exajoules (EJ) per year. In 2002 (2019), this was more energy in one hour (one hour and 25 minutes) than the world used in one year. Photosynthesis captures approximately 3,000 EJ per year in biomass. The potential solar energy that could be used by humans differs from the amount of solar energy present near the surface of the planet because factors such as geography, time variation, cloud cover, and the land available to humans limit the amount of solar energy that we can acquire. In 2021, Carbon Tracker Initiative estimated the land area needed to generate all our energy from solar alone was 450,000 km2 — or about the same as the area of Sweden, or the area of Morocco, or the area of California (0.3% of the Earth's total land area). Solar technologies are categorized as either passive or active depending on the way they capture, convert and distribute sunlight and enable solar energy to be harnessed at different levels around the world, mostly depending on the distance from the Equator. Although solar energy refers primarily to the use of solar radiation for practical ends, all types of renewable energy, other than geothermal power and tidal power, are derived either directly or indirectly from the Sun. Active solar techniques use photovoltaics, concentrated solar power, solar thermal collectors, pumps, and fans to convert sunlight into useful output. Passive solar techniques include selecting materials with favorable thermal properties, designing spaces that naturally circulate air, and referencing the position of a building to the Sun. Active solar technologies increase the supply of energy and are considered supply side technologies, while passive solar technologies reduce the need for alternative resources and are generally considered demand-side technologies. In 2000, the United Nations Development Programme, UN Department of Economic and Social Affairs, and World Energy Council published an estimate of the potential solar energy that could be used by humans each year. This took into account factors such as insolation, cloud cover, and the land that is usable by humans. It was stated that solar energy has a global potential of 1,600 to 49,800 exajoules (4.4×1014 to 1.4×1016 kWh) per year (see table below). == Thermal energy == Solar thermal technologies can be used for water heating, space heating, space cooling and process heat generation. === Early commercial adaptation === In 1878, at the Universal Exposition in Paris, Augustin Mouchot successfully demonstrated a solar steam engine but could not continue development because of cheap coal and other factors. In 1897, Frank Shuman, a US inventor, engineer and solar energy pioneer built a small demonstration solar engine that worked by reflecting solar energy onto square boxes filled with ether, which has a lower boiling point than water and were fitted internally with black pipes which in turn powered a steam engine. In 1908 Shuman formed the Sun Power Company with the intent of building larger solar power plants. He, along with his technical advisor A.S.E. Ackermann and British physicist Sir Charles Vernon Boys, developed an improved system using mirrors to reflect solar energy upon collector boxes, increasing heating capacity to the extent that water could now be used instead of ether. Shuman then constructed a full-scale steam engine powered by low-pressure water, enabling him to patent the entire solar engine system by 1912. Shuman built the world's first solar thermal power station in Maadi, Egypt, between 1912 and 1913. His plant used parabolic troughs to power a 45–52 kilowatts (60–70 hp) engine that pumped more than 22,000 litres (4,800 imp gal; 5,800 US gal) of water per minute from the Nile River to adjacent cotton fields. Although the outbreak of World War I and the discovery of cheap oil in the 1930s discouraged the advancement of solar energy, Shuman's vision, and basic design were resurrected in the 1970s with a new wave of interest in solar thermal energy. In 1916 Shuman was quoted in the media advocating solar energy's utilization, saying: We have proved the commercial profit of sun power in the tropics and have more particularly proved that after our stores of oil and coal are exhausted the human race can receive unlimited power from the rays of the Sun. === Water heating === Solar hot water systems use sunlight to heat water. In middle geographical latitudes (between 40 degrees north and 40 degrees south), 60 to 70% of the domestic hot water use, with water temperatures up to 60 °C (140 °F), can be provided by solar heating systems. The most common types of solar water heaters are evacuated tube collectors (44%) and glazed flat plate collectors (34%) generally used for domestic hot water; and unglazed plastic collectors (21%) used mainly to heat swimming pools. As of 2015, the total installed capacity of solar hot water systems was approximately 436 thermal gigawatt (GWth), and China is the world leader in their deployment with 309 GWth installed, taken up 71% of the market. Israel and Cyprus are the per capita leaders in the use of solar hot water systems with over 90% of homes using them. In the United States, Canada, and Australia, heating swimming pools is the dominant application of solar hot water with an installed capacity of 18 GWth as of 2005. === Heating, cooling and ventilation === In the United States, heating, ventilation and air conditioning (HVAC) systems account for 30% (4.65 EJ/yr) of the energy used in commercial buildings and nearly 50% (10.1 EJ/yr) of the energy used in residential buildings. Solar heating, cooling and ventilation technologies can be used to offset a portion of this energy. Use of solar for heating can roughly be divided into passive solar concepts and active solar concepts, depending on whether active elements such as sun tracking and solar concentrator optics are used. Thermal mass is any material that can be used to store heat—heat from the Sun in the case of solar energy. Common thermal mass materials include stone, cement, and water. Historically they have been used in arid climates or warm temperate regions to keep buildings cool by absorbing solar energy during the day and radiating stored heat to the cooler atmosphere at night. However, they can be used in cold temperate areas to maintain warmth as well. The size and placement of thermal mass depend on several factors such as climate, daylighting, and shading conditions. When duly incorporated, thermal mass maintains space temperatures in a comfortable range and reduces the need for auxiliary heating and cooling equipment. A solar chimney (or thermal chimney, in this context) is a passive solar ventilation system composed of a vertical shaft connecting the interior and exterior of a building. As the chimney warms, the air inside is heated, causing an updraft that pulls air through the building. Performance can be improved by using glazing and thermal mass materials in a way that mimics greenhouses. Deciduous trees and plants have been promoted as a means of controlling solar heating and cooling. When planted on the southern side of a building in the northern hemisphere or the northern side in the southern hemisphere, their leaves provide shade during the summer, while the bare limbs allow light to pass during the winter. Since bare, leafless trees shade 1/3 to 1/2 of incident solar radiation, there is a balance between the benefits of summer shading and the corresponding loss of winter heating. In climates with significant heating loads, deciduous trees should not be planted on the Equator-facing side of a building because they will interfere with winter solar availability. They can, however, be used on the east and west sides to provide a degree of summer shading without appreciably affecting winter solar gain. === Cooking === Solar cookers use sunlight for cooking, drying, and pasteurization. They can be grouped into three broad categories: box cookers, panel cookers, and reflector cookers. The simplest solar cooker is the box cooker first built by Horace de Saussure in 1767. A basic box cooker consists of an insulated container with a transparent lid. It can be used effectively with partially overcast skies and will typically reach temperatures of 90–150 °C (194–302 °F). Panel cookers use a reflective panel to direct sunlight onto an insulated container and reach temperatures comparable to box cookers. Reflector cookers use various concentrating geometries (dish, trough, Fresnel mirrors) to focus light on a cooking container. These cookers reach temperatures of 315 °C (599 °F) and above but require direct light to function properly and must be repositioned to track the Sun. === Process heat === Solar concentrating technologies such as parabolic dish, trough and Scheffler reflectors can provide process heat for commercial and industrial applications. The first commercial system was the Solar Total Energy Project (STEP) in Shenandoah, Georgia, US where a field of 114 parabolic dishes provided 50% of the process heating, air conditioning and electrical requirements for a clothing factory. This grid-connected cogeneration system provided 400 kW of electricity plus thermal energy in the form of 401 kW steam and 468 kW chilled water and had a one-hour peak load thermal storage. Evaporation ponds are shallow pools that concentrate dissolved solids through evaporation. The use of evaporation ponds to obtain salt from seawater is one of the oldest applications of solar energy. Modern uses include concentrating brine solutions used in leach mining and removing dissolved solids from waste streams. Clothes lines, clotheshorses, and clothes racks dry clothes through evaporation by wind and sunlight without consuming electricity or gas. In some states of the United States legislation protects the "right to dry" clothes. Unglazed transpired collectors (UTC) are perforated sun-facing walls used for preheating ventilation air. UTCs can raise the incoming air temperature up to 22 °C (40 °F) and deliver outlet temperatures of 45–60 °C (113–140 °F). The short payback period of transpired collectors (3 to 12 years) makes them a more cost-effective alternative than glazed collection systems. As of 2003, over 80 systems with a combined collector area of 35,000 square metres (380,000 sq ft) had been installed worldwide, including an 860 m2 (9,300 sq ft) collector in Costa Rica used for drying coffee beans and a 1,300 m2 (14,000 sq ft) collector in Coimbatore, India, used for drying marigolds. === Water treatment === Solar distillation can be used to make saline or brackish water potable. The first recorded instance of this was by 16th-century Arab alchemists. A large-scale solar distillation project was first constructed in 1872 in the Chilean mining town of Las Salinas. The plant, which had solar collection area of 4,700 m2 (51,000 sq ft), could produce up to 22,700 L (5,000 imp gal; 6,000 US gal) per day and operate for 40 years. Individual still designs include single-slope, double-slope (or greenhouse type), vertical, conical, inverted absorber, multi-wick, and multiple effect. These stills can operate in passive, active, or hybrid modes. Double-slope stills are the most economical for decentralized domestic purposes, while active multiple effect units are more suitable for large-scale applications. Solar water disinfection (SODIS) involves exposing water-filled plastic polyethylene terephthalate (PET) bottles to sunlight for several hours. Exposure times vary depending on weather and climate from a minimum of six hours to two days during fully overcast conditions. It is recommended by the World Health Organization as a viable method for household water treatment and safe storage. Over two million people in developing countries use this method for their daily drinking water. Solar energy may be used in a water stabilization pond to treat waste water without chemicals or electricity. A further environmental advantage is that algae grow in such ponds and consume carbon dioxide in photosynthesis, although algae may produce toxic chemicals that make the water unusable. === Molten salt technology === Molten salt can be employed as a thermal energy storage method to retain thermal energy collected by a solar tower or solar trough of a concentrated solar power plant so that it can be used to generate electricity in bad weather or at night. It was demonstrated in the Solar Two project from 1995 to 1999. The system is predicted to have an annual efficiency of 99%, a reference to the energy retained by storing heat before turning it into electricity, versus converting heat directly into electricity. The molten salt mixtures vary. The most extended mixture contains sodium nitrate, potassium nitrate and calcium nitrate. It is non-flammable and non-toxic, and has already been used in the chemical and metals industries as a heat-transport fluid. Hence, experience with such systems exists in non-solar applications. The salt melts at 131 °C (268 °F). It is kept liquid at 288 °C (550 °F) in an insulated "cold" storage tank. The liquid salt is pumped through panels in a solar collector where the focused irradiance heats it to 566 °C (1,051 °F). It is then sent to a hot storage tank. This is so well insulated that the thermal energy can be usefully stored for up to a week. When electricity is needed, the hot salt is pumped to a conventional steam-generator to produce superheated steam for a turbine/generator as used in any conventional coal, oil, or nuclear power plant. A 100-megawatt turbine would need a tank about 9.1 metres (30 ft) tall and 24 metres (79 ft) in diameter to drive it for four hours by this design. Several parabolic trough power plants in Spain and solar power tower developer SolarReserve use this thermal energy storage concept. The Solana Generating Station in the U.S. has six hours of storage by molten salt. In Chile, The Cerro Dominador power plant has a 110 MW solar-thermal tower, the heat is transferred to molten salts. The molten salts then transfer their heat in a heat exchanger to water, generating superheated steam, which feeds a turbine that transforms the kinetic energy of the steam into electric energy using the Rankine cycle. In this way, the Cerro Dominador plant is capable of generating around 110 MW of power. The plant has an advanced storage system enabling it to generate electricity for up to 17.5 hours without direct solar radiation, which allows it to provide a stable electricity supply without interruptions if required. The Project secured up to 950 GW·h per year sale. Another project is the María Elena plant is a 400 MW thermo-solar complex in the northern Chilean region of Antofagasta employing molten salt technology. == Electricity production == == Concentrated solar power == Concentrating Solar Power (CSP) systems use lenses or mirrors and tracking systems to focus a large area of sunlight into a small beam. The concentrated heat is then used as a heat source for a conventional power plant. A wide range of concentrating technologies exists; the most developed are the parabolic trough, the solar tower collectors, the concentrating linear Fresnel reflector, and the Stirling dish. Various techniques are used to track the Sun and focus light. In all of these systems, a working fluid is heated by the concentrated sunlight, and is then used for power generation or energy storage. Designs need to account for the risk of a dust storm, hail, or another extreme weather event that can damage the fine glass surfaces of solar power plants. Metal grills would allow a high percentage of sunlight to enter the mirrors and solar panels while also preventing most damage. == Architecture and urban planning == Sunlight has influenced building design since the beginning of architectural history. Advanced solar architecture and urban planning methods were first employed by the Greeks and Chinese, who oriented their buildings toward the south to provide light and warmth. The common features of passive solar architecture are orientation relative to the Sun, compact proportion (a low surface area to volume ratio), selective shading (overhangs) and thermal mass. When these features are tailored to the local climate and environment, they can produce well-lit spaces that stay in a comfortable temperature range. Socrates' Megaron House is a classic example of passive solar design. The most recent approaches to solar design use computer modeling tying together solar lighting, heating and ventilation systems in an integrated solar design package. Active solar equipment such as pumps, fans, and switchable windows can complement passive design and improve system performance. Urban heat islands (UHI) are metropolitan areas with higher temperatures than that of the surrounding environment. The higher temperatures result from increased absorption of solar energy by urban materials such as asphalt and concrete, which have lower albedos and higher heat capacities than those in the natural environment. A straightforward method of counteracting the UHI effect is to paint buildings and roads white and to plant trees in the area. Using these methods, a hypothetical "cool communities" program in Los Angeles has projected that urban temperatures could be reduced by approximately 3 °C at an estimated cost of US$1 billion, giving estimated total annual benefits of US$530 million from reduced air-conditioning costs and healthcare savings. == Agriculture and horticulture == Agriculture and horticulture seek to optimize the capture of solar energy to optimize the productivity of plants. Techniques such as timed planting cycles, tailored row orientation, staggered heights between rows and the mixing of plant varieties can improve crop yields. While sunlight is generally considered a plentiful resource, the exceptions highlight the importance of solar energy to agriculture. During the short growing seasons of the Little Ice Age, French and English farmers employed fruit walls to maximize the collection of solar energy. These walls acted as thermal masses and accelerated ripening by keeping plants warm. Early fruit walls were built perpendicular to the ground and facing south, but over time, sloping walls were developed to make better use of sunlight. In 1699, Nicolas Fatio de Duillier even suggested using a tracking mechanism which could pivot to follow the Sun. Applications of solar energy in agriculture aside from growing crops include pumping water, drying crops, brooding chicks and drying chicken manure. More recently the technology has been embraced by vintners, who use the energy generated by solar panels to power grape presses. Greenhouses convert solar light to heat, enabling year-round production and the growth (in enclosed environments) of specialty crops and other plants not naturally suited to the local climate. Primitive greenhouses were first used during Roman times to produce cucumbers year-round for the Roman emperor Tiberius. The first modern greenhouses were built in Europe in the 16th century to keep exotic plants brought back from explorations abroad. Greenhouses remain an important part of horticulture today. Plastic transparent materials have also been used to similar effect in polytunnels and row covers. == Transport == Development of a solar-powered car has been an engineering goal since the 1980s. The World Solar Challenge is a biannual solar-powered car race, where teams from universities and enterprises compete over 3,021 kilometres (1,877 mi) across central Australia from Darwin to Adelaide. In 1987, when it was founded, the winner's average speed was 67 kilometres per hour (42 mph) and by 2007 the winner's average speed had improved to 90.87 kilometres per hour (56.46 mph). The North American Solar Challenge and the planned South African Solar Challenge are comparable competitions that reflect an international interest in the engineering and development of solar powered vehicles. Some vehicles use solar panels for auxiliary power, such as for air conditioning, to keep the interior cool, thus reducing fuel consumption. In 1975, the first practical solar boat was constructed in England. By 1995, passenger boats incorporating PV panels began appearing and are now used extensively. In 1996, Kenichi Horie made the first solar-powered crossing of the Pacific Ocean, and the Sun21 catamaran made the first solar-powered crossing of the Atlantic Ocean in the winter of 2006–2007. There were plans to circumnavigate the globe in 2010. In 1974, the unmanned AstroFlight Sunrise airplane made the first solar flight. On 29 April 1979, the Solar Riser made the first flight in a solar-powered, fully controlled, man-carrying flying machine, reaching an altitude of 40 ft (12 m). In 1980, the Gossamer Penguin made the first piloted flights powered solely by photovoltaics. This was quickly followed by the Solar Challenger which crossed the English Channel in July 1981. In 1990 Eric Scott Raymond in 21 hops flew from California to North Carolina using solar power. Developments then turned back to unmanned aerial vehicles (UAV) with the Pathfinder (1997) and subsequent designs, culminating in the Helios which set the altitude record for a non-rocket-propelled aircraft at 29,524 metres (96,864 ft) in 2001. The Zephyr, developed by BAE Systems, is the latest in a line of record-breaking solar aircraft, making a 54-hour flight in 2007, and month-long flights were envisioned by 2010. From March 2015 to July 2016, Solar Impulse, an electric aircraft, successfully circumnavigated the globe. It is a single-seat plane powered by solar cells and capable of taking off under its own power. The design allows the aircraft to remain airborne for several days. A solar balloon is a black balloon that is filled with ordinary air. As sunlight shines on the balloon, the air inside is heated and expands, causing an upward buoyancy force, much like an artificially heated hot air balloon. Some solar balloons are large enough for human flight, but usage is generally limited to the toy market as the surface-area to payload-weight ratio is relatively high. === Squad Solar vehicle === The Squad Solar is a Neighborhood Electric Vehicle that has a solar roof and can be plugged into a normal 120 volt outlet to be charged. == Fuel production == Solar chemical processes use solar energy to drive chemical reactions. These processes offset energy that would otherwise come from a fossil fuel source and can also convert solar energy into storable and transportable fuels. Solar induced chemical reactions can be divided into thermochemical or photochemical. A variety of fuels can be produced by artificial photosynthesis. The multielectron catalytic chemistry involved in making carbon-based fuels (such as methanol) from reduction of carbon dioxide is challenging; a feasible alternative is hydrogen production from protons, though use of water as the source of electrons (as plants do) requires mastering the multielectron oxidation of two water molecules to molecular oxygen. Some have envisaged working solar fuel plants in coastal metropolitan areas by 2050 – the splitting of seawater providing hydrogen to be run through adjacent fuel-cell electric power plants and the pure water by-product going directly into the municipal water system. In addition, chemical energy storage is another solution to solar energy storage. Hydrogen production technologies have been a significant area of solar chemical research since the 1970s. Aside from electrolysis driven by photovoltaic or photochemical cells, several thermochemical processes have also been explored. One such route uses concentrators to split water into oxygen and hydrogen at high temperatures (2,300–2,600 °C or 4,200–4,700 °F). Another approach uses the heat from solar concentrators to drive the steam reformation of natural gas thereby increasing the overall hydrogen yield compared to conventional reforming methods. Thermochemical cycles characterized by the decomposition and regeneration of reactants present another avenue for hydrogen production. The Solzinc process under development at the Weizmann Institute of Science uses a 1 MW solar furnace to decompose zinc oxide (ZnO) at temperatures above 1,200 °C (2,200 °F). This initial reaction produces pure zinc, which can subsequently be reacted with water to produce hydrogen. == Energy storage methods == Thermal mass systems can store solar energy in the form of heat at domestically useful temperatures for daily or interseasonal durations. Thermal storage systems generally use readily available materials with high specific heat capacities such as water, earth and stone. Well-designed systems can lower peak demand, shift time-of-use to off-peak hours and reduce overall heating and cooling requirements. Phase change materials such as paraffin wax and Glauber's salt are another thermal storage medium. These materials are inexpensive, readily available, and can deliver domestically useful temperatures (approximately 64 °C or 147 °F). The "Dover House" (in Dover, Massachusetts) was the first to use a Glauber's salt heating system, in 1948. Solar energy can also be stored at high temperatures using molten salts. Salts are an effective storage medium because they are low-cost, have a high specific heat capacity, and can deliver heat at temperatures compatible with conventional power systems. The Solar Two project used this method of energy storage, allowing it to store 1.44 terajoules (400,000 kWh) in its 68 m3 storage tank with an annual storage efficiency of about 99%. Off-grid PV systems have traditionally used rechargeable batteries to store excess electricity. With grid-tied systems, excess electricity can be sent to the transmission grid, while standard grid electricity can be used to meet shortfalls. Net metering programs give household systems credit for any electricity they deliver to the grid. This is handled by 'rolling back' the meter whenever the home produces more electricity than it consumes. If the net electricity use is below zero, the utility then rolls over the kilowatt-hour credit to the next month. Other approaches involve the use of two meters, to measure electricity consumed vs. electricity produced. This is less common due to the increased installation cost of the second meter. Most standard meters accurately measure in both directions, making a second meter unnecessary. Pumped-storage hydroelectricity stores energy in the form of water pumped when energy is available from a lower elevation reservoir to a higher elevation one. The energy is recovered when demand is high by releasing the water, with the pump becoming a hydroelectric power generator. == Development, deployment and economics == Beginning with the surge in coal use, which accompanied the Industrial Revolution, energy consumption steadily transitioned from wood and biomass to fossil fuels. The early development of solar technologies starting in the 1860s was driven by an expectation that coal would soon become scarce. However, development of solar technologies stagnated in the early 20th century in the face of the increasing availability, economy, and utility of coal and petroleum. The 1973 oil embargo and 1979 energy crisis caused a reorganization of energy policies around the world. It brought renewed attention to developing solar technologies. Deployment strategies focused on incentive programs such as the Federal Photovoltaic Utilization Program in the US and the Sunshine Program in Japan. Other efforts included the formation of research facilities in the US (SERI, now NREL), Japan (NEDO), and Germany (Fraunhofer Institute for Solar Energy Systems ISE). Commercial solar water heaters began appearing in the United States in the 1890s. These systems saw increasing use until the 1920s but were gradually replaced by cheaper and more reliable heating fuels. As with photovoltaics, solar water heating attracted renewed attention as a result of the oil crises in the 1970s, but interest subsided in the 1980s due to falling petroleum prices. Development in the solar water heating sector progressed steadily throughout the 1990s, and annual growth rates have averaged 20% since 1999. Although generally underestimated, solar water heating and cooling is by far the most widely deployed solar technology with an estimated capacity of 154 GW as of 2007. The International Energy Agency has said that solar energy can make considerable contributions to solving some of the most urgent problems the world now faces: The development of affordable, inexhaustible, and clean solar energy technologies will have huge longer-term benefits. It will increase countries' energy security through reliance on an indigenous, inexhaustible, and mostly import-independent resource, enhance sustainability, reduce pollution, lower the costs of mitigating climate change, and keep fossil fuel prices lower than otherwise. These advantages are global. Hence the additional costs of the incentives for early deployment should be considered learning investments; they must be wisely spent and need to be widely shared. In 2011, a report by the International Energy Agency found that solar energy technologies such as photovoltaics, solar hot water, and concentrated solar power could provide a third of the world's energy by 2060 if politicians commit to limiting climate change and transitioning to renewable energy. The energy from the Sun could play a key role in de-carbonizing the global economy alongside improvements in energy efficiency and imposing costs on greenhouse gas emitters. "The strength of solar is the incredible variety and flexibility of applications, from small scale to big scale". We have proved ... that after our stores of oil and coal are exhausted the human race can receive unlimited power from the rays of the Sun.In 2021 Lazard estimated the levelized cost of new build unsubsidized utility scale solar electricity at less than 37 dollars per MWh and existing coal-fired power above that amount. The 2021 report also said that new solar was also cheaper than new gas-fired power, but not generally existing gas power. === Emerging technologies === ==== Experimental solar power ==== Concentrated photovoltaics (CPV) systems employ sunlight concentrated onto photovoltaic surfaces for the purpose of electricity generation. Thermoelectric, or "thermovoltaic" devices convert a temperature difference between dissimilar materials into an electric current. ==== Floating solar arrays ==== ==== Solar-assisted heat pump ==== A heat pump is a device that provides heat energy from a source of heat to a destination called a "heat sink". Heat pumps are designed to move thermal energy opposite to the direction of spontaneous heat flow by absorbing heat from a cold space and releasing it to a warmer one. A solar-assisted heat pump represents the integration of a heat pump and thermal solar panels in a single integrated system. Typically these two technologies are used separately (or only placing them in parallel) to produce hot water. In this system the solar thermal panel performs the function of the low temperature heat source and the heat produced is used to feed the heat pump's evaporator. The goal of this system is to get high COP and then produce energy in a more efficient and less expensive way. It is possible to use any type of solar thermal panel (sheet and tubes, roll-bond, heat pipe, thermal plates) or hybrid (mono/polycrystalline, thin film) in combination with the heat pump. The use of a hybrid panel is preferable because it allows covering a part of the electricity demand of the heat pump and reduces the power consumption and consequently the variable costs of the system. ==== Solar aircraft ==== An electric aircraft is an aircraft that runs on electric motors rather than internal combustion engines, with electricity coming from fuel cells, solar cells, ultracapacitors, power beaming, or batteries. Currently, flying manned electric aircraft are mostly experimental demonstrators, though many small unmanned aerial vehicles are powered by batteries. Electrically powered model aircraft have been flown since the 1970s, with one report in 1957. The first man-carrying electrically powered flights were made in 1973. Between 2015 and 2016, a manned, solar-powered plane, Solar Impulse 2, completed a circumnavigation of the Earth. == See also == == References == == Further reading ==
Wikipedia/Solar_energy
An energy system is a system primarily designed to supply energy-services to end-users.: 941  The intent behind energy systems is to minimise energy losses to a negligible level, as well as to ensure the efficient use of energy. The IPCC Fifth Assessment Report defines an energy system as "all components related to the production, conversion, delivery, and use of energy".: 1261  The first two definitions allow for demand-side measures, including daylighting, retrofitted building insulation, and passive solar building design, as well as socio-economic factors, such as aspects of energy demand management and remote work, while the third does not. Neither does the third account for the informal economy in traditional biomass that is significant in many developing countries. The analysis of energy systems thus spans the disciplines of engineering and economics.: 1  Merging ideas from both areas to form a coherent description, particularly where macroeconomic dynamics are involved, is challenging. The concept of an energy system is evolving as new regulations, technologies, and practices enter into service – for example, emissions trading, the development of smart grids, and the greater use of energy demand management, respectively. == Treatment == From a structural perspective, an energy system is like any system and is made up of a set of interacting component parts, located within an environment. These components derive from ideas found in engineering and economics. Taking a process view, an energy system "consists of an integrated set of technical and economic activities operating within a complex societal framework".: 423  The identification of the components and behaviors of an energy system depends on the circumstances, the purpose of the analysis, and the questions under investigation. The concept of an energy system is therefore an abstraction which usually precedes some form of computer-based investigation, such as the construction and use of a suitable energy model. Viewed in engineering terms, an energy system lends itself to representation as a flow network: the vertices map to engineering components like power stations and pipelines and the edges map to the interfaces between these components. This approach allows collections of similar or adjacent components to be aggregated and treated as one to simplify the model. Once described thus, flow network algorithms, such as minimum cost flow, may be applied. The components themselves can be treated as simple dynamical systems in their own right. === Economic modeling === Conversely, relatively pure economic modeling may adopt a sectoral approach with only limited engineering detail present. The sector and sub-sector categories published by the International Energy Agency are often used as a basis for this analysis. A 2009 study of the UK residential energy sector contrasts the use of the technology-rich Markal model with several UK sectoral housing stock models. ==== Data ==== International energy statistics are typically broken down by carrier, sector and sub-sector, and country. Energy carriers (aka energy products) are further classified as primary energy and secondary (or intermediate) energy and sometimes final (or end-use) energy. Published energy datasets are normally adjusted so that they are internally consistent, meaning that all energy stocks and flows must balance. The IEA regularly publishes energy statistics and energy balances with varying levels of detail and cost and also offers mid-term projections based on this data. The notion of an energy carrier, as used in energy economics, is distinct and different from the definition of energy used in physics. === Scopes === Energy systems can range in scope, from local, municipal, national, and regional, to global, depending on issues under investigation. Researchers may or may not include demand side measures within their definition of an energy system. The Intergovernmental Panel on Climate Change (IPCC) does so, for instance, but covers these measures in separate chapters on transport, buildings, industry, and agriculture.: 1261 : 516  Household consumption and investment decisions may also be included within the ambit of an energy system. Such considerations are not common because consumer behavior is difficult to characterize, but the trend is to include human factors in models. Household decision-taking may be represented using techniques from bounded rationality and agent-based behavior. The American Association for the Advancement of Science (AAAS) specifically advocates that "more attention should be paid to incorporating behavioral considerations other than price- and income-driven behavior into economic models [of the energy system]".: 6  == Energy-services == The concept of an energy-service is central, particularly when defining the purpose of an energy system: It is important to realize that the use of energy is no end in itself but is always directed to satisfy human needs and desires. Energy services are the ends for which the energy system provides the means.: 941  Energy-services can be defined as amenities that are either furnished through energy consumption or could have been thus supplied.: 2  More explicitly: Demand should, where possible, be defined in terms of energy-service provision, as characterized by an appropriate intensity – for example, air temperature in the case of space-heating or lux levels for illuminance. This approach facilitates a much greater set of potential responses to the question of supply, including the use of energetically-passive techniques – for instance, retrofitted insulation and daylighting.: 156  A consideration of energy-services per capita and how such services contribute to human welfare and individual quality of life is paramount to the debate on sustainable energy. People living in poor regions with low levels of energy-services consumption would clearly benefit from greater consumption, but the same is not generally true for those with high levels of consumption. The notion of energy-services has given rise to energy-service companies (ESCo) who contract to provide energy-services to a client for an extended period. The ESCo is then free to choose the best means to do so, including investments in the thermal performance and HVAC equipment of the buildings in question. == International standards == ISO 13600, ISO 13601, and ISO 13602 form a set of international standards covering technical energy systems (TES). Although withdrawn prior to 2016, these documents provide useful definitions and a framework for formalizing such systems. The standards depict an energy system broken down into supply and demand sectors, linked by the flow of tradable energy commodities (or energywares). Each sector has a set of inputs and outputs, some intentional and some harmful byproducts. Sectors may be further divided into subsectors, each fulfilling a dedicated purpose. The demand sector is ultimately present to supply energyware-based services to consumers (see energy-services). == Energy system redesign and transformation == Energy system design includes the redesigning of energy systems to ensure sustainability of the system and its dependents and for meeting requirements of the Paris Agreement for climate change mitigation. Researchers are designing energy systems models and transformational pathways for renewable energy transitions towards 100% renewable energy, often in the form of peer-reviewed text documents created once by small teams of scientists and published in a journal. Considerations include the system's intermittency management, air pollution, various risks (such as for human safety, environmental risks, cost risks and feasibility risks), stability for prevention of power outages (including grid dependence or grid-design), resource requirements (including water and rare minerals and recyclability of components), technology/development requirements, costs, feasibility, other affected systems (such as land-use that affects food systems), carbon emissions, available energy quantity and transition-concerning factors (including costs, labor-related issues and speed of deployment). Energy system design can also consider energy consumption, such as in terms of absolute energy demand, waste and consumption reduction (e.g. via reduced energy-use, increased efficiency and flexible timing), process efficiency enhancement and waste heat recovery. A study noted significant potential for a type of energy systems modelling to "move beyond single disciplinary approaches towards a sophisticated integrated perspective". == See also == Control volume – a concept from mechanics and thermodynamics Electric power system – a network of electrical components used to generate, transfer, and use electric power Energy development – the effort to provide societies with sufficient energy under the reduced social and environmental impact Energy modeling – the process of building computer models of energy systems Energy industry – the supply-side of the energy sector Insular energy system - where an energy system is isolated from other nearby energy systems Mathematical model – the representation of a system using mathematics and often solved using computers Object-oriented programming – a computer programming paradigm suited to the representation of energy systems as networks Network science – the study of complex networks Open energy system databases – database projects which collect, clean, and republish energy-related datasets Open energy system models – a review of energy system models that are also open source Sankey diagram – used to show energy flows through a system == Notes == == References == == External links ==
Wikipedia/Energy_system
In physics, sound energy is a form of energy that can be heard by living things. Only those waves that have a frequency of 16 Hz to 20 kHz are audible to humans. However, this range is an average and will slightly change from individual to individual. Sound waves that have frequencies below 16 Hz are called infrasonic and those above 20 kHz are called ultrasonic. Sound is a mechanical wave and as such consists physically in oscillatory elastic compression and in oscillatory displacement of a fluid. Therefore, the medium acts as storage for both potential and kinetic energy. Consequently, the sound energy in a volume of interest is defined as the sum of the potential and kinetic energy densities integrated over that volume: W = W p o t e n t i a l + W k i n e t i c = ∫ V p 2 2 ρ 0 c 2 d V + ∫ V ρ v 2 2 d V , {\displaystyle W=W_{\mathrm {potential} }+W_{\mathrm {kinetic} }=\int _{V}{\frac {p^{2}}{2\rho _{0}c^{2}}}\,\mathrm {d} V+\int _{V}{\frac {\rho v^{2}}{2}}\,\mathrm {d} V,} where V is the volume of interest; p is the sound pressure; v is the particle velocity; ρ0 is the density of the medium without sound present; ρ is the local density of the medium; and c is the speed of sound. == See also == Sound energy density == References ==
Wikipedia/Sound_energy
Gravitational energy or gravitational potential energy is the potential energy an object with mass has due to the gravitational potential of its position in a gravitational field. Mathematically, it is the minimum mechanical work that has to be done against the gravitational force to bring a mass from a chosen reference point (often an "infinite distance" from the mass generating the field) to some other point in the field, which is equal to the change in the kinetic energies of the objects as they fall towards each other. Gravitational potential energy increases when two objects are brought further apart and is converted to kinetic energy as they are allowed to fall towards each other. == Formulation == For two pairwise interacting point particles, the gravitational potential energy U {\displaystyle U} is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): U = − W g = − ∫ F → g ⋅ d r → {\displaystyle U=-W_{g}=-\int {\vec {F}}_{g}\cdot d{\vec {r}}} where d r → {\textstyle d{\vec {r}}} is the displacement vector of the mass, F g → {\displaystyle {\vec {F_{g}}}} is gravitational force acting on it and ⋅ {\textstyle \cdot } denotes scalar product. == Newtonian mechanics == In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude & direction of gravitational force experienced by a point mass m {\displaystyle m} , due to the presence of another point mass M {\displaystyle M} at a distance r {\displaystyle r} , is given by Newton's law of gravitation. Taking origin to be at the position of M {\displaystyle M} , F g → = − G M m r 2 r ^ {\displaystyle {\vec {F_{g}}}=-{\frac {GMm}{r^{2}}}{\hat {r}}} To get the total work done by the gravitational force in bringing point mass m {\displaystyle m} from infinity to final distance R {\displaystyle R} (for example, the radius of Earth) from point mass M {\textstyle M} , the force is integrated with respect to displacement: W g = ∫ F → g ⋅ d r → = − ∫ ∞ R G M m r 2 d r = G M m r | ∞ R = G M m R {\displaystyle W_{g}=\int {\vec {F}}_{g}\cdot d{\vec {r}}=-\int _{\infty }^{R}{\frac {GMm}{r^{2}}}dr=\left.{\frac {GMm}{r}}\right|_{\infty }^{R}={\frac {GMm}{R}}} Gravitational potential energy being the minimum (quasi-static) work that needs to be done against gravitational force in this procedure, === Simplified version for Earth's surface === In the common situation where a much smaller mass m {\displaystyle m} is moving near the surface of a much larger object with mass M {\displaystyle M} , the gravitational field is nearly constant and so the expression for gravitational energy can be considerably simplified. The change in potential energy moving from the surface (a distance R {\displaystyle R} from the center) to a height h {\displaystyle h} above the surface is Δ U = G M m R − G M m R + h = G M m R ( 1 − 1 1 + h / R ) {\displaystyle {\begin{aligned}\Delta U&={\frac {GMm}{R}}-{\frac {GMm}{R+h}}\\&={\frac {GMm}{R}}\left(1-{\frac {1}{1+h/R}}\right)\end{aligned}}} If h / R {\displaystyle h/R} is small, as it must be close to the surface where g {\displaystyle g} is constant, then this expression can be simplified using the binomial approximation 1 1 + h / R ≈ 1 − h R {\displaystyle {\frac {1}{1+h/R}}\approx 1-{\frac {h}{R}}} to Δ U ≈ G M m R [ 1 − ( 1 − h R ) ] Δ U ≈ G M m h R 2 Δ U ≈ m ( G M R 2 ) h {\displaystyle {\begin{aligned}\Delta U&\approx {\frac {GMm}{R}}\left[1-\left(1-{\frac {h}{R}}\right)\right]\\\Delta U&\approx {\frac {GMmh}{R^{2}}}\\\Delta U&\approx m\left({\frac {GM}{R^{2}}}\right)h\end{aligned}}} As the gravitational field is g = G M / R 2 {\displaystyle g=GM/R^{2}} , this reduces to Δ U ≈ m g h {\displaystyle \Delta U\approx mgh} Note, this is the change of energy in gaining some height h {\displaystyle h} from the surface. == General relativity == In general relativity gravitational energy is extremely complex, and there is no single agreed upon definition of the concept. It is sometimes modelled via the Landau–Lifshitz pseudotensor that allows retention for the energy–momentum conservation laws of classical mechanics. Addition of the matter stress–energy tensor to the Landau–Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor that has a vanishing 4-divergence in all frames—ensuring the conservation law. Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a tensor. == See also == Gravitational binding energy Gravitational potential Gravitational potential energy storage Positive energy theorem == References ==
Wikipedia/Gravitational_energy
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically phrased mathematical formulation. There are multiple possible alternative ways to express such a condition such that can be applied to the matter content of the theory. The hope is then that any reasonable matter theory will satisfy this condition or at least will preserve the condition if it is satisfied by the starting conditions. Energy conditions are not physical constraints per se, but are rather mathematically imposed boundary conditions that attempt to capture a belief that "energy should be positive". Many energy conditions are known to not correspond to physical reality—for example, the observable effects of dark energy are well known to violate the strong energy condition. In general relativity, energy conditions are often used (and required) in proofs of various important theorems about black holes, such as the no hair theorem or the laws of black hole thermodynamics. == Motivation == In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy–momentum tensor (or matter tensor) T a b {\displaystyle T^{ab}} . However, the Einstein field equation in itself does not specify what kinds of states of matter or non-gravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be maximally independent of any assumptions concerning non-gravitational physics, and a weakness, because without some further criterion the Einstein field equation admits putative solutions with properties most physicists regard as unphysical, i.e. too weird to resemble anything in the real universe even approximately. The energy conditions represent such criteria. Roughly speaking, they crudely describe properties common to all (or almost all) states of matter and all non-gravitational fields that are well-established in physics while being sufficiently strong to rule out many unphysical "solutions" of the Einstein field equation. Mathematically speaking, the most apparent distinguishing feature of the energy conditions is that they are essentially restrictions on the eigenvalues and eigenvectors of the matter tensor. A more subtle but no less important feature is that they are imposed eventwise, at the level of tangent spaces. Therefore, they have no hope of ruling out objectionable global features, such as closed timelike curves. == Some observable quantities == In order to understand the statements of the various energy conditions, one must be familiar with the physical interpretation of some scalar and vector quantities constructed from arbitrary timelike or null vectors and the matter tensor. First, a unit timelike vector field X → {\displaystyle {\vec {X}}} can be interpreted as defining the world lines of some family of (possibly noninertial) ideal observers. Then the scalar field ρ = T a b X a X b {\displaystyle \rho =T_{ab}X^{a}X^{b}} can be interpreted as the total mass–energy density (matter plus field energy of any non-gravitational fields) measured by the observer from our family (at each event on his world line). Similarly, the vector field with components − T a b X b {\displaystyle -{T^{a}}_{b}X^{b}} represents (after a projection) the momentum measured by our observers. Second, given an arbitrary null vector field k → , {\displaystyle {\vec {k}},} the scalar field ν = T a b k a k b {\displaystyle \nu =T_{ab}k^{a}k^{b}} can be considered a kind of limiting case of the mass–energy density. Third, in the case of general relativity, given an arbitrary timelike vector field X → {\displaystyle {\vec {X}}} , again interpreted as describing the motion of a family of ideal observers, the Raychaudhuri scalar is the scalar field obtained by taking the trace of the tidal tensor corresponding to those observers at each event: E [ X → ] m m = R a b X a X b {\displaystyle {E[{\vec {X}}]^{m}}_{m}=R_{ab}X^{a}X^{b}} This quantity plays a crucial role in Raychaudhuri's equation. Then from Einstein field equation we immediately obtain 1 8 π E [ X → ] m m = 1 8 π R a b X a X b = ( T a b − 1 2 T g a b ) X a X b , {\displaystyle {\frac {1}{8\pi }}{E[{\vec {X}}]^{m}}_{m}={\frac {1}{8\pi }}R_{ab}X^{a}X^{b}=\left(T_{ab}-{\frac {1}{2}}Tg_{ab}\right)X^{a}X^{b},} where T = T m m {\displaystyle T={T^{m}}_{m}} is the trace of the matter tensor. == Mathematical statement == There are several alternative energy conditions in common use: === Null energy condition === The null energy condition stipulates that for every future-pointing null vector field k → {\displaystyle {\vec {k}}} , ν = T a b k a k b ≥ 0. {\displaystyle \nu =T_{ab}k^{a}k^{b}\geq 0.} Each of these has an averaged version, in which the properties noted above are to hold only on average along the flowlines of the appropriate vector fields. Otherwise, the Casimir effect leads to exceptions. For example, the averaged null energy condition states that for every flowline (integral curve) C {\displaystyle C} of the null vector field k → , {\displaystyle {\vec {k}},} we must have ∫ C T a b k a k b d λ ≥ 0. {\displaystyle \int _{C}T_{ab}k^{a}k^{b}d\lambda \geq 0.} === Weak energy condition === The weak energy condition stipulates that for every timelike vector field X → , {\displaystyle {\vec {X}},} the matter density observed by the corresponding observers is always non-negative: ρ = T a b X a X b ≥ 0. {\displaystyle \rho =T_{ab}X^{a}X^{b}\geq 0.} === Dominant energy condition === The dominant energy condition stipulates that, in addition to the weak energy condition holding true, for every future-pointing causal vector field (either timelike or null) Y → , {\displaystyle {\vec {Y}},} the vector field − T a b Y b {\displaystyle -{T^{a}}_{b}Y^{b}} must be a future-pointing causal vector. That is, mass–energy can never be observed to be flowing faster than light. === Strong energy condition === The strong energy condition stipulates that for every timelike vector field X → {\displaystyle {\vec {X}}} , the trace of the tidal tensor measured by the corresponding observers is always non-negative: ( T a b − 1 2 T g a b ) X a X b ≥ 0 {\displaystyle \left(T_{ab}-{\frac {1}{2}}Tg_{ab}\right)X^{a}X^{b}\geq 0} There are many classical matter configurations which violate the strong energy condition, at least from a mathematical perspective. For instance, a scalar field with a positive potential can violate this condition. Moreover, observations of dark energy/cosmological constant show that the strong energy condition fails to describe our universe, even when averaged across cosmological scales. Furthermore, it is strongly violated in any cosmological inflationary process (even one not driven by a scalar field). == Perfect fluids == Perfect fluids possess a matter tensor of form T a b = ρ u a u b + p h a b , {\displaystyle T^{ab}=\rho u^{a}u^{b}+ph^{ab},} where u → {\displaystyle {\vec {u}}} is the four-velocity of the matter particles and where h a b ≡ g a b + u a u b {\displaystyle h^{ab}\equiv g^{ab}+u^{a}u^{b}} is the projection tensor onto the spatial hyperplane elements orthogonal to the four-velocity, at each event. (Notice that these hyperplane elements will not form a spatial hyperslice unless the velocity is vorticity-free, that is, irrotational.) With respect to a frame aligned with the motion of the matter particles, the components of the matter tensor take the diagonal form T a ^ b ^ = [ ρ 0 0 0 0 p 0 0 0 0 p 0 0 0 0 p ] . {\displaystyle T^{{\hat {a}}{\hat {b}}}={\begin{bmatrix}\rho &0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{bmatrix}}.} Here, ρ {\displaystyle \rho } is the energy density and p {\displaystyle p} is the pressure. The energy conditions can then be reformulated in terms of these eigenvalues: The null energy condition stipulates that ρ + p ≥ 0. {\displaystyle \rho +p\geq 0.} The weak energy condition stipulates that ρ ≥ 0 , ρ + p ≥ 0. {\displaystyle \rho \geq 0,\;\;\rho +p\geq 0.} The dominant energy condition stipulates that ρ ≥ | p | . {\displaystyle \rho \geq |p|.} The strong energy condition stipulates that ρ + p ≥ 0 , ρ + 3 p ≥ 0. {\displaystyle \rho +p\geq 0,\;\;\rho +3p\geq 0.} The implications among these conditions are indicated in the figure at right. Note that some of these conditions allow negative pressure. Also, note that despite the names the strong energy condition does not imply the weak energy condition even in the context of perfect fluids. == Non-perfect fluids == Finally, there are proposals for extension of the energy conditions to spacetimes containing non-perfect fluids, where the second law of thermodynamics provides a natural Lyapunov function to probe both stability and causality, where the physical origin of the connection between stability and causality lies in the relationship between entropy and information. These attempts generalize the Hawking-Ellis vacuum conservation theorem (according to which, if energy can enter an empty region faster than the speed of light, then the dominant energy condition is violated, and the energy density may become negative in some reference frame) to spacetimes containing out-of-equilibrium matter at finite temperature and chemical potential. Indeed, the idea that there is a connection between causality violation and fluid instabilities has a long history. For example, in the words of W. Israel: “If the source of an effect can be delayed, it should be possible for a system to borrow energy from its ground state, and this implies instability”. It is possible to show that this is a restatement of the Hawking-Ellis vacuum conservation theorem at finite temperature and chemical potential. == Attempts at falsifying the energy conditions == While the intent of the energy conditions is to provide simple criteria that rule out many unphysical situations while admitting any physically reasonable situation, in fact, at least when one introduces an effective field modeling of some quantum mechanical effects, some possible matter tensors which are known to be physically reasonable and even realistic because they have been experimentally verified, actually fail various energy conditions. In particular, in the Casimir effect, in the region between two conducting plates held parallel at a very small separation d, there is a negative energy density ε = − π 2 720 ℏ d 4 {\displaystyle \varepsilon ={\frac {-\pi ^{2}}{720}}{\frac {\hbar }{d^{4}}}} between the plates. (Be mindful, though, that the Casimir effect is topological, in that the sign of the vacuum energy depends on both the geometry and topology of the configuration. Being negative for parallel plates, the vacuum energy is positive for a conducting sphere.) However, various quantum inequalities suggest that a suitable averaged energy condition may be satisfied in such cases. In particular, the averaged null energy condition is satisfied in the Casimir effect. Indeed, for energy–momentum tensors arising from effective field theories on Minkowski spacetime, the averaged null energy condition holds for everyday quantum fields. Extending these results is an open problem. The strong energy condition is obeyed by all normal/Newtonian matter, but a false vacuum can violate it. Consider the linear barotropic equation state p = w ρ , {\displaystyle p=w\rho ,} where ρ {\displaystyle \rho } is the matter energy density, p {\displaystyle p} is the matter pressure, and w {\displaystyle w} is a constant. Then the strong energy condition requires w ≥ − 1 / 3 {\displaystyle w\geq -1/3} ; but for the state known as a false vacuum, we have w = − 1 {\displaystyle w=-1} . == See also == Congruence (general relativity) Exact solutions in general relativity Frame fields in general relativity Positive energy theorem Quantum inequalities == Notes == == References == Hawking, Stephen; Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press. ISBN 0-521-09906-4. The energy conditions are discussed in §4.3. Poisson, Eric (2004). A Relativist's Toolkit: The Mathematics of Black Hole Mechanics. Cambridge: Cambridge University Press. Bibcode:2004rtmb.book.....P. ISBN 0-521-83091-5. Various energy conditions (including all of those mentioned above) are discussed in Section 2.1. Carroll, Sean M. (2004). Spacetime and Geometry: An Introduction to General Relativity. San Francisco: Addison-Wesley. ISBN 0-8053-8732-3. Various energy conditions are discussed in Section 4.6. Wald, Robert M. (1984). General Relativity. Chicago: University of Chicago Press. ISBN 0-226-87033-2. Common energy conditions are discussed in Section 9.2. Ellis, G. F. R.; Maartens, R.; MacCallum, M.A.H. (2012). Relativistic Cosmology. Cambridge: Cambridge University Press. ISBN 978-0-521-38115-4. Violations of the strong energy condition is discussed in Section 6.1.
Wikipedia/Energy_condition
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is non-zero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged. Because of mass–energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared. Systems whose four-momentum is a null vector, a light-like vector within the context of Minkowski space (for example, a single photon or many photons moving in exactly the same direction) have zero invariant mass and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass. If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system's invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy. For an isolated massive system, the center of mass of the system moves in a straight line with a steady subluminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center-of-momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c2. This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames. Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon. == Sum of rest masses == The invariant mass of a system includes the mass of any kinetic energy of the system constituents that remains in the center of momentum frame, so the invariant mass of a system may be greater than sum of the invariant masses (rest masses) of its separate constituents. For example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in general not an additive quantity (although there are a few rare situations where it may be, as is the case when massive particles in a system without potential or kinetic energy can be added to a total mass). Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest (in any particular frame of reference). The magnitude of invariant mass of this two-body system (see definition below) is different from the sum of rest mass (i.e. their respective mass when stationary). Even if we consider the same system from center-of-momentum frame, where net momentum is zero, the magnitude of the system's invariant mass is not equal to the sum of the rest masses of the particles within it. The kinetic energy of such particles and the potential energy of the force fields increase the total energy above the sum of the particle rest masses, and both terms contribute to the invariant mass of the system. The sum of the particle kinetic energies as calculated by an observer is smallest in the center of momentum frame (again, called the "rest frame" if the system is bound). They will often also interact through one or more of the fundamental forces, giving them a potential energy of interaction, possibly negative. == As defined in particle physics == In particle physics, the invariant mass m0 is equal to the mass in the rest frame of the particle, and can be calculated by the particle's energy E and its momentum p as measured in any frame, by the energy–momentum relation: m 0 2 c 2 = ( E c ) 2 − ‖ p ‖ 2 {\displaystyle m_{0}^{2}c^{2}=\left({\frac {E}{c}}\right)^{2}-\left\|\mathbf {p} \right\|^{2}} or in natural units where c = 1, m 0 2 = E 2 − ‖ p ‖ 2 . {\displaystyle m_{0}^{2}=E^{2}-\left\|\mathbf {p} \right\|^{2}.} This invariant mass is the same in all frames of reference (see also special relativity). This equation says that the invariant mass is the pseudo-Euclidean length of the four-vector (E, p), calculated using the relativistic version of the Pythagorean theorem which has a different sign for the space and time dimensions. This length is preserved under any Lorentz boost or rotation in four dimensions, just like the ordinary length of a vector is preserved under rotations. In quantum theory the invariant mass is a parameter in the relativistic Dirac equation for an elementary particle. The Dirac quantum operator corresponds to the particle four-momentum vector. Since the invariant mass is determined from quantities which are conserved during a decay, the invariant mass calculated using the energy and momentum of the decay products of a single particle is equal to the mass of the particle that decayed. The mass of a system of particles can be calculated from the general formula: ( W c 2 ) 2 = ( ∑ E ) 2 − ‖ ∑ p c ‖ 2 , {\displaystyle \left(Wc^{2}\right)^{2}=\left(\sum E\right)^{2}-\left\|\sum \mathbf {p} c\right\|^{2},} where W {\displaystyle W} is the invariant mass of the system of particles, equal to the mass of the decay particle. ∑ E {\textstyle \sum E} is the sum of the energies of the particles ∑ p {\textstyle \sum \mathbf {p} } is the vector sum of the momentum of the particles (includes both magnitude and direction of the momenta) The term invariant mass is also used in inelastic scattering experiments. Given an inelastic reaction with total incoming energy larger than the total detected energy (i.e. not all outgoing particles are detected in the experiment), the invariant mass (also known as the "missing mass") W of the reaction is defined as follows (in natural units): W 2 = ( ∑ E in − ∑ E out ) 2 − ‖ ∑ p in − ∑ p out ‖ 2 . {\displaystyle W^{2}=\left(\sum E_{\text{in}}-\sum E_{\text{out}}\right)^{2}-\left\|\sum \mathbf {p} _{\text{in}}-\sum \mathbf {p} _{\text{out}}\right\|^{2}.} If there is one dominant particle which was not detected during an experiment, a plot of the invariant mass will show a sharp peak at the mass of the missing particle. In those cases when the momentum along one direction cannot be measured (i.e. in the case of a neutrino, whose presence is only inferred from the missing energy) the transverse mass is used. == Example: two-particle collision == In a two-particle collision (or a two-particle decay) the square of the invariant mass (in natural units) is M 2 = ( E 1 + E 2 ) 2 − ‖ p 1 + p 2 ‖ 2 = m 1 2 + m 2 2 + 2 ( E 1 E 2 − p 1 ⋅ p 2 ) . {\displaystyle {\begin{aligned}M^{2}&=(E_{1}+E_{2})^{2}-\left\|\mathbf {p} _{1}+\mathbf {p} _{2}\right\|^{2}\\&=m_{1}^{2}+m_{2}^{2}+2\left(E_{1}E_{2}-\mathbf {p} _{1}\cdot \mathbf {p} _{2}\right).\end{aligned}}} === Massless particles === The invariant mass of a system made of two massless particles whose momenta form an angle θ {\displaystyle \theta } has a convenient expression: M 2 = ( E 1 + E 2 ) 2 − ‖ p 1 + p 2 ‖ 2 = [ ( p 1 , 0 , 0 , p 1 ) + ( p 2 , 0 , p 2 sin ⁡ θ , p 2 cos ⁡ θ ) ] 2 = ( p 1 + p 2 ) 2 − p 2 2 sin 2 ⁡ θ − ( p 1 + p 2 cos ⁡ θ ) 2 = 2 p 1 p 2 ( 1 − cos ⁡ θ ) . {\displaystyle {\begin{aligned}M^{2}&=(E_{1}+E_{2})^{2}-\left\|{\textbf {p}}_{1}+{\textbf {p}}_{2}\right\|^{2}\\&=[(p_{1},0,0,p_{1})+(p_{2},0,p_{2}\sin \theta ,p_{2}\cos \theta )]^{2}\\&=(p_{1}+p_{2})^{2}-p_{2}^{2}\sin ^{2}\theta -(p_{1}+p_{2}\cos \theta )^{2}\\&=2p_{1}p_{2}(1-\cos \theta ).\end{aligned}}} === Collider experiments === In particle collider experiments, one often defines the angular position of a particle in terms of an azimuthal angle ϕ {\displaystyle \phi } and pseudorapidity η {\displaystyle \eta } . Additionally the transverse momentum, p T {\displaystyle p_{T}} , is usually measured. In this case if the particles are massless, or highly relativistic ( E ≫ m {\displaystyle E\gg m} ) then the invariant mass becomes: M 2 = 2 p T 1 p T 2 ( cosh ⁡ ( η 1 − η 2 ) − cos ⁡ ( ϕ 1 − ϕ 2 ) ) . {\displaystyle M^{2}=2p_{T1}p_{T2}(\cosh(\eta _{1}-\eta _{2})-\cos(\phi _{1}-\phi _{2})).} == Rest energy == Rest energy (also called rest mass energy) is the energy associated with a particle's invariant mass. The rest energy E 0 {\displaystyle E_{0}} of a particle is defined as: E 0 = m 0 c 2 , {\displaystyle E_{0}=m_{0}c^{2},} where c {\displaystyle c} is the speed of light in vacuum. In general, only differences in energy have physical significance. The concept of rest energy follows from the special theory of relativity that leads to Einstein's famous conclusion about equivalence of energy and mass. See Special relativity § Relativistic dynamics and invariance. == See also == Mass in special relativity Invariant (physics) Transverse mass == References == Landau, L.D.; Lifshitz, E.M. (1975). The Classical Theory of Fields: 4-th revised English Edition: Course of Theoretical Physics Vol. 2. Butterworth Heinemann. ISBN 0-7506-2768-9. Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2. == Citations ==
Wikipedia/Rest_energy
An energy carrier is a substance (fuel) or sometimes a phenomenon (energy system) that contains energy that can be later converted to other forms such as mechanical work or heat or to operate chemical or physical processes. Such carriers include springs, electrical batteries, capacitors, pressurized air, dammed water, hydrogen, metal energy carriers,petroleum, coal, wood, and natural gas. An energy carrier does not produce energy; it simply contains energy imbued by another system. == Definition according to ISO 13600 == According to ISO 13600, an energy carrier is either a substance or a phenomenon that can be used to produce mechanical work or heat or to operate chemical or physical processes. It is any system or substance that contains energy for conversion as usable energy later or somewhere else. This could be converted for use in, for example, an appliance or vehicle. Such carriers include springs, electrical batteries, capacitors, pressurized air, dammed water, hydrogen, petroleum, coal, wood, and natural gas. ISO 13600 series (ISO 13600, ISO 13601, and ISO 13602) are intended to be used as tools to define, describe, analyse and compare technical energy systems (TES) at micro and macro levels: ISO 13600 (Technical energy systems — Basic concepts) covers basic definitions and terms needed to define and describe TESs in general and TESs of energyware supply and demand sectors in particular. ISO 13601 (Technical energy systems — Structure for analysis — Energyware supply and demand sectors) covers structures that shall be used to describe and analyse sub-sectors at the macro level of energyware supply and demand ISO 13602 (all parts) facilitates the description and analysis of any technical energy systems. == Definition within the field of energetics == In the field of energetics, an energy carrier is produced by human technology from a primary energy source. Only the energy sector uses primary energy sources. Other sectors of society use an energy carrier to perform useful activities (end-uses). The distinction between "Energy Carriers" (EC) and "Primary Energy Sources" (PES) is extremely important. An energy carrier can be more valuable (have a higher quality) than a primary energy source. For example 1 megajoule (MJ) of electricity produced by a hydroelectric plant is equivalent to 3 MJ of oil. Sunlight is a main source of primary energy, which can be transformed into plants and then into coal, oil and gas. Solar power and wind power are other derivatives of sunlight. Note that although coal, oil and natural gas are derived from sunlight, they are considered primary energy sources which are extracted from the earth (fossil fuels). Natural uranium is also a primary energy source extracted from the earth but does not come from the decomposition of organisms (mineral fuel). == See also == Capital goods Coefficient of performance Embedded energy Energy and society Energy crisis Energy pay-back Energy resource Energy source Energy storage Energyware Entropy Exergy Future energy development Hydrogen economy ISO 14000 Liquid nitrogen economy Lithium economy Methanol economy Metal Energy Carriers Renewable resource Vegetable oil economy Renewable Energy == References == == Further reading == European Nuclear Society info pool/glossary: Energy carrier Archived September 27, 2006, at the Wayback Machine Our Energy Futures glossary: Energy Carriers Störungsdienst, Elektriker (in German) == External links == "Boron: a better energy carrier than hydrogen?" paper by Graham Cowan ISO 13600 Technical energy systems -- Basic concepts: gives the basic concepts needed to define and describe technical energy systems.
Wikipedia/Energy_carrier
In cosmology, phantom dark energy is a hypothetical form of dark energy. It possesses negative kinetic energy, and predicts expansion of the universe in excess of that predicted by a cosmological constant, which leads to a Big Rip. The idea of phantom dark energy is often dismissed, as it would suggest that the vacuum is unstable with negative mass particles bursting into existence. The concept is hence tied to emerging theories of a continuously created negative mass dark fluid, in which the cosmological constant can vary as a function of time. It is a special type of quintessence. The term was coined by Robert R. Caldwell in 1999. == Equation of state == In cosmology, the equation of state of a perfect fluid is given by p = w ρ , {\displaystyle p=w\rho ,} where p is the pressure, ρ is the energy density and w is the ratio between the two. For normal baryonic matter w = 0 {\displaystyle w=0} and for a cosmological constant w = − 1 {\displaystyle w=-1} . Phantom dark energy is defined as having w < − 1 {\displaystyle w<-1} . == Big Rip mechanism == The existence of phantom dark energy could cause the expansion of the universe to accelerate so quickly that a scenario known as the Big Rip, a possible end to the universe, occurs. The expansion of the universe reaches an infinite degree in finite time, causing expansion to accelerate without bounds. This acceleration necessarily passes the speed of light (since it involves expansion of the universe itself, not particles moving within it), causing more and more objects to leave our observable universe faster than its expansion, as light and information emitted from distant stars and other cosmic sources cannot "catch up" with the expansion. As the observable universe expands, objects will be unable to interact with each other via fundamental forces, and eventually, the expansion will prevent any action of forces between any particles, even within atoms, "ripping apart" the universe, making distances between individual particles infinite. One application of phantom dark energy in 2007 was to a cyclic model of the universe, which reverses its expansion extremely shortly before the would-be Big Rip. This cyclic model can be more complicated if the mass–energy of every point in the universe is dense enough to collapse into black hole core substance that will bounce after reaching a maximum threshold of compression causing the next big bang (the overall scenario is highly unlikely). == Possible evidence == In 2025, the Dark Energy Spectroscopic Instrument (DESI) collaboration, published a survey on baryon acoustic oscillations. They found violations of the standard model of cosmology, the Lambda-CDM model, within 4 standard deviations. They reported acceleration of the universe that was stronger in the past, suggesting the presence of phantom dark energy in the early universe. == See also == Quintom scenario == References == == Further reading == Robert R. Caldwell et al.: Phantom Energy and Cosmic Doomsday
Wikipedia/Phantom_energy
World energy supply and consumption refers to the global supply of energy resources and its consumption. The system of global energy supply consists of the energy development, refinement, and trade of energy. Energy supplies may exist in various forms such as raw resources or more processed and refined forms of energy. The raw energy resources include for example coal, unprocessed oil and gas, uranium. In comparison, the refined forms of energy include for example refined oil that becomes fuel and electricity. Energy resources may be used in various different ways, depending on the specific resource (e.g. coal), and intended end use (industrial, residential, etc.). Energy production and consumption play a significant role in the global economy. It is needed in industry and global transportation. The total energy supply chain, from production to final consumption, involves many activities that cause a loss of useful energy. As of 2022, energy consumption is still about 80% from fossil fuels. The Gulf States and Russia are major energy exporters. Their customers include for example the European Union and China, who are not producing enough energy in their own countries to satisfy their energy demand. Total energy consumption tends to increase by about 1–2% per year. More recently, renewable energy has been growing rapidly, averaging about 20% increase per year in the 2010s. Two key problems with energy production and consumption are greenhouse gas emissions and environmental pollution. Of about 50 billion tonnes worldwide annual total greenhouse gas emissions, 36 billion tonnes of carbon dioxide was a result of energy use (almost all from fossil fuels) in 2021. Many scenarios have been envisioned to reduce greenhouse gas emissions, usually by the name of net zero emissions. There is a clear connection between energy consumption per capita, and GDP per capita. A significant lack of energy supplies is called an energy crisis. == Primary energy production == Primary energy refers to the first form of energy encountered, as raw resources collected directly from energy production, before any conversion or transformation of the energy occurs. Energy production is usually classified as: Fossil, using coal, crude oil, and natural gas; Nuclear, using uranium; Renewable, using biomass, geothermal, hydropower, solar, wind, tidal, wave, among others. Primary energy assessment by IEA follows certain rules to ease measurement of different kinds of energy. These rules are controversial. Water and air flow energy that drives hydro and wind turbines, and sunlight that powers solar panels, are not taken as PE, which is set at the electric energy produced. But fossil and nuclear energy are set at the reaction heat, which is about three times the electric energy. This measurement difference can lead to underestimating the economic contribution of renewable energy. Enerdata displays data for "Total energy / production: Coal, Oil, Gas, Biomass, Heat and Electricity" and for "Renewables / % in electricity production: Renewables, non-renewables". The table lists worldwide PE and the countries producing most (76%) of that in 2021, using Enerdata. The amounts are rounded and given in million tonnes of oil equivalent per year (1 Mtoe = 11.63 TWh (41.9 petajoules), where 1 TWh = 109 kWh) and % of Total. Renewable is Biomass plus Heat plus renewable percentage of Electricity production (hydro, wind, solar). Nuclear is nonrenewable percentage of Electricity production. The above-mentioned underestimation of hydro, wind and solar energy, compared to nuclear and fossil energy, applies also to Enerdata. The 2021 world total energy production of 14,800 MToe corresponds to a little over 172 PWh / year, or about 19.6 TW of power generation. == Energy conversion == Energy resources must be processed in order to make it suitable for final consumption. For example, there may be various impurities in raw coal mined or raw natural gas that was produced from an oil well that may make it unsuitable to be burned in a power plant. Primary energy is converted in many ways to energy carriers, also known as secondary energy: Coal mainly goes to thermal power stations. Coke is derived by destructive distillation of bituminous coal. Crude oil goes mainly to oil refineries Natural-gas goes to natural-gas processing plants to remove contaminants such as water, carbon dioxide and hydrogen sulfide, and to adjust the heating value. It is used as fuel gas, also in thermal power stations. Nuclear reaction heat is used in thermal power stations. Biomass is used directly or converted to biofuel. Electricity generators are driven by steam or gas turbines in a thermal plant, or water turbines in a hydropower station, or wind turbines, usually in a wind farm. The invention of the solar cell in 1954 started electricity generation by solar panels, connected to a power inverter. Mass production of panels around the year 2000 made this economic. == Energy trade == Much primary and converted energy is traded among countries. The table lists countries with large difference of export and import in 2021, expressed in Mtoe. A negative value indicates that much energy import is needed for the economy. Russian gas exports were reduced a lot in 2022, as pipelines to Asia plus LNG export capacity is much less than the gas no longer sent to Europe. Transport of energy carriers is done by tanker ship, tank truck, LNG carrier, rail freight transport, pipeline and by electric power transmission. == Total energy supply == Total energy supply (TES) indicates the sum of production and imports subtracting exports and storage changes. For the whole world TES nearly equals primary energy PE because imports and exports cancel out, but for countries TES and PE differ in quantity, and also in quality as secondary energy is involved, e.g., import of an oil refinery product. TES is all energy required to supply energy for end users. The tables list TES and PE for some countries where these differ much, both in 2021 and TES history. Most growth of TES since 1990 occurred in Asia. The amounts are rounded and given in Mtoe. Enerdata labels TES as Total energy consumption. 25% of worldwide primary production is used for conversion and transport, and 6% for non-energy products like lubricants, asphalt and petrochemicals. In 2019 TES was 606 EJ and final consumption was 418 EJ, 69% of TES. Most of the energy lost by conversion occurs in thermal electricity plants and the energy industry own use. === Discussion about energy loss === There are different qualities of energy. Heat, especially at a relatively low temperature, is low-quality energy of random motion, whereas electricity is high-quality energy that flows smoothly through wires. It takes around 3 kWh of heat to produce 1 kWh of electricity. But by the same token, a kilowatt-hour of this high-quality electricity can be used to pump several kilowatt-hours of heat into a building using a heat pump. It turns out that the loss of useful energy incurred in thermal electricity plants is very much more than the loss due to, say, resistance in power lines, because of quality differences. Electricity can also be used in many ways in which heat cannot. In fact, the loss in thermal plants is due to poor conversion of chemical energy of fuel to motion by combustion. Otherwise chemical energy of fuel is not inherently low-quality; for example, conversion of chemical energy to electricity in batteries can approach 100%. So energy loss in thermal plants is real loss. == Final consumption == Total final consumption (TFC) is the worldwide consumption of energy by end-users (whereas primary energy consumption (Eurostat) or total energy supply (IEA) is total energy demand and thus also includes what the energy sector uses itself and transformation and distribution losses). This energy consists of fuel (78%) and electricity (22%). The tables list amounts, expressed in million tonnes of oil equivalent per year (1 Mtoe = 11.63 TWh) and how much of these is renewable energy. Non-energy products are not considered here. The data are of 2018. The world's renewable share of TFC was 18% in 2018: 7% traditional biomass, 3.6% hydropower and 7.4% other renewables. In the period 2005–2017 worldwide final consumption of coal increased by 23%, of oil and gas increased by 18%, and that of electricity increased by 41%. Fuel comes in three types: Fossil fuel is natural gas, fuel derived from petroleum (LPG, gasoline, kerosene, gas/diesel, fuel oil), or from coal (anthracite, bituminous coal, coke, blast furnace gas). Secondly, there is renewable fuel (biofuel and fuel derived from waste). And lastly, the fuel used for district heating. The amounts of fuel in the tables are based on lower heating value. The first table lists final consumption in the countries/regions which use most (85%), and per person as of 2018. In developing countries fuel consumption per person is low and more renewable. Canada, Venezuela and Brazil generate most electricity with hydropower. The next table shows countries consuming most (85%) in Europe. === Energy for energy === Some fuel and electricity is used to construct, maintain and demolish/recycle installations that produce fuel and electricity, such as oil platforms, uranium isotope separators and wind turbines. For these producers to be economical the ratio of energy returned on energy invested (EROEI) or energy return on investment (EROI) should be large enough. If the final energy delivered for consumption is E and the EROI equals R, then the net energy available is E-E/R. The percentage available energy is 100-100/R. For R>10 more than 90% is available but for R=2 only 50% and for R=1 none. This steep decline is known as the net energy cliff. == Availability of data == Many countries publish statistics on the energy supply and consumption of either their own country, of other countries of interest, or of all countries combined in one chart. One of the largest organizations in this field, the International Energy Agency (IEA), sells yearly comprehensive energy data which makes this data paywalled and difficult to access for internet users. The organization Enerdata on the other hand publishes a free Yearbook, making the data more accessible. Another trustworthy organization that provides accurate energy data, mainly referring to the USA, is the U.S. Energy Information Administration. == Trends and outlook == Due to the COVID-19 pandemic, there was a significant decline in energy usage worldwide in 2020, but total energy demand worldwide had recovered by 2021, and has hit a record high in 2022. In 2022, consumers worldwide spent nearly USD 10 trillion on energy, averaging more than USD 1,200 per person. This reflects a 20% increase over the previous five-year average, highlighting the significant economic impact and the increasing financial burden of energy consumption on a global scale.: 13  === IEA scenarios === In World Energy Outlook 2023 the IEA notes that "We are on track to see all fossil fuels peak before 2030".: 18  The IEA presents three scenarios:: 17  The Stated Policies Scenario (STEPS) provides an outlook based on the latest policy settings. The share of fossil fuel in global energy supply – stuck for decades around 80% – starts to edge downwards and reaches 73% by 2030.: 18  This undercuts the rationale for any increase in fossil fuel investment.: 19  Renewables are set to contribute 80% of new power capacity to 2030, with solar PV alone accounting for more than half.: 20  The STEPS sees a peak in energy-related CO2 emissions in the mid-2020s but emissions remain high enough to push up global average temperatures to around 2.4 °C in 2100.: 22  Total energy demand continues to increase through to 2050.: 23  Total energy investment remains at about US$3 trillion per year.: 49  The Announced Pledges Scenario (APS) assumes all national energy and climate targets made by governments are met in full and on time. The APS is associated with a temperature rise of 1.7 °C in 2100 (with a 50% probability).: 92  Total energy investment rises to about US$4 trillion per year after 2030.: 49  The Net Zero Emissions by 2050 (NZE) Scenario limits global warming to 1.5 °C.: 17  The share of fossil fuel reaches 62% in 2030.: 101  Methane emissions from fossil fuel supply cuts by 75% in 2030.: 45  Total energy investment rises to almost US$5 trillion per year after 2030.: 49  Clean energy investment needs to rise everywhere, but the steepest increases are needed in emerging market and developing economies other than China, requiring enhanced international support.: 46  The share of electricity in final consumption exceeds 50% by 2050 in NZE. The share of nuclear power in electricity generation remains broadly stable over time in all scenarios, about 9%.: 106  The IEA's "Electricity 2024" report details a 2.2% growth in global electricity demand for 2023, forecasting an annual increase of 3.4% through 2026, with notable contributions from emerging economies like China and India, despite a slump in advanced economies due to economic and inflationary pressures. The report underscores the significant impact of data centers, artificial intelligence and cryptocurrency, projecting a potential doubling of electricity consumption to 1,000 TWh by 2026, which is on par with Japan's current usage. Notably, 85% of the additional demand is expected to originate from China and India, with India's demand alone predicted to grow over 6% annually until 2026, driven by economic expansion and increasing air conditioning use. Southeast Asia's electricity demand is also forecasted to climb by 5% annually through 2026. In the United States, a decrease was seen in 2023, but a moderate rise is anticipated in the coming years, largely fueled by data centers. The report also anticipates that a surge in electricity generation from low-emissions sources will meet the global demand growth over the next three years, with renewable energy sources predicted to surpass coal by early 2025. === Alternative scenarios === The goal set in the Paris Agreement to limit climate change will be difficult to achieve. Various scenarios for achieving the Paris Climate Agreement Goals have been developed, using IEA data but proposing transition to nearly 100% renewables by mid-century, along with steps such as reforestation. Nuclear power and carbon capture are excluded in these scenarios. The researchers say the costs will be far less than the $5 trillion per year governments currently spend subsidizing the fossil fuel industries responsible for climate change.: ix  In the +2.0 C (global warming) Scenario total primary energy demand in 2040 can be 450 EJ = 10,755 Mtoe, or 400 EJ = 9560 Mtoe in the +1.5 Scenario, well below the current production. Renewable sources can increase their share to 300 EJ in the +2.0 C Scenario or 330 EJ in the +1.5 Scenario in 2040. In 2050 renewables can cover nearly all energy demand. Non-energy consumption will still include fossil fuels.: xxvii Fig. 5  Global electricity generation from renewable energy sources will reach 88% by 2040 and 100% by 2050 in the alternative scenarios. "New" renewables—mainly wind, solar and geothermal energy—will contribute 83% of the total electricity generated.: xxiv  The average annual investment required between 2015 and 2050, including costs for additional power plants to produce hydrogen and synthetic fuels and for plant replacement, will be around $1.4 trillion.: 182  Shifts from domestic aviation to rail and from road to rail are needed. Passenger car use must decrease in the OECD countries (but increase in developing world regions) after 2020. The passenger car use decline will be partly compensated by strong increase in public transport rail and bus systems.: xxii Fig.4  CO2 emission can reduce from 32 Gt in 2015 to 7 Gt (+2.0 Scenario) or 2.7 Gt (+1.5 Scenario) in 2040, and to zero in 2050.: xxviii  == See also == Electric energy consumption – Worldwide consumption of electricity Energy demand management – Modification of consumer energy usage during peak hours Energy intensity – Measure of an economy's energy inefficiency Energy policy – How a government or business deals with energy Sustainable energy – Energy that responsibly meets social, economic, and environmental needs World Energy Outlook – Publication of the International Energy Agency World energy resources – Estimated maximum capacity for energy production on Earth Lists List of countries by energy intensity List of countries by electricity consumption List of countries by electricity production List of countries by energy consumption per capita List of countries by greenhouse gas emissions List of countries by energy consumption and production == Notes == == References == == External links == Enerdata - World Energy & Climate Statistics International Energy Outlook, by the U.S. Energy Information Administration World Energy Outlook from the IEA
Wikipedia/World_energy_supply_and_consumption
Energy is sustainable if it "meets the needs of the present without compromising the ability of future generations to meet their own needs." Definitions of sustainable energy usually look at its effects on the environment, the economy, and society. These impacts range from greenhouse gas emissions and air pollution to energy poverty and toxic waste. Renewable energy sources such as wind, hydro, solar, and geothermal energy can cause environmental damage but are generally far more sustainable than fossil fuel sources. The role of non-renewable energy sources in sustainable energy is controversial. Nuclear power does not produce carbon pollution or air pollution, but has drawbacks that include radioactive waste, the risk of nuclear proliferation, and the risk of accidents. Switching from coal to natural gas has environmental benefits, including a lower climate impact, but may lead to a delay in switching to more sustainable options. Carbon capture and storage can be built into power plants to remove their carbon dioxide (CO2) emissions, but this technology is expensive and has rarely been implemented. Fossil fuels provide 85% of the world's energy consumption, and the energy system is responsible for 76% of global greenhouse gas emissions. Around 790 million people in developing countries lack access to electricity, and 2.6 billion rely on polluting fuels such as wood or charcoal to cook. Cooking with biomass plus fossil fuel pollution causes an estimated 7 million deaths each year. Limiting global warming to 2 °C (3.6 °F) will require transforming energy production, distribution, storage, and consumption. Universal access to clean electricity can have major benefits to the climate, human health, and the economies of developing countries. Climate change mitigation pathways have been proposed to limit global warming to 2 °C (3.6 °F). These include phasing out coal-fired power plants, conserving energy, producing more electricity from clean sources such as wind and solar, and switching from fossil fuels to electricity for transport and heating buildings. Power output from some renewable energy sources varies depending on when the wind blows and the sun shines. Switching to renewable energy can therefore require electrical grid upgrades, such as the addition of energy storage. Some processes that are difficult to electrify can use hydrogen fuel produced from low-emission energy sources. In the International Energy Agency's proposal for achieving net zero emissions by 2050, about 35% of the reduction in emissions depends on technologies that are still in development as of 2023. Wind and solar market share grew to 8.5% of worldwide electricity in 2019, and costs continue to fall. The Intergovernmental Panel on Climate Change (IPCC) estimates that 2.5% of world gross domestic product (GDP) would need to be invested in the energy system each year between 2016 and 2035 to limit global warming to 1.5 °C (2.7 °F). Governments can fund the research, development, and demonstration of new clean energy technologies. They can also build infrastructure for electrification and sustainable transport. Finally, governments can encourage clean energy deployment with policies such as carbon pricing, renewable portfolio standards, and phase-outs of fossil fuel subsidies. These policies may also increase energy security. == Definitions and background == === Definitions === The United Nations Brundtland Commission described the concept of sustainable development, for which energy is a key component, in its 1987 report Our Common Future. It defined sustainable development as meeting "the needs of the present without compromising the ability of future generations to meet their own needs". This description of sustainable development has since been referenced in many definitions and explanations of sustainable energy. There is no universally accepted interpretation of how the concept of sustainability applies to energy on a global scale. Working definitions of sustainable energy encompass multiple dimensions of sustainability such as environmental, economic, and social dimensions. Historically, the concept of sustainable energy development has focused on emissions and on energy security. Since the early 1990s, the concept has broadened to encompass wider social and economic issues. The environmental dimension of sustainability includes greenhouse gas emissions, impacts on biodiversity and ecosystems, hazardous waste and toxic emissions, water consumption, and depletion of non-renewable resources. Energy sources with low environmental impact are sometimes called green energy or clean energy. The economic dimension of sustainability covers economic development, efficient use of energy, and energy security to ensure that each country has constant access to sufficient energy. Social issues include access to affordable and reliable energy for all people, workers' rights, and land rights. === Environmental impacts === The current energy system contributes to many environmental problems, including climate change, air pollution, biodiversity loss, the release of toxins into the environment, and water scarcity. As of 2019, 85% of the world's energy needs are met by burning fossil fuels. Energy production and consumption are responsible for 76% of annual human-caused greenhouse gas emissions as of 2018. The 2015 international Paris Agreement on climate change aims to limit global warming to well below 2 °C (3.6 °F) and preferably to 1.5 °C (2.7 °F); achieving this goal will require that emissions be reduced as soon as possible and reach net-zero by mid-century. The burning of fossil fuels and biomass is a major source of air pollution, which causes an estimated 7 million deaths each year, with the greatest attributable disease burden seen in low and middle-income countries. Fossil-fuel burning in power plants, vehicles, and factories is the main source of emissions that combine with oxygen in the atmosphere to cause acid rain. Air pollution is the second-leading cause of death from non-infectious disease. An estimated 99% of the world's population lives with levels of air pollution that exceed the World Health Organization recommended limits. Cooking with polluting fuels such as wood, animal dung, coal, or kerosene is responsible for nearly all indoor air pollution, which causes an estimated 1.6 to 3.8 million deaths annually, and also contributes significantly to outdoor air pollution. Health effects are concentrated among women, who are likely to be responsible for cooking, and young children. Environmental impacts extend beyond the by-products of combustion. Oil spills at sea harm marine life and may cause fires which release toxic emissions. Around 10% of global water use goes to energy production, mainly for cooling in thermal energy plants. In dry regions, this contributes to water scarcity. Bioenergy production, coal mining and processing, and oil extraction also require large amounts of water. Excessive harvesting of wood and other combustible material for burning can cause serious local environmental damage, including desertification. === Sustainable development goals === Meeting existing and future energy demands in a sustainable way is a critical challenge for the global goal of limiting climate change while maintaining economic growth and enabling living standards to rise. Reliable and affordable energy, particularly electricity, is essential for health care, education, and economic development. As of 2020, 790 million people in developing countries do not have access to electricity, and around 2.6 billion rely on burning polluting fuels for cooking. Improving energy access in the least-developed countries and making energy cleaner are key to achieving most of the United Nations 2030 Sustainable Development Goals, which cover issues ranging from climate action to gender equality. Sustainable Development Goal 7 calls for "access to affordable, reliable, sustainable and modern energy for all", including universal access to electricity and to clean cooking facilities by 2030. == Energy conservation == Energy efficiency—using less energy to deliver the same goods or services, or delivering comparable services with less goods—is a cornerstone of many sustainable energy strategies. The International Energy Agency (IEA) has estimated that increasing energy efficiency could achieve 40% of greenhouse gas emission reductions needed to fulfil the Paris Agreement's goals. Energy can be conserved by increasing the technical efficiency of appliances, vehicles, industrial processes, and buildings. Another approach is to use fewer materials whose production requires a lot of energy, for example through better building design and recycling. Behavioural changes such as using videoconferencing rather than business flights, or making urban trips by cycling, walking or public transport rather than by car, are another way to conserve energy. Government policies to improve efficiency can include building codes, performance standards, carbon pricing, and the development of energy-efficient infrastructure to encourage changes in transport modes. The energy intensity of the global economy (the amount of energy consumed per unit of gross domestic product (GDP)) is a rough indicator of the energy efficiency of economic production. In 2010, global energy intensity was 5.6 megajoules (1.6 kWh) per US dollar of GDP. United Nations goals call for energy intensity to decrease by 2.6% each year between 2010 and 2030. In recent years this target has not been met. For instance, between 2017 and 2018, energy intensity decreased by only 1.1%. Efficiency improvements often lead to a rebound effect in which consumers use the money they save to buy more energy-intensive goods and services. For example, recent technical efficiency improvements in transport and buildings have been largely offset by trends in consumer behaviour, such as selecting larger vehicles and homes. == Sustainable energy sources == === Renewable energy sources === Renewable energy sources are essential to sustainable energy, as they generally strengthen energy security and emit far fewer greenhouse gases than fossil fuels. Renewable energy projects sometimes raise significant sustainability concerns, such as risks to biodiversity when areas of high ecological value are converted to bioenergy production or wind or solar farms. Hydropower is the largest source of renewable electricity while solar and wind energy are growing rapidly. Photovoltaic solar and onshore wind are the cheapest forms of new power generation capacity in most countries. For more than half of the 770 million people who currently lack access to electricity, decentralised renewable energy such as solar-powered mini-grids is likely the cheapest method of providing it by 2030. United Nations targets for 2030 include substantially increasing the proportion of renewable energy in the world's energy supply. According to the International Energy Agency, renewable energy sources like wind and solar power are now a commonplace source of electricity, making up 70% of all new investments made in the world's power generation. The Agency expects renewables to become the primary energy source for electricity generation globally in the next three years, overtaking coal. ==== Solar ==== The Sun is Earth's primary source of energy, a clean and abundantly available resource in many regions. In 2019, solar power provided around 3% of global electricity, mostly through solar panels based on photovoltaic cells (PV). Solar PV is expected to be the electricity source with the largest installed capacity worldwide by 2027. The panels are mounted on top of buildings or installed in utility-scale solar parks. Costs of solar photovoltaic cells have dropped rapidly, driving strong growth in worldwide capacity. The cost of electricity from new solar farms is competitive with, or in many places, cheaper than electricity from existing coal plants. Various projections of future energy use identify solar PV as one of the main sources of energy generation in a sustainable mix. Most components of solar panels can be easily recycled, but this is not always done in the absence of regulation. Panels typically contain heavy metals, so they pose environmental risks if put in landfills. It takes fewer than two years for a solar panel to produce as much energy as was used for its production. Less energy is needed if materials are recycled rather than mined. In concentrated solar power, solar rays are concentrated by a field of mirrors, heating a fluid. Electricity is produced from the resulting steam with a heat engine. Concentrated solar power can support dispatchable power generation, as some of the heat is typically stored to enable electricity to be generated when needed. In addition to electricity production, solar energy is used more directly; solar thermal heating systems are used for hot water production, heating buildings, drying, and desalination. ==== Wind power ==== Wind has been an important driver of development over millennia, providing mechanical energy for industrial processes, water pumps, and sailing ships. Modern wind turbines are used to generate electricity and provided approximately 6% of global electricity in 2019. Electricity from onshore wind farms is often cheaper than existing coal plants and competitive with natural gas and nuclear. Wind turbines can also be placed offshore, where winds are steadier and stronger than on land but construction and maintenance costs are higher. Onshore wind farms, often built in wild or rural areas, have a visual impact on the landscape. While collisions with wind turbines kill both bats and to a lesser extent birds, these impacts are lower than from other infrastructure such as windows and transmission lines. The noise and flickering light created by the turbines can cause annoyance and constrain construction near densely populated areas. Wind power, in contrast to nuclear and fossil fuel plants, does not consume water. Little energy is needed for wind turbine construction compared to the energy produced by the wind power plant itself. Turbine blades are not fully recyclable, and research into methods of manufacturing easier-to-recycle blades is ongoing. ==== Hydropower ==== Hydroelectric plants convert the energy of moving water into electricity. In 2020, hydropower supplied 17% of the world's electricity, down from a high of nearly 20% in the mid-to-late 20th century. In conventional hydropower, a reservoir is created behind a dam. Conventional hydropower plants provide a highly flexible, dispatchable electricity supply. They can be combined with wind and solar power to meet peaks in demand and to compensate when wind and sun are less available. Compared to reservoir-based facilities, run-of-the-river hydroelectricity generally has less environmental impact. However, its ability to generate power depends on river flow, which can vary with daily and seasonal weather. Reservoirs provide water quantity controls that are used for flood control and flexible electricity output while also providing security during drought for drinking water supply and irrigation. Hydropower ranks among the energy sources with the lowest levels of greenhouse gas emissions per unit of energy produced, but levels of emissions vary enormously between projects. The highest emissions tend to occur with large dams in tropical regions. These emissions are produced when the biological matter that becomes submerged in the reservoir's flooding decomposes and releases carbon dioxide and methane. Deforestation and climate change can reduce energy generation from hydroelectric dams. Depending on location, large dams can displace residents and cause significant local environmental damage; potential dam failure could place the surrounding population at risk. ==== Geothermal ==== Geothermal energy is produced by tapping into deep underground heat and harnessing it to generate electricity or to heat water and buildings. The use of geothermal energy is concentrated in regions where heat extraction is economical: a combination is needed of high temperatures, heat flow, and permeability (the ability of the rock to allow fluids to pass through). Power is produced from the steam created in underground reservoirs. Geothermal energy provided less than 1% of global energy consumption in 2020. Geothermal energy is a renewable resource because thermal energy is constantly replenished from neighbouring hotter regions and the radioactive decay of naturally occurring isotopes. On average, the greenhouse gas emissions of geothermal-based electricity are less than 5% that of coal-based electricity. Geothermal energy carries a risk of inducing earthquakes, needs effective protection to avoid water pollution, and releases toxic emissions which can be captured. ==== Bioenergy ==== Biomass is renewable organic material that comes from plants and animals. It can either be burned to produce heat and electricity or be converted into biofuels such as biodiesel and ethanol, which can be used to power vehicles. The climate impact of bioenergy varies considerably depending on where biomass feedstocks come from and how they are grown. For example, burning wood for energy releases carbon dioxide; those emissions can be significantly offset if the trees that were harvested are replaced by new trees in a well-managed forest, as the new trees will absorb carbon dioxide from the air as they grow. However, the establishment and cultivation of bioenergy crops can displace natural ecosystems, degrade soils, and consume water resources and synthetic fertilisers. Approximately one-third of all wood used for traditional heating and cooking in tropical areas is harvested unsustainably. Bioenergy feedstocks typically require significant amounts of energy to harvest, dry, and transport; the energy usage for these processes may emit greenhouse gases. In some cases, the impacts of land-use change, cultivation, and processing can result in higher overall carbon emissions for bioenergy compared to using fossil fuels. Use of farmland for growing biomass can result in less land being available for growing food. In the United States, around 10% of motor gasoline has been replaced by corn-based ethanol, which requires a significant proportion of the harvest. In Malaysia and Indonesia, clearing forests to produce palm oil for biodiesel has led to serious social and environmental effects, as these forests are critical carbon sinks and habitats for diverse species. Since photosynthesis captures only a small fraction of the energy in sunlight, producing a given amount of bioenergy requires a large amount of land compared to other renewable energy sources. Second-generation biofuels which are produced from non-food plants or waste reduce competition with food production, but may have other negative effects including trade-offs with conservation areas and local air pollution. Relatively sustainable sources of biomass include algae, waste, and crops grown on soil unsuitable for food production. Carbon capture and storage technology can be used to capture emissions from bioenergy power plants. This process is known as bioenergy with carbon capture and storage (BECCS) and can result in net carbon dioxide removal from the atmosphere. However, BECCS can also result in net positive emissions depending on how the biomass material is grown, harvested, and transported. Deployment of BECCS at scales described in some climate change mitigation pathways would require converting large amounts of cropland. ==== Marine energy ==== Marine energy has the smallest share of the energy market. It includes OTEC, tidal power, which is approaching maturity, and wave power, which is earlier in its development. Two tidal barrage systems in France and in South Korea make up 90% of global production. While single marine energy devices pose little risk to the environment, the impacts of larger devices are less well known. === Non-renewable energy sources === ==== Fossil fuel switching and mitigation ==== Switching from coal to natural gas has advantages in terms of sustainability. For a given unit of energy produced, the life-cycle greenhouse-gas emissions of natural gas are around 40 times the emissions of wind or nuclear energy but are much less than coal. Burning natural gas produces around half the emissions of coal when used to generate electricity and around two-thirds the emissions of coal when used to produce heat. Natural gas combustion also produces less air pollution than coal. However, natural gas is a potent greenhouse gas in itself, and leaks during extraction and transportation can negate the advantages of switching away from coal. The technology to curb methane leaks is widely available but it is not always used. Switching from coal to natural gas reduces emissions in the short term and thus contributes to climate change mitigation. However, in the long term it does not provide a path to net-zero emissions. Developing natural gas infrastructure risks carbon lock-in and stranded assets, where new fossil infrastructure either commits to decades of carbon emissions, or has to be written off before it makes a profit. The greenhouse gas emissions of fossil fuel and biomass power plants can be significantly reduced through carbon capture and storage (CCS). Most studies use a working assumption that CCS can capture 85–90% of the carbon dioxide (CO2) emissions from a power plant. Even if 90% of emitted CO2 is captured from a coal-fired power plant, its uncaptured emissions are still many times greater than the emissions of nuclear, solar or wind energy per unit of electricity produced. Since coal plants using CCS are less efficient, they require more coal and thus increase the pollution associated with mining and transporting coal. CCS is one of the most expensive ways of reducing emissions in the energy sector. Deployment of this technology is very limited. As of 2024, CCS is used in only 5 power plants and in 39 other facilities. ==== Nuclear power ==== Nuclear power has been used since the 1950s as a low-carbon source of baseload electricity. Nuclear power plants in over 30 countries generate about 10% of global electricity. As of 2019, nuclear generated over a quarter of all low-carbon energy, making it the second largest source after hydropower. Nuclear power's lifecycle greenhouse gas emissions—including the mining and processing of uranium—are similar to the emissions from renewable energy sources. Nuclear power uses little land per unit of energy produced, compared to the major renewables. Additionally, Nuclear power does not create local air pollution. Although the uranium ore used to fuel nuclear fission plants is a non-renewable resource, enough exists to provide a supply for hundreds to thousands of years. However, uranium resources that can be accessed in an economically feasible manner, at the present state, are limited and uranium production could hardly keep up during the expansion phase. Climate change mitigation pathways consistent with ambitious goals typically see an increase in power supply from nuclear. There is controversy over whether nuclear power is sustainable, in part due to concerns around nuclear waste, nuclear weapon proliferation, and accidents. Radioactive nuclear waste must be managed for thousands of years. For each unit of energy produced, nuclear energy has caused far fewer accidental and pollution-related deaths than fossil fuels, and the historic fatality rate of nuclear is comparable to renewable sources. Public opposition to nuclear energy often makes nuclear plants politically difficult to implement. Reducing the time and the cost of building new nuclear plants have been goals for decades but costs remain high and timescales long. Various new forms of nuclear energy are in development, hoping to address the drawbacks of conventional plants. Fast breeder reactors are capable of recycling nuclear waste and therefore can significantly reduce the amount of waste that requires geological disposal, but have not yet been deployed on a large-scale commercial basis. Nuclear power based on thorium (rather than uranium) may be able to provide higher energy security for countries that do not have a large supply of uranium. Small modular reactors may have several advantages over current large reactors: It should be possible to build them faster and their modularization would allow for cost reductions via learning-by-doing. They are also considered safer to use than traditional power plants. Several countries are attempting to develop nuclear fusion reactors, which would generate small amounts of waste and no risk of explosions. Although fusion power has taken steps forward in the lab, the multi-decade timescale needed to bring it to commercialization and then scale means it will not contribute to a 2050 net zero goal for climate change mitigation. == Energy system transformation == === Decarbonisation of the global energy system === The emissions reductions necessary to keep global warming below 2 °C will require a system-wide transformation of the way energy is produced, distributed, stored, and consumed. For a society to replace one form of energy with another, multiple technologies and behaviours in the energy system must change. For example, transitioning from oil to solar power as the energy source for cars requires the generation of solar electricity, modifications to the electrical grid to accommodate fluctuations in solar panel output or the introduction of variable battery chargers and higher overall demand, adoption of electric cars, and networks of electric vehicle charging facilities and repair shops. Many climate change mitigation pathways envision three main aspects of a low-carbon energy system: The use of low-emission energy sources to produce electricity Electrification – that is increased use of electricity instead of directly burning fossil fuels Accelerated adoption of energy efficiency measures Some energy-intensive technologies and processes are difficult to electrify, including aviation, shipping, and steelmaking. There are several options for reducing the emissions from these sectors: biofuels and synthetic carbon-neutral fuels can power many vehicles that are designed to burn fossil fuels, however biofuels cannot be sustainably produced in the quantities needed and synthetic fuels are currently very expensive. For some applications, the most prominent alternative to electrification is to develop a system based on sustainably-produced hydrogen fuel. Full decarbonisation of the global energy system is expected to take several decades and can mostly be achieved with existing technologies. In the IEA's proposal for achieving net zero emissions by 2050, about 35% of the reduction in emissions depends on technologies that are still in development as of 2023. Technologies that are relatively immature include batteries and processes to create carbon-neutral fuels. Developing new technologies requires research and development, demonstration, and cost reductions via deployment. The transition to a zero-carbon energy system will bring strong co-benefits for human health: The World Health Organization estimates that efforts to limit global warming to 1.5 °C could save millions of lives each year from reductions to air pollution alone. With good planning and management, pathways exist to provide universal access to electricity and clean cooking by 2030 in ways that are consistent with climate goals. Historically, several countries have made rapid economic gains through coal usage. However, there remains a window of opportunity for many poor countries and regions to "leapfrog" fossil fuel dependency by developing their energy systems based on renewables, given adequate international investment and knowledge transfer. === Integrating variable energy sources === To deliver reliable electricity from variable renewable energy sources such as wind and solar, electrical power systems require flexibility. Most electrical grids were constructed for non-intermittent energy sources such as coal-fired power plants. As larger amounts of solar and wind energy are integrated into the grid, changes have to be made to the energy system to ensure that the supply of electricity is matched to demand. In 2019, these sources generated 8.5% of worldwide electricity, a share that has grown rapidly. There are various ways to make the electricity system more flexible. In many places, wind and solar generation are complementary on a daily and a seasonal scale: there is more wind during the night and in winter when solar energy production is low. Linking different geographical regions through long-distance transmission lines allows for further cancelling out of variability. Energy demand can be shifted in time through energy demand management and the use of smart grids, matching the times when variable energy production is highest. With grid energy storage, energy produced in excess can be released when needed. Further flexibility could be provided from sector coupling, that is coupling the electricity sector to the heat and mobility sector via power-to-heat-systems and electric vehicles. Building overcapacity for wind and solar generation can help ensure that enough electricity is produced even during poor weather. In optimal weather, energy generation may have to be curtailed if excess electricity cannot be used or stored. The final demand-supply mismatch may be covered by using dispatchable energy sources such as hydropower, bioenergy, or natural gas. ==== Energy storage ==== Energy storage helps overcome barriers to intermittent renewable energy and is an important aspect of a sustainable energy system. The most commonly used and available storage method is pumped-storage hydroelectricity, which requires locations with large differences in height and access to water. Batteries, especially lithium-ion batteries, are also deployed widely. Batteries typically store electricity for short periods; research is ongoing into technology with sufficient capacity to last through seasons. Costs of utility-scale batteries in the US have fallen by around 70% since 2015, however the cost and low energy density of batteries makes them impractical for the very large energy storage needed to balance inter-seasonal variations in energy production. Pumped hydro storage and power-to-gas (converting electricity to gas and back) with capacity for multi-month usage has been implemented in some locations. === Electrification === Compared to the rest of the energy system, emissions can be reduced much faster in the electricity sector. As of 2019, 37% of global electricity is produced from low-carbon sources (renewables and nuclear energy). Fossil fuels, primarily coal, produce the rest of the electricity supply. One of the easiest and fastest ways to reduce greenhouse gas emissions is to phase out coal-fired power plants and increase renewable electricity generation. Climate change mitigation pathways envision extensive electrification—the use of electricity as a substitute for the direct burning of fossil fuels for heating buildings and for transport. Ambitious climate policy would see a doubling of energy share consumed as electricity by 2050, from 20% in 2020. One of the challenges in providing universal access to electricity is distributing power to rural areas. Off-grid and mini-grid systems based on renewable energy, such as small solar PV installations that generate and store enough electricity for a village, are important solutions. Wider access to reliable electricity would lead to less use of kerosene lighting and diesel generators, which are currently common in the developing world. Infrastructure for generating and storing renewable electricity requires minerals and metals, such as cobalt and lithium for batteries and copper for solar panels. Recycling can meet some of this demand if product lifecycles are well-designed, however achieving net zero emissions would still require major increases in mining for 17 types of metals and minerals. A small group of countries or companies sometimes dominate the markets for these commodities, raising geopolitical concerns. Most of the world's cobalt, for instance, is mined in the Democratic Republic of the Congo, a politically unstable region where mining is often associated with human rights risks. More diverse geographical sourcing may ensure a more flexible and less brittle supply chain. === Hydrogen === Hydrogen gas is widely discussed as a fuel with potential to reduce greenhouse gas emissions. This requires hydrogen to be produced cleanly, in quantities to supply in sectors and applications where cheaper and more energy efficient mitigation alternatives are limited. These applications include heavy industry and long-distance transport. Hydrogen can be deployed as an energy source in fuel cells to produce electricity, or via combustion to generate heat. When hydrogen is consumed in fuel cells, the only emission at the point of use is water vapour. Combustion of hydrogen can lead to the thermal formation of harmful nitrogen oxides. The overall lifecycle emissions of hydrogen depend on how it is produced. Nearly all of the world's current supply of hydrogen is created from fossil fuels. The main method of producing hydrogen is steam methane reforming, in which hydrogen is produced from a chemical reaction between steam and methane, the main component of natural gas. Producing one tonne of hydrogen through this process emits 6.6–9.3 tonnes of carbon dioxide. While carbon capture and storage (CCS) could remove a large fraction of these emissions, the overall carbon footprint of hydrogen from natural gas is difficult to assess as of 2021, in part because of emissions (including vented and fugitive methane) created in the production of the natural gas itself. Electricity can be used to split water molecules, producing sustainable hydrogen provided the electricity was generated sustainably. However, this electrolysis process is currently more expensive than creating hydrogen from methane without CCS and the efficiency of energy conversion is inherently low. Hydrogen can be produced when there is a surplus of variable renewable electricity, then stored and used to generate heat or to re-generate electricity. It can be further transformed into liquid fuels such as green ammonia and green methanol. Innovation in hydrogen electrolysers could make large-scale production of hydrogen from electricity more cost-competitive. Hydrogen fuel can produce the intense heat required for industrial production of steel, cement, glass, and chemicals, thus contributing to the decarbonisation of industry alongside other technologies, such as electric arc furnaces for steelmaking. For steelmaking, hydrogen can function as a clean fuel and simultaneously as a low-carbon catalyst replacing coal-derived coke. Hydrogen used to decarbonise transportation is likely to find its largest applications in shipping, aviation and to a lesser extent heavy goods vehicles. For light duty vehicles including passenger cars, hydrogen is far behind other alternative fuel vehicles, especially compared with the rate of adoption of battery electric vehicles, and may not play a significant role in future. Disadvantages of hydrogen as a fuel include high costs of storage and distribution due to hydrogen's explosivity, its large volume compared to other fuels, and its tendency to make pipes brittle. === Energy usage technologies === ==== Transport ==== Transport accounts for 14% of global greenhouse gas emissions, but there are multiple ways to make transport more sustainable. Public transport typically emits fewer greenhouse gases per passenger than personal vehicles, since trains and buses can carry many more passengers at once. Short-distance flights can be replaced by high-speed rail, which is more efficient, especially when electrified. Promoting non-motorised transport such as walking and cycling, particularly in cities, can make transport cleaner and healthier. The energy efficiency of cars has increased over time, but shifting to electric vehicles is an important further step towards decarbonising transport and reducing air pollution. A large proportion of traffic-related air pollution consists of particulate matter from road dust and the wearing-down of tyres and brake pads. Substantially reducing pollution from these non-tailpipe sources cannot be achieved by electrification; it requires measures such as making vehicles lighter and driving them less. Light-duty cars in particular are a prime candidate for decarbonization using battery technology. 25% of the world's CO2 emissions still originate from the transportation sector. Long-distance freight transport and aviation are difficult sectors to electrify with current technologies, mostly because of the weight of batteries needed for long-distance travel, battery recharging times, and limited battery lifespans. Where available, freight transport by ship and rail is generally more sustainable than by air and by road. Hydrogen vehicles may be an option for larger vehicles such as lorries. Many of the techniques needed to lower emissions from shipping and aviation are still early in their development, with ammonia (produced from hydrogen) a promising candidate for shipping fuel. Aviation biofuel may be one of the better uses of bioenergy if emissions are captured and stored during manufacture of the fuel. ==== Buildings ==== Over one-third of energy use is in buildings and their construction. To heat buildings, alternatives to burning fossil fuels and biomass include electrification through heat pumps or electric heaters, geothermal energy, central solar heating, reuse of waste heat, and seasonal thermal energy storage. Heat pumps provide both heat and air conditioning through a single appliance. The IEA estimates heat pumps could provide over 90% of space and water heating requirements globally. A highly efficient way to heat buildings is through district heating, in which heat is generated in a centralised location and then distributed to multiple buildings through insulated pipes. Traditionally, most district heating systems have used fossil fuels, but modern and cold district heating systems are designed to use high shares of renewable energy.Cooling of buildings can be made more efficient through passive building design, planning that minimises the urban heat island effect, and district cooling systems that cool multiple buildings with piped cold water. Air conditioning requires large amounts of electricity and is not always affordable for poorer households. Some air conditioning units still use refrigerants that are greenhouse gases, as some countries have not ratified the Kigali Amendment to only use climate-friendly refrigerants. ==== Cooking ==== In developing countries where populations suffer from energy poverty, polluting fuels such as wood or animal dung are often used for cooking. Cooking with these fuels is generally unsustainable, because they release harmful smoke and because harvesting wood can lead to forest degradation. The universal adoption of clean cooking facilities, which are already ubiquitous in rich countries, would dramatically improve health and have minimal negative effects on climate. Clean cooking facilities, e.g. cooking facilities that produce less indoor soot, typically use natural gas, liquefied petroleum gas (both of which consume oxygen and produce carbon-dioxide) or electricity as the energy source; biogas systems are a promising alternative in some contexts. Improved cookstoves that burn biomass more efficiently than traditional stoves are an interim solution where transitioning to clean cooking systems is difficult. ==== Industry ==== Over one-third of energy use is by industry. Most of that energy is deployed in thermal processes: generating heat, drying, and refrigeration. The share of renewable energy in industry was 14.5% in 2017—mostly low-temperature heat supplied by bioenergy and electricity. The most energy-intensive activities in industry have the lowest shares of renewable energy, as they face limitations in generating heat at temperatures over 200 °C (390 °F). For some industrial processes, commercialisation of technologies that have not yet been built or operated at full scale will be needed to eliminate greenhouse gas emissions. Steelmaking, for instance, is difficult to electrify because it traditionally uses coke, which is derived from coal, both to create very high-temperature heat and as an ingredient in the steel itself. The production of plastic, cement, and fertilisers also requires significant amounts of energy, with limited possibilities available to decarbonise. A switch to a circular economy would make industry more sustainable as it involves recycling more and thereby using less energy compared to investing energy to mine and refine new raw materials. == Government policies == Well-designed government policies that promote energy system transformation can lower greenhouse gas emissions and improve air quality simultaneously, and in many cases can also increase energy security and lessen the financial burden of using energy. === Regulations === Environmental regulations have been used since the 1970s to promote more sustainable use of energy. Some governments have committed to dates for phasing out coal-fired power plants and ending new fossil fuel exploration. Governments can require that new cars produce zero emissions, or new buildings are heated by electricity instead of gas. Renewable portfolio standards in several countries require utilities to increase the percentage of electricity they generate from renewable sources. Governments can accelerate energy system transformation by leading the development of infrastructure such as long-distance electrical transmission lines, smart grids, and hydrogen pipelines. In transport, appropriate infrastructure and incentives can make travel more efficient and less car-dependent. Urban planning that discourages sprawl can reduce energy use in local transport and buildings while enhancing quality of life. Government-funded research, procurement, and incentive policies have historically been critical to the development and maturation of clean energy technologies, such as solar and lithium batteries. In the IEA's scenario for a net zero-emission energy system by 2050, public funding is rapidly mobilised to bring a range of newer technologies to the demonstration phase and to encourage deployment. === Carbon pricing === Carbon pricing (such as a tax on CO2 emissions) gives industries and consumers an incentive to reduce emissions while letting them choose how to do so. For example, they can shift to low-emission energy sources, improve energy efficiency, or reduce their use of energy-intensive products and services. Carbon pricing has encountered strong political pushback in some jurisdictions, whereas energy-specific policies tend to be politically safer. Most studies indicate that to limit global warming to 1.5 °C, carbon pricing would need to be complemented by stringent energy-specific policies. As of 2019, the price of carbon in most regions is too low to achieve the goals of the Paris Agreement. Carbon taxes provide a source of revenue that can be used to lower other taxes or help lower-income households afford higher energy costs. Some governments, such as the EU and the UK, are exploring the use of carbon border adjustments. These place tariffs on imports from countries with less stringent climate policies, to ensure that industries subject to internal carbon prices remain competitive. === Pace === The scale and pace of policy reforms that have been initiated as of 2020 are far less than needed to fulfil the climate goals of the Paris Agreement. In addition to domestic policies, greater international cooperation is required to accelerate innovation and to assist poorer countries in establishing a sustainable path to full energy access. Countries may support renewables to create jobs. The International Labour Organization estimates that efforts to limit global warming to 2 °C would result in net job creation in most sectors of the economy. It predicts that 24 million new jobs would be created by 2030 in areas such as renewable electricity generation, improving energy-efficiency in buildings, and the transition to electric vehicles. Six million jobs would be lost, in sectors such as mining and fossil fuels. Governments can make the transition to sustainable energy more politically and socially feasible by ensuring a just transition for workers and regions that depend on the fossil fuel industry, to ensure they have alternative economic opportunities. == Finance == Raising enough money for innovation and investment is a prerequisite for the energy transition. The IPCC estimates that to limit global warming to 1.5 °C, US$2.4 trillion would need to be invested in the energy system each year between 2016 and 2035. Most studies project that these costs, equivalent to 2.5% of world GDP, would be small compared to the economic and health benefits. Average annual investment in low-carbon energy technologies and energy efficiency would need to be six times more by 2050 compared to 2015. Underfunding is particularly acute in the least developed countries, which are not attractive to the private sector. The United Nations Framework Convention on Climate Change estimates that climate financing totalled $681 billion in 2016. Most of this is private-sector investment in renewable energy deployment, public-sector investment in sustainable transport, and private-sector investment in energy efficiency. The Paris Agreement includes a pledge of an extra $100 billion per year from developed countries to poor countries, to do climate change mitigation and adaptation. This goal has not been met and measurement of progress has been hampered by unclear accounting rules. If energy-intensive businesses like chemicals, fertilizers, ceramics, steel, and non-ferrous metals invest significantly in R&D, its usage in industry might amount to between 5% and 20% of all energy used. Fossil fuel funding and subsidies are a significant barrier to the energy transition. Direct global fossil fuel subsidies were $319 billion in 2017. This rises to $5.2 trillion when indirect costs are priced in, like the effects of air pollution. Ending these could lead to a 28% reduction in global carbon emissions and a 46% reduction in air pollution deaths. Funding for clean energy has been largely unaffected by the COVID-19 pandemic, and pandemic-related economic stimulus packages offer possibilities for a green recovery. == References == === Sources === == External links ==
Wikipedia/Sustainable_energy
The gravitational binding energy of a system is the minimum energy which must be added to it in order for the system to cease being in a gravitationally bound state. A gravitationally bound system has a lower (i.e., more negative) gravitational potential energy than the sum of the energies of its parts when these are completely separated—this is what keeps the system aggregated in accordance with the minimum total potential energy principle. The gravitational binding energy can be conceptually different within the theories of Newtonian gravity and Albert Einstein's theory of gravity called General Relativity. In Newtonian gravity, the binding energy can be considered to be the linear sum of the interactions between all pairs of microscopic components of the system, while in General Relativity, this is only approximately true if the gravitational fields are all weak. When stronger fields are present within a system, the binding energy is a nonlinear property of the entire system, and it cannot be conceptually attributed among the elements of the system. In this case the binding energy can be considered to be the (negative) difference between the ADM mass of the system, as it is manifest in its gravitational interaction with other distant systems, and the sum of the energies of all the atoms and other elementary particles of the system if disassembled. For a spherical body of uniform density, the gravitational binding energy U is given in Newtonian gravity by the formula U = − 3 G M 2 5 R {\displaystyle U=-{\frac {3GM^{2}}{5R}}} where G is the gravitational constant, M is the mass of the sphere, and R is its radius. Assuming that the Earth is a sphere of uniform density (which it is not, but is close enough to get an order-of-magnitude estimate) with M = 5.97×1024 kg and r = 6.37×106 m, then U = 2.24×1032 J. This is roughly equal to one week of the Sun's total energy output. It is 37.5 MJ/kg, 60% of the absolute value of the potential energy per kilogram at the surface. The actual depth-dependence of density, inferred from seismic travel times (see Adams–Williamson equation), is given in the Preliminary Reference Earth Model (PREM). Using this, the real gravitational binding energy of Earth can be calculated numerically as U = 2.49×1032 J. According to the virial theorem, the gravitational binding energy of a star is about two times its internal thermal energy in order for hydrostatic equilibrium to be maintained. As the gas in a star becomes more relativistic, the gravitational binding energy required for hydrostatic equilibrium approaches zero and the star becomes unstable (highly sensitive to perturbations), which may lead to a supernova in the case of a high-mass star due to strong radiation pressure or to a black hole in the case of a neutron star. == Derivation within Newtonian gravity for a uniform sphere == The gravitational binding energy of a sphere with radius R {\displaystyle R} is found by imagining that it is pulled apart by successively moving spherical shells to infinity, the outermost first, and finding the total energy needed for that. Assuming a constant density ρ {\displaystyle \rho } , the masses of a shell and the sphere inside it are: m s h e l l = 4 π r 2 ρ d r {\displaystyle m_{\mathrm {shell} }=4\pi r^{2}\rho \,dr} and m i n t e r i o r = 4 3 π r 3 ρ {\displaystyle m_{\mathrm {interior} }={\frac {4}{3}}\pi r^{3}\rho } The required energy for a shell is the negative of the gravitational potential energy: d U = − G m s h e l l m i n t e r i o r r {\displaystyle dU=-G{\frac {m_{\mathrm {shell} }m_{\mathrm {interior} }}{r}}} Integrating over all shells yields: U = − G ∫ 0 R ( 4 π r 2 ρ ) ( 4 3 π r 3 ρ ) r d r = − G 16 3 π 2 ρ 2 ∫ 0 R r 4 d r = − G 16 15 π 2 ρ 2 R 5 {\displaystyle U=-G\int _{0}^{R}{\frac {\left(4\pi r^{2}\rho \right)\left({\tfrac {4}{3}}\pi r^{3}\rho \right)}{r}}dr=-G{\frac {16}{3}}\pi ^{2}\rho ^{2}\int _{0}^{R}{r^{4}}dr=-G{\frac {16}{15}}{\pi }^{2}{\rho }^{2}R^{5}} Since ρ {\displaystyle \rho } is simply equal to the mass of the whole divided by its volume for objects with uniform density, therefore ρ = M 4 3 π R 3 {\displaystyle \rho ={\frac {M}{{\frac {4}{3}}\pi R^{3}}}} And finally, plugging this into our result leads to U = − G 16 15 π 2 R 5 ( M 4 3 π R 3 ) 2 = − 3 G M 2 5 R {\displaystyle U=-G{\frac {16}{15}}\pi ^{2}R^{5}\left({\frac {M}{{\frac {4}{3}}\pi R^{3}}}\right)^{2}=-{\frac {3GM^{2}}{5R}}} == Negative mass component == Two bodies, placed at the distance R from each other and reciprocally not moving, exert a gravitational force on a third body slightly smaller when R is small. This can be seen as a negative mass component of the system, equal, for uniformly spherical solutions, to: M b i n d i n g = − 3 G M 2 5 R c 2 {\displaystyle M_{\mathrm {binding} }=-{\frac {3GM^{2}}{5Rc^{2}}}} For example, the fact that Earth is a gravitationally-bound sphere of its current size costs 2.49421×1015 kg of mass (roughly one fourth the mass of Phobos – see above for the same value in Joules), and if its atoms were sparse over an arbitrarily large volume the Earth would weigh its current mass plus 2.49421×1015 kg kilograms (and its gravitational pull over a third body would be accordingly stronger). It can be easily demonstrated that this negative component can never exceed the positive component of a system. A negative binding energy greater than the mass of the system itself would indeed require that the radius of the system be smaller than: R ≤ 3 G M 5 c 2 {\displaystyle R\leq {\frac {3GM}{5c^{2}}}} which is smaller than 3 10 {\textstyle {\frac {3}{10}}} its Schwarzschild radius: R ≤ 3 10 r s {\displaystyle R\leq {\frac {3}{10}}r_{\mathrm {s} }} and therefore never visible to an external observer. However this is only a Newtonian approximation and in relativistic conditions other factors must be taken into account as well. == Non-uniform spheres == Planets and stars have radial density gradients from their lower density surfaces to their much denser compressed cores. Degenerate matter objects (white dwarfs; neutron star pulsars) have radial density gradients plus relativistic corrections. Neutron star relativistic equations of state include a graph of radius vs. mass for various models. The most likely radii for a given neutron star mass are bracketed by models AP4 (smallest radius) and MS2 (largest radius). BE is the ratio of gravitational binding energy mass equivalent to observed neutron star gravitational mass of M with radius R, B E = 0.60 β 1 − β 2 {\displaystyle BE={\frac {0.60\,\beta }{1-{\frac {\beta }{2}}}}} β = G M R c 2 . {\displaystyle \beta ={\frac {GM}{Rc^{2}}}.} Given current values G = 6.6743 × 10 − 11 m 3 ⋅ k g − 1 ⋅ s − 2 {\displaystyle G=6.6743\times 10^{-11}\,\mathrm {m^{3}\cdot kg^{-1}\cdot s^{-2}} } c 2 = 8.98755 × 10 16 m 2 ⋅ s − 2 {\displaystyle c^{2}=8.98755\times 10^{16}\,\mathrm {m^{2}\cdot s^{-2}} } M ⊙ = 1.98844 × 10 30 k g {\displaystyle M_{\odot }=1.98844\times 10^{30}\,\mathrm {kg} } and the star mass M expressed relative to the solar mass, M x = M M ⊙ , {\displaystyle M_{x}={\frac {M}{M_{\odot }}},} then the relativistic fractional binding energy of a neutron star is B E = 885.975 M x R − 738.313 M x {\displaystyle BE={\frac {885.975\,M_{x}}{R-738.313\,M_{x}}}} == See also == Stress–energy tensor Stress–energy–momentum pseudotensor Nordtvedt effect == References ==
Wikipedia/Gravitational_binding_energy
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the electrostatic force or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb. Coulomb's law was essential to the development of the theory of electromagnetism and maybe even its starting point, as it allowed meaningful discussions of the amount of electric charge in a particle. The law states that the magnitude, or absolute value, of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. Coulomb discovered that bodies with like electrical charges repel: It follows therefore from these three tests, that the repulsive force that the two balls – [that were] electrified with the same kind of electricity – exert on each other, follows the inverse proportion of the square of the distance. Coulomb also showed that oppositely charged bodies attract according to an inverse-square law: | F | = k e | q 1 | | q 2 | r 2 {\displaystyle |F|=k_{\text{e}}{\frac {|q_{1}||q_{2}|}{r^{2}}}} Here, ke is a constant, q1 and q2 are the quantities of each charge, and the scalar r is the distance between the charges. The force is along the straight line joining the two charges. If the charges have the same sign, the electrostatic force between them makes them repel; if they have different signs, the force between them makes them attract. Being an inverse-square law, the law is similar to Isaac Newton's inverse-square law of universal gravitation, but gravitational forces always make things attract, while electrostatic forces make charges attract or repel. Also, gravitational forces are much weaker than electrostatic forces. Coulomb's law can be used to derive Gauss's law, and vice versa. In the case of a single point charge at rest, the two laws are equivalent, expressing the same physical law in different ways. The law has been tested extensively, and observations have upheld the law on the scale from 10−16 m to 108 m. == History == Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers and pieces of paper. Thales of Miletus made the first recorded description of static electricity around 600 BC, when he noticed that friction could make a piece of amber attract small objects. In 1600, English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber. He coined the Neo-Latin word electricus ("of amber" or "like amber", from ἤλεκτρον [elektron], the Greek word for "amber") to refer to the property of attracting small objects after being rubbed. This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646. Early investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Franz Aepinus who supposed the inverse-square law in 1758. Based on experiments with electrically charged spheres, Joseph Priestley of England was among the first to propose that electrical force followed an inverse-square law, similar to Newton's law of universal gravitation. However, he did not generalize or elaborate on this. In 1767, he conjectured that the force between charges varied as the inverse square of the distance. In 1769, Scottish physicist John Robison announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x−2.06. In the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England. In his notes, Cavendish wrote, "We may therefore conclude that the electric attraction and repulsion must be inversely as some power of the distance between that of the 2 + ⁠1/50⁠th and that of the 2 − ⁠1/50⁠th, and there is no reason to think that it differs at all from the inverse duplicate ratio". Finally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism. He used a torsion balance to study the repulsion and attraction forces of charged particles, and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law. == Mathematical form == Coulomb's law states that the electrostatic force F 1 {\textstyle \mathbf {F} _{1}} experienced by a charge, q 1 {\displaystyle q_{1}} at position r 1 {\displaystyle \mathbf {r} _{1}} , in the vicinity of another charge, q 2 {\displaystyle q_{2}} at position r 2 {\displaystyle \mathbf {r} _{2}} , in a vacuum is equal to F 1 = q 1 q 2 4 π ε 0 r ^ 12 | r 12 | 2 {\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{12} \over {|\mathbf {r} _{12}|}^{2}}} where r 12 = r 1 − r 2 {\textstyle \mathbf {r_{12}=r_{1}-r_{2}} } is the displacement vector between the charges, r ^ 12 {\textstyle {\hat {\mathbf {r} }}_{12}} a unit vector pointing from q 2 {\textstyle q_{2}} to q 1 {\textstyle q_{1}} , and ε 0 {\displaystyle \varepsilon _{0}} the electric constant. Here, r ^ 12 {\textstyle \mathbf {\hat {r}} _{12}} is used for the vector notation. The electrostatic force F 2 {\textstyle \mathbf {F} _{2}} experienced by q 2 {\displaystyle q_{2}} , according to Newton's third law, is F 2 = − F 1 {\textstyle \mathbf {F} _{2}=-\mathbf {F} _{1}} . If both charges have the same sign (like charges) then the product q 1 q 2 {\displaystyle q_{1}q_{2}} is positive and the direction of the force on q 1 {\displaystyle q_{1}} is given by r ^ 12 {\textstyle {\widehat {\mathbf {r} }}_{12}} ; the charges repel each other. If the charges have opposite signs then the product q 1 q 2 {\displaystyle q_{1}q_{2}} is negative and the direction of the force on q 1 {\displaystyle q_{1}} is − r ^ 12 {\textstyle -{\hat {\mathbf {r} }}_{12}} ; the charges attract each other. === System of discrete charges === The law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed. Force F {\textstyle \mathbf {F} } on a small charge q {\displaystyle q} at position r {\displaystyle \mathbf {r} } , due to a system of n {\textstyle n} discrete charges in vacuum is F ( r ) = q 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 , {\displaystyle \mathbf {F} (\mathbf {r} )={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}},} where q i {\displaystyle q_{i}} is the magnitude of the ith charge, r i {\textstyle \mathbf {r} _{i}} is the vector from its position to r {\displaystyle \mathbf {r} } and r ^ i {\textstyle {\hat {\mathbf {r} }}_{i}} is the unit vector in the direction of r i {\displaystyle \mathbf {r} _{i}} . === Continuous charge distribution === In this case, the principle of linear superposition is also used. For a continuous charge distribution, an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge d q {\displaystyle dq} . The distribution of charge is usually linear, surface or volumetric. For a linear charge distribution (a good approximation for charge in a wire) where λ ( r ′ ) {\displaystyle \lambda (\mathbf {r} ')} gives the charge per unit length at position r ′ {\displaystyle \mathbf {r} '} , and d ℓ ′ {\displaystyle d\ell '} is an infinitesimal element of length, d q ′ = λ ( r ′ ) d ℓ ′ . {\displaystyle dq'=\lambda (\mathbf {r'} )\,d\ell '.} For a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where σ ( r ′ ) {\displaystyle \sigma (\mathbf {r} ')} gives the charge per unit area at position r ′ {\displaystyle \mathbf {r} '} , and d A ′ {\displaystyle dA'} is an infinitesimal element of area, d q ′ = σ ( r ′ ) d A ′ . {\displaystyle dq'=\sigma (\mathbf {r'} )\,dA'.} For a volume charge distribution (such as charge within a bulk metal) where ρ ( r ′ ) {\displaystyle \rho (\mathbf {r} ')} gives the charge per unit volume at position r ′ {\displaystyle \mathbf {r} '} , and d V ′ {\displaystyle dV'} is an infinitesimal element of volume, d q ′ = ρ ( r ′ ) d V ′ . {\displaystyle dq'=\rho ({\boldsymbol {r'}})\,dV'.} The force on a small test charge q {\displaystyle q} at position r {\displaystyle {\boldsymbol {r}}} in vacuum is given by the integral over the distribution of charge F ( r ) = q 4 π ε 0 ∫ d q ′ r − r ′ | r − r ′ | 3 . {\displaystyle \mathbf {F} (\mathbf {r} )={\frac {q}{4\pi \varepsilon _{0}}}\int dq'{\frac {\mathbf {r} -\mathbf {r'} }{|\mathbf {r} -\mathbf {r'} |^{3}}}.} The "continuous charge" version of Coulomb's law is never supposed to be applied to locations for which | r − r ′ | = 0 {\displaystyle |\mathbf {r} -\mathbf {r'} |=0} because that location would directly overlap with the location of a charged particle (e.g. electron or proton) which is not a valid location to analyze the electric field or potential classically. Charge is always discrete in reality, and the "continuous charge" assumption is just an approximation that is not supposed to allow | r − r ′ | = 0 {\displaystyle |\mathbf {r} -\mathbf {r'} |=0} to be analyzed. == Coulomb constant == The constant of proportionality, 1 4 π ε 0 {\displaystyle {\frac {1}{4\pi \varepsilon _{0}}}} , in Coulomb's law: F 1 = q 1 q 2 4 π ε 0 r ^ 12 | r 12 | 2 {\displaystyle \mathbf {F} _{1}={\frac {q_{1}q_{2}}{4\pi \varepsilon _{0}}}{{\hat {\mathbf {r} }}_{12} \over {|\mathbf {r} _{12}|}^{2}}} is a consequence of historical choices for units.: 4–2  The constant ε 0 {\displaystyle \varepsilon _{0}} is the vacuum electric permittivity. Using the CODATA 2022 recommended value for ε 0 {\displaystyle \varepsilon _{0}} , the Coulomb constant is k e = 1 4 π ε 0 = 8.987 551 7862 ( 14 ) × 10 9 N ⋅ m 2 ⋅ C − 2 {\displaystyle k_{\text{e}}={\frac {1}{4\pi \varepsilon _{0}}}=8.987\ 551\ 7862(14)\times 10^{9}\ \mathrm {N{\cdot }m^{2}{\cdot }C^{-2}} } == Limitations == There are three conditions to be fulfilled for the validity of Coulomb's inverse square law: The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). The charges must not overlap (e.g. they must be distinct point charges). The charges must be stationary with respect to a nonaccelerating frame of reference. The last of these is known as the electrostatic approximation. When movement takes place, an extra factor is introduced, which alters the force produced on the two objects. This extra part of the force is called the magnetic force. For slow movement, the magnetic force is minimal and Coulomb's law can still be considered approximately correct. A more accurate approximation in this case is, however, the Weber force. When the charges are moving more quickly in relation to each other or accelerations occur, Maxwell's equations and Einstein's theory of relativity must be taken into consideration. == Electric field == An electric field is a vector field that associates to each point in space the Coulomb force experienced by a unit test charge. The strength and direction of the Coulomb force F {\textstyle \mathbf {F} } on a charge q t {\textstyle q_{t}} depends on the electric field E {\textstyle \mathbf {E} } established by other charges that it finds itself in, such that F = q t E {\textstyle \mathbf {F} =q_{t}\mathbf {E} } . In the simplest case, the field is considered to be generated solely by a single source point charge. More generally, the field can be generated by a distribution of charges who contribute to the overall by the principle of superposition. If the field is generated by a positive source point charge q {\textstyle q} , the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge q t {\textstyle q_{t}} would move if placed in the field. For a negative point source charge, the direction is radially inwards. The magnitude of the electric field E can be derived from Coulomb's law. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field E created by a single source point charge Q at a certain distance from it r in vacuum is given by | E | = k e | q | r 2 {\displaystyle |\mathbf {E} |=k_{\text{e}}{\frac {|q|}{r^{2}}}} A system of n discrete charges q i {\displaystyle q_{i}} stationed at r i = r − r i {\textstyle \mathbf {r} _{i}=\mathbf {r} -\mathbf {r} _{i}} produces an electric field whose magnitude and direction is, by superposition E ( r ) = 1 4 π ε 0 ∑ i = 1 n q i r ^ i | r i | 2 {\displaystyle \mathbf {E} (\mathbf {r} )={1 \over 4\pi \varepsilon _{0}}\sum _{i=1}^{n}q_{i}{{\hat {\mathbf {r} }}_{i} \over {|\mathbf {r} _{i}|}^{2}}} == Atomic forces == Coulomb's law holds even within atoms, correctly describing the force between the positively charged atomic nucleus and each of the negatively charged electrons. This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the force of attraction, and binding energy, approach zero and ionic bonding is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable. == Relation to Gauss's law == === Deriving Gauss's law from Coulomb's law === === Deriving Coulomb's law from Gauss's law === Strictly speaking, Coulomb's law cannot be derived from Gauss's law alone, since Gauss's law does not give any information regarding the curl of E (see Helmholtz decomposition and Faraday's law). However, Coulomb's law can be proven from Gauss's law if it is assumed, in addition, that the electric field from a point charge is spherically symmetric (this assumption, like Coulomb's law itself, is exactly true if the charge is stationary, and approximately true if the charge is in motion). == In relativity == Coulomb's law can be used to gain insight into the form of the magnetic field generated by moving charges since by special relativity, in certain cases the magnetic field can be shown to be a transformation of forces caused by the electric field. When no acceleration is involved in a particle's history, Coulomb's law can be assumed on any test particle in its own inertial frame, supported by symmetry arguments in solving Maxwell's equation, shown above. Coulomb's law can be expanded to moving test particles to be of the same form. This assumption is supported by Lorentz force law which, unlike Coulomb's law is not limited to stationary test charges. Considering the charge to be invariant of observer, the electric and magnetic fields of a uniformly moving point charge can hence be derived by the Lorentz transformation of the four force on the test charge in the charge's frame of reference given by Coulomb's law and attributing magnetic and electric fields by their definitions given by the form of Lorentz force. The fields hence found for uniformly moving point charges are given by: E = q 4 π ϵ 0 r 3 1 − β 2 ( 1 − β 2 sin 2 ⁡ θ ) 3 / 2 r {\displaystyle \mathbf {E} ={\frac {q}{4\pi \epsilon _{0}r^{3}}}{\frac {1-\beta ^{2}}{(1-\beta ^{2}\sin ^{2}\theta )^{3/2}}}\mathbf {r} } B = q 4 π ϵ 0 r 3 1 − β 2 ( 1 − β 2 sin 2 ⁡ θ ) 3 / 2 v × r c 2 = v × E c 2 {\displaystyle \mathbf {B} ={\frac {q}{4\pi \epsilon _{0}r^{3}}}{\frac {1-\beta ^{2}}{(1-\beta ^{2}\sin ^{2}\theta )^{3/2}}}{\frac {\mathbf {v} \times \mathbf {r} }{c^{2}}}={\frac {\mathbf {v} \times \mathbf {E} }{c^{2}}}} where q {\displaystyle q} is the charge of the point source, r {\displaystyle \mathbf {r} } is the position vector from the point source to the point in space, v {\displaystyle \mathbf {v} } is the velocity vector of the charged particle, β {\displaystyle \beta } is the ratio of speed of the charged particle divided by the speed of light and θ {\displaystyle \theta } is the angle between r {\displaystyle \mathbf {r} } and v {\displaystyle \mathbf {v} } . This form of solutions need not obey Newton's third law as is the case in the framework of special relativity (yet without violating relativistic-energy momentum conservation). Note that the expression for electric field reduces to Coulomb's law for non-relativistic speeds of the point charge and that the magnetic field in non-relativistic limit (approximating β ≪ 1 {\displaystyle \beta \ll 1} ) can be applied to electric currents to get the Biot–Savart law. These solutions, when expressed in retarded time also correspond to the general solution of Maxwell's equations given by solutions of Liénard–Wiechert potential, due to the validity of Coulomb's law within its specific range of application. Also note that the spherical symmetry for gauss law on stationary charges is not valid for moving charges owing to the breaking of symmetry by the specification of direction of velocity in the problem. Agreement with Maxwell's equations can also be manually verified for the above two equations. == Coulomb potential == === Quantum field theory === The Coulomb potential admits continuum states (with E > 0), describing electron-proton scattering, as well as discrete bound states, representing the hydrogen atom. It can also be derived within the non-relativistic limit between two charged particles, as follows: Under Born approximation, in non-relativistic quantum mechanics, the scattering amplitude A ( | p ⟩ → | p ′ ⟩ ) {\textstyle {\mathcal {A}}(|\mathbf {p} \rangle \to |\mathbf {p} '\rangle )} is: A ( | p ⟩ → | p ′ ⟩ ) − 1 = 2 π δ ( E p − E p ′ ) ( − i ) ∫ d 3 r V ( r ) e − i ( p − p ′ ) r {\displaystyle {\mathcal {A}}(|\mathbf {p} \rangle \to |\mathbf {p} '\rangle )-1=2\pi \delta (E_{p}-E_{p'})(-i)\int d^{3}\mathbf {r} \,V(\mathbf {r} )e^{-i(\mathbf {p} -\mathbf {p} ')\mathbf {r} }} This is to be compared to the: ∫ d 3 k ( 2 π ) 3 e i k r 0 ⟨ p ′ , k | S | p , k ⟩ {\displaystyle \int {\frac {d^{3}k}{(2\pi )^{3}}}e^{ikr_{0}}\langle p',k|S|p,k\rangle } where we look at the (connected) S-matrix entry for two electrons scattering off each other, treating one with "fixed" momentum as the source of the potential, and the other scattering off that potential. Using the Feynman rules to compute the S-matrix element, we obtain in the non-relativistic limit with m 0 ≫ | p | {\displaystyle m_{0}\gg |\mathbf {p} |} ⟨ p ′ , k | S | p , k ⟩ | c o n n = − i e 2 | p − p ′ | 2 − i ε ( 2 m ) 2 δ ( E p , k − E p ′ , k ) ( 2 π ) 4 δ ( p − p ′ ) {\displaystyle \langle p',k|S|p,k\rangle |_{conn}=-i{\frac {e^{2}}{|\mathbf {p} -\mathbf {p} '|^{2}-i\varepsilon }}(2m)^{2}\delta (E_{p,k}-E_{p',k})(2\pi )^{4}\delta (\mathbf {p} -\mathbf {p} ')} Comparing with the QM scattering, we have to discard the ( 2 m ) 2 {\displaystyle (2m)^{2}} as they arise due to differing normalizations of momentum eigenstate in QFT compared to QM and obtain: ∫ V ( r ) e − i ( p − p ′ ) r d 3 r = e 2 | p − p ′ | 2 − i ε {\displaystyle \int V(\mathbf {r} )e^{-i(\mathbf {p} -\mathbf {p} ')\mathbf {r} }d^{3}\mathbf {r} ={\frac {e^{2}}{|\mathbf {p} -\mathbf {p} '|^{2}-i\varepsilon }}} where Fourier transforming both sides, solving the integral and taking ε → 0 {\displaystyle \varepsilon \to 0} at the end will yield V ( r ) = e 2 4 π r {\displaystyle V(r)={\frac {e^{2}}{4\pi r}}} as the Coulomb potential. However, the equivalent results of the classical Born derivations for the Coulomb problem are thought to be strictly accidental. The Coulomb potential, and its derivation, can be seen as a special case of the Yukawa potential, which is the case where the exchanged boson – the photon – has no rest mass. == Verification == It is possible to verify Coulomb's law with a simple experiment. Consider two small spheres of mass m {\displaystyle m} and same-sign charge q {\displaystyle q} , hanging from two ropes of negligible mass of length l {\displaystyle l} . The forces acting on each sphere are three: the weight m g {\displaystyle mg} , the rope tension T {\displaystyle \mathbf {T} } and the electric force F {\displaystyle \mathbf {F} } . In the equilibrium state: and Dividing (1) by (2): Let L 1 {\displaystyle \mathbf {L} _{1}} be the distance between the charged spheres; the repulsion force between them F 1 {\displaystyle \mathbf {F} _{1}} , assuming Coulomb's law is correct, is equal to so: If we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge q 2 {\textstyle {\frac {q}{2}}} . In the equilibrium state, the distance between the charges will be L 2 < L 1 {\textstyle \mathbf {L} _{2}<\mathbf {L} _{1}} and the repulsion force between them will be: We know that F 2 = m g tan ⁡ θ 2 {\displaystyle \mathbf {F} _{2}=mg\tan \theta _{2}} and: q 2 4 4 π ε 0 L 2 2 = m g tan ⁡ θ 2 {\displaystyle {\frac {\frac {q^{2}}{4}}{4\pi \varepsilon _{0}L_{2}^{2}}}=mg\tan \theta _{2}} Dividing (4) by (5), we get: Measuring the angles θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} and the distance between the charges L 1 {\displaystyle \mathbf {L} _{1}} and L 2 {\displaystyle \mathbf {L} _{2}} is sufficient to verify that the equality is true taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation: Using this approximation, the relationship (6) becomes the much simpler expression: In this way, the verification is limited to measuring the distance between the charges and checking that the division approximates the theoretical value. == See also == == References == Spavieri, G., Gillies, G. T., & Rodriguez, M. (2004). Physical implications of Coulomb’s Law. Metrologia, 41(5), S159–S170. doi:10.1088/0026-1394/41/5/s06 == Related reading == Coulomb, Charles Augustin (1788) [1785]. "Premier mémoire sur l'électricité et le magnétisme". Histoire de l'Académie Royale des Sciences. Imprimerie Royale. pp. 569–577. Coulomb, Charles Augustin (1788) [1785]. "Second mémoire sur l'électricité et le magnétisme". Histoire de l'Académie Royale des Sciences. Imprimerie Royale. pp. 578–611. Coulomb, Charles Augustin (1788) [1785]. "Troisième mémoire sur l'électricité et le magnétisme". Histoire de l'Académie Royale des Sciences. Imprimerie Royale. pp. 612–638. Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 978-0-13-805326-0. Tamm, Igor E. (1979) [1976]. Fundamentals of the Theory of Electricity (9th ed.). Moscow: Mir. pp. 23–27. Tipler, Paul A.; Mosca, Gene (2008). Physics for Scientists and Engineers (6th ed.). New York: W. H. Freeman and Company. ISBN 978-0-7167-8964-2. LCCN 2007010418. Young, Hugh D.; Freedman, Roger A. (2010). Sears and Zemansky's University Physics: With Modern Physics (13th ed.). Addison-Wesley (Pearson). ISBN 978-0-321-69686-1. == External links == Coulomb's Law on Project PHYSNET Electricity and the Atom Archived 2009-02-21 at the Wayback Machine—a chapter from an online textbook A maze game for teaching Coulomb's law—a game created by the Molecular Workbench software Electric Charges, Polarization, Electric Force, Coulomb's Law Walter Lewin, 8.02 Electricity and Magnetism, Spring 2002: Lecture 1 (video). MIT OpenCourseWare. License: Creative Commons Attribution-Noncommercial-Share Alike.
Wikipedia/Coulomb_force
Geothermal energy is thermal energy extracted from the ground (geology)|crust]]. It combines energy from the formation of the planet and from radioactive decay. Geothermal energy has been exploited as a source of heat and/or electric power for millennia. Geothermal heating, using water from hot springs, for example, has been used for bathing since Paleolithic times and for space heating since Roman times. Geothermal power (generation of electricity from geothermal energy), has been used since the 20th century. Unlike wind and solar energy, geothermal plants produce power at a constant rate, without regard to weather conditions. Geothermal resources are theoretically more than adequate to supply humanity's energy needs. Most extraction occurs in areas near tectonic plate boundaries. The cost of generating geothermal power decreased by 25% during the 1980s and 1990s. Technological advances continued to reduce costs and thereby expand the amount of viable resources. In 2021, the US Department of Energy estimated that power from a plant "built today" costs about $0.05/kWh. In 2019, 13,900 megawatts (MW) of geothermal power was available worldwide. An additional 28 gigawatts provided heat for district heating, space heating, spas, industrial processes, desalination, and agricultural applications as of 2010. As of 2019 the industry employed about one hundred thousand people. The adjective geothermal originates from the Greek roots γῆ (gê), meaning Earth, and θερμός (thermós), meaning hot. == History == Hot springs have been used for bathing since at least Paleolithic times. The oldest known spa is at the site of the Huaqing Chi palace. In the first century CE, Romans conquered Aquae Sulis, now Bath, Somerset, England, and used the hot springs there to supply public baths and underfloor heating. The admission fees for these baths probably represent the first commercial use of geothermal energy. The world's oldest geothermal district heating system, in Chaudes-Aigues, France, has been operating since the 15th century. The earliest industrial exploitation began in 1827 with the use of geyser steam to extract boric acid from volcanic mud in Larderello, Italy. In 1892, the US's first district heating system in Boise, Idaho was powered by geothermal energy. It was copied in Klamath Falls, Oregon, in 1900. The world's first known building to utilize geothermal energy as its primary heat source was the Hot Lake Hotel in Union County, Oregon, beginning in 1907. A geothermal well was used to heat greenhouses in Boise in 1926, and geysers were used to heat greenhouses in Iceland and Tuscany at about the same time. Charles Lieb developed the first downhole heat exchanger in 1930 to heat his house. Geyser steam and water began heating homes in Iceland in 1943. In the 20th century, geothermal energy came into use as a generating source. Prince Piero Ginori Conti tested the first geothermal power generator on 4 July 1904, at the Larderello steam field. It successfully lit four light bulbs. In 1911, the world's first commercial geothermal power plant was built there. It was the only industrial producer of geothermal power until New Zealand built a plant in 1958. In 2012, it produced some 594 megawatts. In 1960, Pacific Gas and Electric began operation of the first US geothermal power plant at The Geysers in California. The original turbine lasted for more than 30 years and produced 11 MW net power. An organic fluid based binary cycle power station was first demonstrated in 1967 in the USSR and later introduced to the US in 1981. This technology allows the use of temperature resources as low as 81 °C. In 2006, a binary cycle plant in Chena Hot Springs, Alaska, came on-line, producing electricity from a record low temperature of 57 °C (135 °F). == Resources == The Earth has an internal heat content of 1031 joules (3·1015 TWh), About 20% of this is residual heat from planetary accretion; the remainder is attributed to past and current radioactive decay of naturally occurring isotopes. For example, a 5275 m deep borehole in United Downs Deep Geothermal Power Project in Cornwall, England, found granite with very high thorium content, whose radioactive decay is believed to power the high temperature of the rock. Earth's interior temperature and pressure are high enough to cause some rock to melt and the solid mantle to behave plastically. Parts of the mantle convect upward since it is lighter than the surrounding rock. Temperatures at the core–mantle boundary can reach over 4,000 °C (7,230 °F). The Earth's internal thermal energy flows to the surface by conduction at a rate of 44.2 terawatts (TW), and is replenished by radioactive decay of minerals at a rate of 30 TW. These power rates are more than double humanity's current energy consumption from all primary sources, but most of this energy flux is not recoverable. In addition to the internal heat flows, the top layer of the surface to a depth of 10 m (33 ft) is heated by solar energy during the summer, and cools during the winter. Outside of the seasonal variations, the geothermal gradient of temperatures through the crust is 25–30 °C (77–86 °F) per km of depth in most of the world. The conductive heat flux averages 0.1 MW/km2. These values are much higher near tectonic plate boundaries where the crust is thinner. They may be further augmented by combinations of fluid circulation, either through magma conduits, hot springs, hydrothermal circulation. The thermal efficiency and profitability of electricity generation is particularly sensitive to temperature. Applications receive the greatest benefit from a high natural heat flux most easily from a hot spring. The next best option is to drill a well into a hot aquifer. An artificial hot water reservoir may be built by injecting water to hydraulically fracture bedrock. The systems in this last approach are called enhanced geothermal systems. 2010 estimates of the potential for electricity generation from geothermal energy vary sixfold, from 0.035to2TW depending on the scale of investments. Upper estimates of geothermal resources assume wells as deep as 10 kilometres (6 mi), although 20th century wells rarely reached more than 3 kilometres (2 mi) deep. Wells of this depth are common in the petroleum industry. == Geothermal power == Geothermal power is electrical power generated from geothermal energy. Dry steam, flash steam, and binary cycle power stations have been used for this purpose. As of 2010 geothermal electricity was generated in 26 countries. As of 2019, worldwide geothermal power capacity amounted to 15.4 gigawatts (GW), of which 23.86 percent or 3.68 GW were in the United States. Geothermal energy supplies a significant share of the electrical power in Iceland, El Salvador, Kenya, the Philippines and New Zealand. Geothermal power is considered to be a renewable energy because heat extraction rates are insignificant compared to the Earth's heat content. The greenhouse gas emissions of geothermal electric stations are on average 45 grams of carbon dioxide per kilowatt-hour of electricity, or less than 5 percent of that of coal-fired plants. Geothermal electric plants were traditionally built on the edges of tectonic plates where high-temperature geothermal resources approach the surface. The development of binary cycle power plants and improvements in drilling and extraction technology enable enhanced geothermal systems over a greater geographical range. Demonstration projects are operational in Landau-Pfalz, Germany, and Soultz-sous-Forêts, France, while an earlier effort in Basel, Switzerland, was shut down after it triggered earthquakes. Other demonstration projects are under construction in Australia, the United Kingdom, and the US. In Myanmar over 39 locations are capable of geothermal power production, some of which are near Yangon. == Geothermal heating == Geothermal heating is the use of geothermal energy to heat buildings and water for human use. Humans have done this since the Paleolithic era. Approximately seventy countries made direct use of a total of 270 PJ of geothermal heating in 2004. As of 2007, 28 GW of geothermal heating satisfied 0.07% of global primary energy consumption. Thermal efficiency is high since no energy conversion is needed, but capacity factors tend to be low (around 20%) since the heat is mostly needed in the winter. Even cold ground contains heat: below 6 metres (20 ft) the undisturbed ground temperature is consistently at the Mean Annual Air Temperature that may be extracted with a ground source heat pump. == Types == === Hydrothermal systems === Hydrothermal systems produce geothermal energy by accessing naturally-occurring hydrothermal reservoirs. Hydrothermal systems come in either vapor-dominated or liquid-dominated forms. ==== Vapor-dominated plants ==== Larderello and The Geysers are vapor-dominated. Vapor-dominated sites offer temperatures from 240 to 300 °C that produce superheated steam. ==== Liquid-dominated plants ==== Liquid-dominated reservoirs (LDRs) are more common with temperatures greater than 200 °C (392 °F) and are found near volcanoes in/around the Pacific Ocean and in rift zones and hot spots. Flash plants are the common way to generate electricity from these sources. Steam from the well is sufficient to power the plant. Most wells generate 2–10 MW of electricity. Steam is separated from liquid via cyclone separators and drives electric generators. Condensed liquid returns down the well for reheating/reuse. As of 2013, the largest liquid system was Cerro Prieto in Mexico, which generates 750 MW of electricity from temperatures reaching 350 °C (662 °F). Lower-temperature LDRs (120–200 °C) require pumping. They are common in extensional terrains, where heating takes place via deep circulation along faults, such as in the Western US and Turkey. Water passes through a heat exchanger in a Rankine cycle binary plant. The water vaporizes an organic working fluid that drives a turbine. These binary plants originated in the Soviet Union in the late 1960s and predominate in new plants. Binary plants have no emissions. === Engineered geothermal systems === An engineered geothermal system is a geothermal system that engineers have artificially created or improved. Engineered geothermal systems are used in a variety of geothermal reservoirs that have hot rocks but insufficient natural reservoir quality, for example, insufficient geofluid quantity or insufficient rock permeability or porosity, to operate as natural hydrothermal systems. Types of engineered geothermal systems include enhanced geothermal systems, closed-loop or advanced geothermal systems, and some superhot rock geothermal systems. ==== Enhanced geothermal systems ==== Enhanced geothermal systems (EGS) actively inject water into wells to be heated and pumped back out. The water is injected under high pressure to expand existing rock fissures to enable the water to flow freely. The technique was adapted from oil and gas fracking techniques. The geologic formations are deeper and no toxic chemicals are used, reducing the possibility of environmental damage. Instead proppants such as sand or ceramic particles are used to keep the cracks open and producing optimal flow rates. Drillers can employ directional drilling to expand the reservoir size. Small-scale EGS have been installed in the Rhine Graben at Soultz-sous-Forêts in France and at Landau and Insheim in Germany. ==== Closed-loop geothermal systems ==== Closed-loop geothermal systems, sometimes colloquially referred to as Advanced Geothermal Systems (AGS), are engineered geothermal systems containing subsurface working fluid that is heated in the hot rock reservoir without direct contact with rock pores and fractures. Instead, the subsurface working fluid stays inside a closed loop of deeply buried pipes that conduct Earth's heat. The advantages of a deep, closed-loop geothermal circuit include: (1) no need for a geofluid, (2) no need for the hot rock to be permeable or porous, and (3) all the introduced working fluid can be recirculated with zero loss. Eavortm, a Canadian-based geothermal startup, piloted their closed-loop system in shallow soft rock formations in Alberta, Canada. Situated within a sedimentary basin, the geothermal gradient proved to be insufficient for electrical power generation. However, the system successfully produced approximately 11,000 MWh of thermal energy during its initial two years of operation." == Economics == As with wind and solar energy, geothermal power has minimal operating costs; capital costs dominate. Drilling accounts for over half the costs, and not all wells produce exploitable resources. For example, a typical well pair (one for extraction and one for injection) in Nevada can produce 4.5 megawatts (MW) and costs about $10 million to drill, with a 20% failure rate, making the average cost of a successful well $50 million. Drilling geothermal wells is more expensive than drilling oil and gas wells of comparable depth for several reasons: Geothermal reservoirs are usually in igneous or metamorphic rock, which is harder to penetrate than the sedimentary rock of typical hydrocarbon reservoirs. The rock is often fractured, which causes vibrations that damage bits and other drilling tools. The rock is often abrasive, with high quartz content, and sometimes contains highly corrosive fluids. The rock is hot, which limits use of downhole electronics. Well casing must be cemented from top to bottom, to resist the casing's tendency to expand and contract with temperature changes. Oil and gas wells are usually cemented only at the bottom. Well diameters are considerably larger than typical oil and gas wells. As of 2007 plant construction and well drilling cost about €2–5 million per MW of electrical capacity, while the break-even price was 0.04–0.10 € per kW·h. Enhanced geothermal systems tend to be on the high side of these ranges, with capital costs above $4 million per MW and break-even above $0.054 per kW·h. Between 2013 and 2020, private investments were the main source of funding for renewable energy, comprising approximately 75% of total financing. The mix between private and public funding varies among different renewable energy technologies, influenced by their market appeal and readiness. In 2020, geothermal energy received just 32% of its investment from private sources. === Socioeconomic benefits === In January 2024, the Energy Sector Management Assistance Program (ESMAP) report "Socioeconomic Impacts of Geothermal Energy Development" was published, highlighting the substantial socioeconomic benefits of geothermal energy development, which notably exceeds those of wind and solar by generating an estimated 34 jobs per megawatt across various sectors. The report details how geothermal projects contribute to skill development through practical on-the-job training and formal education, thereby strengthening the local workforce and expanding employment opportunities. It also underscores the collaborative nature of geothermal development with local communities, which leads to improved infrastructure, skill-building programs, and revenue-sharing models, thereby enhancing access to reliable electricity and heat. These improvements have the potential to boost agricultural productivity and food security. The report further addresses the commitment to advancing gender equality and social inclusion by offering job opportunities, education, and training to underrepresented groups, ensuring fair access to the benefits of geothermal development. Collectively, these efforts are instrumental in driving domestic economic growth, increasing fiscal revenues, and contributing to more stable and diverse national economies, while also offering significant social benefits such as better health, education, and community cohesion. == Development == Geothermal projects have several stages of development. Each phase has associated risks. Many projects are canceled during the stages of reconnaissance and geophysical surveys, which are unsuitable for traditional lending. At later stages can often be equity-financed. === Precipitate scaling === A common issue encountered in geothermal systems arises when the system is situated in carbonate-rich formations. In such cases, the fluids extracting heat from the subsurface often dissolve fragments of the rock during their ascent towards the surface, where they subsequently cool. As the fluids cool, dissolved cations precipitate out of solution, leading to the formation of calcium scale, a phenomenon known as calcite scaling. This calcite scaling has the potential to decrease flow rates and necessitate system downtime for maintenance purposes. == Sustainability == Geothermal energy is considered to be sustainable because the heat extracted is so small compared to the Earth's heat content, which is approximately 100 billion times 2010 worldwide annual energy consumption. Earth's heat flows are not in equilibrium; the planet is cooling on geologic timescales. Anthropic heat extraction typically does not accelerate the cooling process. Wells can further be considered renewable because they return the extracted water to the borehole for reheating and re-extraction, albeit at a lower temperature. Replacing material use with energy has reduced the human environmental footprint in many applications. Geothermal has the potential to allow further reductions. For example, Iceland has sufficient geothermal energy to eliminate fossil fuels for electricity production and to heat Reykjavik sidewalks and eliminate the need for gritting. However, local effects of heat extraction must be considered. Over the course of decades, individual wells draw down local temperatures and water levels. The three oldest sites, at Larderello, Wairakei, and the Geysers experienced reduced output because of local depletion. Heat and water, in uncertain proportions, were extracted faster than they were replenished. Reducing production and injecting additional water could allow these wells to recover their original capacity. Such strategies have been implemented at some sites. These sites continue to provide significant energy. The Wairakei power station was commissioned in November 1958, and it attained its peak generation of 173 MW in 1965, but already the supply of high-pressure steam was faltering. In 1982 it was down-rated to intermediate pressure and the output to 157 MW. In 2005 two 8 MW isopentane systems were added, boosting output by about 14 MW. Detailed data were lost due to re-organisations. == Environmental effects == Fluids drawn from underground carry a mixture of gasses, notably carbon dioxide (CO2), hydrogen sulfide (H2S), methane (CH4) and ammonia (NH3). These pollutants contribute to global warming, acid rain and noxious smells if released. Existing geothermal electric plants emit an average of 122 kilograms (269 lb) of CO2 per megawatt-hour (MW·h) of electricity, a small fraction of the emission intensity of fossil fuel plants. A few plants emit more pollutants than gas-fired power, at least in the first few years, such as some geothermal power in Turkey. Plants that experience high levels of acids and volatile chemicals are typically equipped with emission-control systems to reduce the exhaust. New emerging closed looped technologies developed by Eavor have the potential to reduce these emissions to zero. Water from geothermal sources may hold in solution trace amounts of toxic elements such as mercury, arsenic, boron, and antimony. These chemicals precipitate as the water cools, and can damage surroundings if released. The modern practice of returning geothermal fluids into the Earth to stimulate production has the side benefit of reducing this environmental impact. Construction can adversely affect land stability. Subsidence occurred in the Wairakei field. In Staufen im Breisgau, Germany, tectonic uplift occurred instead. A previously isolated anhydrite layer came in contact with water and turned it into gypsum, doubling its volume. Enhanced geothermal systems can trigger earthquakes as part of hydraulic fracturing. A project in Basel, Switzerland was suspended because more than 10,000 seismic events measuring up to 3.4 on the Richter Scale occurred over the first 6 days of water injection. Geothermal power production has minimal land and freshwater requirements. Geothermal plants use 3.5 square kilometres (1.4 sq mi) per gigawatt of electrical production (not capacity) versus 32 square kilometres (12 sq mi) and 12 square kilometres (4.6 sq mi) for coal facilities and wind farms respectively. They use 20 litres (5.3 US gal) of freshwater per MW·h versus over 1,000 litres (260 US gal) per MW·h for nuclear, coal, or oil. == Production == === Philippines === The Philippines began geothermal research in 1962 when the Philippine Institute of Volcanology and Seismology inspected the geothermal region in Tiwi, Albay. The first geothermal power plant in the Philippines was built in 1977, located in Tongonan, Leyte. The New Zealand government contracted with the Philippines to build the plant in 1972. The Tongonan Geothermal Field (TGF) added the Upper Mahiao, Matlibog, and South Sambaloran plants, which resulted in a 508 MV capacity. The first geothermal power plant in the Tiwi region opened in 1979, while two other plants followed in 1980 and 1982. The Tiwi geothermal field is located about 450 km from Manila. The three geothermal power plants in the Tiwi region produce 330 MWe, putting the Philippines behind the United States and Mexico in geothermal growth. The Philippines has 7 geothermal fields and continues to exploit geothermal energy by creating the Philippine Energy Plan 2012–2030 that aims to produce 70% of the country's energy by 2030. === United States === According to the Geothermal Energy Association (GEA) installed geothermal capacity in the United States grew by 5%, or 147.05 MW, in 2013. This increase came from seven geothermal projects that began production in 2012. GEA revised its 2011 estimate of installed capacity upward by 128 MW, bringing installed US geothermal capacity to 3,386 MW. === Hungary === The municipal government of Szeged is trying to cut down its gas consumption by 50 percent by utilizing geothermal energy for its district heating system. The Szeged geothermal power station has 27 wells, 16 heating plants, and 250 kilometres of distribution pipes. == See also == 2010 World Geothermal Congress Deep water source cooling Earth's internal heat budget Geothermal activity Hydrothermal vent International Geothermal Association Ocean thermal energy conversion Relative cost of electricity generated by different sources List of renewable energy topics by country and territory Thermal battery == References == == External links == "The Future of Geothermal Energy" (PDF). International Energy Agency (IEA). December 2024. Archived (PDF) from the original on 14 December 2024. "Hawai'i Groundwater & Geothermal Resources Center". University of Hawaii at Manoa. 2023-07-16. Retrieved 2023-08-07. "Geothermal Rising :: Using the Earth to Save the Earth". www.geothermal.org. Retrieved 2023-08-07. Energy Efficiency and Renewable Energy – Geothermal Technologies Office International Energy Agency Geothermal Energy Homepage NREL – Geothermal Research 2022 discussion of geothermal energy advantages and challenges
Wikipedia/Geothermal_energy
Energy conservation is the effort to reduce wasteful energy consumption by using fewer energy services. This can be done by using energy more effectively (using less and better sources of energy for continuous service) or changing one's behavior to use less and better source of service (for example, by driving vehicles which consume renewable energy or energy with more efficiency). Energy conservation can be achieved through efficient energy use, which has some advantages, including a reduction in greenhouse gas emissions and a smaller carbon footprint, as well as cost, water, and energy savings. Green engineering practices improve the life cycle of the components of machines which convert energy from one form into another. Energy can be conserved by reducing waste and losses, improving efficiency through technological upgrades, improving operations and maintenance, changing users' behaviors through user profiling or user activities, monitoring appliances, shifting load to off-peak hours, and providing energy-saving recommendations. Observing appliance usage, establishing an energy usage profile, and revealing energy consumption patterns in circumstances where energy is used poorly, can pinpoint user habits and behaviors in energy consumption. Appliance energy profiling helps identify inefficient appliances with high energy consumption and energy load. Seasonal variations also greatly influence energy load, as more air-conditioning is used in warmer seasons and heating in colder seasons. Achieving a balance between energy load and user comfort is complex yet essential for energy preservation. On a large scale, a few factors affect energy consumption trends, including political issues, technological developments, economic growth, and environmental concerns. == User-oriented energy conservation == User behavior has a significant effect on energy conservation. It involves user activity detection, profiling, and appliance interaction behaviors. User profiling consists of the identification of energy usage patterns of the user and replacing required system settings with automated settings that can be initiated on request. Within user profiling, personal characteristics are instrumental in affecting energy conservation behavior. These characteristics include household income, education, gender, age, and social norms. User behavior also relies on the impact of personality traits, social norms, and attitudes on energy conservation behavior. Beliefs and attitudes toward a convenient lifestyle, environmentally friendly transport, energy security, and residential location choices affect energy conservation behavior. As a result, energy conservation can be made possible by adopting pro-environmental behavior and energy-efficient systems. Education on approaches to energy conservation can result in wise energy use. The choices made by the users yield energy usage patterns. Rigorous analysis of these usage patterns identifies waste energy patterns, and improving those patterns may reduce significant energy load. Therefore, human behavior is critical to determining the implications of energy conservation measures and solving environmental problems. Substantial energy conservation may be achieved if users' habit loops are modified. == User habits == User habits significantly impact energy demand; thus, providing recommendations for improving user habits contributes to energy conservation. Micro-moments are essential in realizing energy consumption patterns and are identified using a variety of sensing units positioned in prominent areas across the home. The micro-moment is an event that changes the state of the appliance from inactive to active and helps in building users' energy consumption profiles according to their activities. Energy conservation can be achieved through user habits by following energy-saving recommendations at micro-moments. Unnecessary energy usage can be decreased by selecting a suitable schedule for appliance operation. Creating an effective scheduling system requires an understanding of user habits regarding appliances. == Off-peak scheduling == Many techniques for energy conservation comprise off-peak scheduling, which means operating an appliance in a low-price energy hour. This schedule can be achieved after user habits regarding appliance use are understood. Most energy providers divide the energy tariff into high and low-price hours; therefore, scheduling an appliance to work an off-peak hour will significantly reduce electricity bills. == User activity detection == User activity detection leads to the precise detection of appliances required for an activity. If an appliance is active but not required for a user's current activity, it wastes energy and can be turned off to conserve energy. The precise identification of user activities is necessary to achieve this method of energy conservation. == Energy conservation opportunities by sector == === Buildings === ==== Existing buildings ==== Energy conservation measures have primarily focused on technological innovations to improve efficiencies and financial incentives with theoretical explanations obtained from the mentioned analytical traditions. Existing buildings can improve energy efficiency by changing structural maintenance materials, adjusting the composition of air conditioning systems, selecting energy-saving equipment, and formulating subsidy policies. These measures can improve users' thermal comfort and reduce buildings' environmental impact. The selection of combinatorial optimization schemes that contain measures to guide and restrict users' behavior in addition to carrying out demand-side management can dynamically adjust energy consumption. At the same time, economic means should enable users to change their behavior and achieve a low-carbon life. Combination optimization and pricing incentives reduce building energy consumption and carbon emissions and reduce users' costs. Energy monitoring through energy audits can achieve energy efficiency in existing buildings. An energy audit is an inspection and analysis of energy use and flows for energy conservation in a structure, process, or system intending to reduce energy input without negatively affecting output. Energy audits can determine specific opportunities for energy conservation and efficiency measures as well as determine cost-effective strategies. Training professionals typically accomplish this and can be part of some national programs discussed above. The recent development of smartphone apps enables homeowners to complete relatively sophisticated energy audits themselves. For instance, smart thermostats can connect to standard HVAC systems to maintain energy-efficient indoor temperatures. In addition, data loggers can also be installed to monitor the interior temperature and humidity levels to provide a more precise understanding of the conditions. If the data gathered is compared with the users' perceptions of comfort, more fine-tuning of the interiors can be implemented (e.g., increasing the temperature where A.C. is used to prevent over-cooling). Building technologies and smart meters can allow commercial and residential energy users to visualize the impact their energy use can have in their workplaces or homes. Advanced real-time energy metering can help people save energy through their actions. Another approach towards energy conservation is the implementation of ECMs in commercial buildings, which often employ Energy Service Companies (ESCOs) experienced in energy performance contracting. This industry has been around since the 1970s and is more prevalent than ever today. The US-based organization EVO (Efficiency Valuation Organization) has created a set of guidelines for ESCOs to adhere to in evaluating the savings achieved by ECMs. These guidelines are called the International Performance Measurement and Verification Protocol (IPMVP). Energy efficiency can also be achieved by upgrading certain aspects of existing buildings. Making thermal improvements by adding insulation to crawl spaces and ensuring no leaks achieves an efficient building envelope, reducing the need for mechanical systems to heat and cool the space. High-performance insulation is also supported by adding double/triple-glazed windows to minimize thermal heat transmission. Minor upgrades in existing buildings include changing mixers to low flow greatly aids in water conservation, changing light bulbs to LED lights results in 70-90% less energy consumption than a standard incandescent or C.F.L. bulb, changing inefficient appliances with Energy Star-rated appliances will consume less energy, and finally adding vegetation in the landscape surrounding the building to function as a shading element. A window windcatcher can reduce the total energy use of a building by 23.3%. Energy conservation through users' behaviors requires understanding household occupants' lifestyle, social, and behavioral factors in analyzing energy consumption. This involves one-time investments in energy efficiency, such as purchasing new energy-efficient appliances or upgrading the building insulation without curtailing economic utility or the level of energy services, and energy curtailment behaviors which are theorized to be driven more by social-psychological factors and environmental concerns in comparison to the energy efficiency behaviors. Replacing existing appliances with newer and more efficient ones leads to energy efficiency as less energy is wasted throughout. Overall, energy efficiency behaviors are identified more with one-time, cost-incurring investments in efficient appliances and retrofits, while energy curtailment behaviors include repetitive, low-cost energy-saving efforts. To identify and optimize residential energy use, conventional and behavioral economics, technology adoption theory and attitude-based decision-making, social and environmental psychology, and sociology must be analyzed. The techno-economic and psychological literature analysis focuses on the individual attitude, behavior, and choice/context/external conditions. In contrast, the sociological literature relies more on the energy consumption practices shaped by the social, cultural, and economic factors in a dynamic setting. ==== New buildings ==== Many steps can be taken toward energy conservation and efficiency when designing new buildings. Firstly, the building can be designed to optimize building performance by having an efficient building envelope with high-performing insulation and window glazing systems, window facades strategically oriented to optimize daylighting, shading elements to mitigate unwanted glare, and passive energy systems for appliances. In passive solar building designs, windows, walls, and floors are made to collect, store, and distribute solar energy in the form of heat in the winter and reject solar heat in the summer. The key to designing a passive solar building is to best take advantage of the local climate. Elements to be considered include window placement and glazing type, thermal insulation, thermal mass, and shading. Optimizing daylighting can decrease energy waste from incandescent bulbs, windows, and balconies, allow natural ventilation, reduce the need for heating and cooling, low flow mixers aid in water conservation, and upgrade to Energy star rated appliances consume less energy. Designing a building according to LEED guidelines while incorporating smart home technology can help save a lot of energy and money in the long run. Passive solar design techniques can be applied most easily to new buildings, but existing buildings can be retrofitted. Mainly, energy conservation is achieved by modifying user habits or providing an energy-saving recommendation of curtailing an appliance or scheduling it to low-price energy tariff hours. Besides changing user habits and appliance control, identifying irrelevant appliances concerning user activities in smart homes saves energy. Smart home technology can advise users on energy-saving strategies according to their behavior, encouraging behavioral change that leads to energy conservation. This guidance includes reminders to turn off lights, leakage sensors to prevent plumbing issues, running appliances on off-peak hours, and smart sensors that save energy. Such technology learns user-appliance activity patterns, gives a complete overview of various energy-consuming appliances, and can provide guidance to improve these patterns to contribute to energy conservation. As a result, they can strategically schedule appliances by monitoring the energy consumption profiles of the appliances, schedule devices to the energy-efficient mode, or plan to work during off-peak hours. Appliance-oriented approaches emphasize appliance profiling, curtailing, and scheduling to off-peak hours, as supervision of appliances is key to energy preservation. It usually leads to appliance curtailment in which an appliance is either scheduled to work another time or is turned off. Appliance curtailment involves appliance recognition, activity-appliances model, unattended appliance detection, and energy conservation service. The appliance recognition module detects active appliances to identify the activities of smart home users. After identifying users' activities, the association between the functional appliances and user activities is established. The unattended appliance detection module looks for active appliances but is unrelated to user activity. These functional appliances waste energy and can be turned off by providing recommendations to the user. Based on the smart home recommendations, users can give weight to certain appliances that increase user comfort and satisfaction while conserving energy. Energy consumption models of energy consumption of appliances and the level of comfort they create can balance priorities among smart home comfort levels and energy consumption. According to Kashimoto, Ogura, Yamamoto, Yasumoto, and Ito, the energy supply reduces based on the historical state of the appliance and increases according to the comfort level requirement of the user, leading to a targeted energy-saving ratio. Scenarios-based energy consumption can be employed as a strategy for energy conservation, with each scenario encompassing a specific set of rules for energy consumption. === Transportation === Transporting people, goods, and services represented 29% of U.S. energy consumption in 2007. The transportation sector also accounted for about 33% of U.S. carbon dioxide emissions in 2006, with highway vehicles accounting for about 84% of that, making transportation an essential target for addressing global climate change (E.I.A., 2008). Suburban infrastructure evolved during an age of relatively easy access to fossil fuels, leading to transportation-dependent living systems.[citation needed] The amount of energy used to transport people to and from a facility, whether they are commuters, customers, vendors, or homeowners, is known as the transportation energy intensity of the building. Land is developing at a faster rate than population growth, leading to urban sprawl and, therefore, high transportation energy intensity as more people need to commute longer distances to jobs. As a result, the location of a building is essential in decreasing embodied emissions. In transportation, state and local efforts in energy conservation and efficiency measures tend to be more targeted and smaller in scale. However, with more robust fuel economy standards, new targets for the use of alternative transportation fuels, and new efforts in electric and hybrid electric vehicles, EPAct05 and EISA provide a new set of national policy signals and financial incentives to the private sector and state and local governments for the transportation sector. Zoning reforms that allow greater urban density and designs for walking and bicycling can greatly reduce energy consumed for transportation. Many Americans work in jobs that allow for remote work instead of commuting daily, which is a significant opportunity to conserve energy.[citation needed] Intelligent transportation systems (ITS) provide a solution to traffic congestion and C.E.s caused by increased vehicles. ITS combines improvements in information technology and systems, communications, sensors, controllers, and advanced mathematical methods with the traditional world of transportation infrastructure. It improves traffic safety and mobility, reduces environmental impact, promotes sustainable transportation, and increases productivity. The ITS strengthens the connection and cooperation between people, vehicles, roads, and the environment while improving road capacity, reducing traffic accidents, and improving transportation efficiency and safety by alleviating traffic congestion and reducing pollution. It makes full use of traffic information as an application service, which can enhance the operational efficiency of existing traffic facilities. The most significant energy-saving potential is that there are the most problems in urban transportation in various countries, such as management systems, policies and regulations, planning, technology, operation, and management mechanism. Improvements in one or several aspects will improve road transportation. Efficiency has a positive impact, which leads to the improvement of the urban traffic environment and efficiency. In addition to ITS, transit-oriented development (T.O.D.) significantly improves transportation in urban areas by emphasizing density, proximity to transit, diversity of uses, and streetscape design. Density is important for optimizing location and is a way to cut down on driving. Planners can regulate development rights by exchanging them from ecologically sensitive areas to growth-friendly zones according to density transfer procedures. Distance is defined as the accessibility of rail and bus transits, which serve as deterrents for driving. For transit-oriented development to be feasible, transportation stops must be close to where people live. Diversity refers to mixed-use areas that offer essential services close to homes and offices and include residential spaces for different socioeconomic categories, commercial and retail. This creates a pedestrian shed where one area can meet people's everyday needs on foot. Lastly, the streetscapes design involves minimal parking and walkable areas that calm traffic. Generous parking incentivizes people to use cars, whereas minimal and expensive parking deters commuters. At the same time, streetscapes can be designed to incorporate bicycling lanes and designated bicycle paths and trails. People may commute by bicycle to work without being concerned about their bicycles becoming wet because of covered bicycle storage. This encourages commuters to use bicycles rather than other modes of transportation and contributes to energy saving. People will be happy to walk a few blocks from a train stop if there are attractive, pedestrian-friendly outdoor spaces nearby with good lighting, park benches, outdoor tables at cafés, shade tree plantings, pedestrian courts that are blocked off to cars, and public internet connection. Additionally, this strategy calms traffic, improving the intended pedestrian environment. New urban planning schemes can be designed to improve connectivity in cities through networks of interconnected streets that spread out traffic flow, slow down vehicles, and make walking more pleasant. By dividing the number of road links by the number of road nodes, the connectivity index is calculated. The higher the connectivity index, the greater the route choices and the better the pedestrian access. Realizing the transportation impacts associated with buildings allows commuters to take steps toward energy conservation. Connectivity encourages energy-conserving behaviors as commuters use fewer cars, walk and bike more, and use public transportation. For commuters who do not have the option of public transportation, smaller vehicles that are hybrid or have better mileage can be used. === Consumer products === Homeowners implementing ECMs in their residential buildings often start with an energy audit. This is a way homeowners look at what areas of their homes are using, and possibly losing energy. Residential energy auditors are accredited by the Building Performance Institute (BPI) or the Residential Energy Services Network (RESNET). Homeowners can hire a professional or do it themselves or use a smartphone to help do an audit. Energy conservation measures are often combined into larger guaranteed Energy Savings Performance Contracts to maximize energy savings while minimizing disruption to building occupants by coordinating renovations. Some ECMs cost less to implement yet return higher energy savings. Traditionally, lighting projects were a good example of "low hanging fruit" that could be used to drive implementation of more substantial upgrades to HVAC systems in large facilities. Smaller buildings might combine window replacement with modern insulation using advanced building foams to improve energy for performance. Energy dashboard projects are a new kind of ECM that relies on the behavioral change of building occupants to save energy. When implemented as part of a program, case studies, such as that for the DC Schools, report energy savings up 30%. Under the right circumstances, open energy dashboards can even be implemented for free to improve upon these savings even more. Consumers are often poorly informed of the savings of energy-efficient products. A prominent example of this is the energy savings that can be made by replacing an incandescent light bulb with a more modern alternative. When purchasing light bulbs, many consumers opt for cheap incandescent bulbs, failing to take into account their higher energy costs and lower lifespans when compared to modern compact fluorescent and LED bulbs. Although these energy-efficient alternatives have a higher upfront cost, their long lifespan and low energy use can save consumers a considerable amount of money. The price of LED bulbs has also been steadily decreasing in the past five years due to improvements in semiconductor technology. Many LED bulbs on the market qualify for utility rebates that further reduce the price of the purchase to the consumer. Estimates by the U.S. Department of Energy state that widespread adoption of LED lighting over the next 20 years could result in about $265 billion worth of savings in United States energy costs. The research one must put into conserving energy is often too time-consuming and costly for the average consumer when there are cheaper products and technology available using today's fossil fuels. Some governments and NGOs are attempting to reduce this complexity with Eco-labels that make differences in energy efficiency easy to research while shopping. To provide the kind of information and support people need to invest money, time and effort in energy conservation, it is important to understand and link to people's topical concerns. For instance, some retailers argue that bright lighting stimulates purchasing. However, health studies have demonstrated that headache, stress, blood pressure, fatigue and worker error all generally increase with the common over-illumination present in many workplace and retail settings. It has been shown that natural daylighting increases productivity levels of workers, while reducing energy consumption. In warm climates where air conditioning is used, any household device that gives off heat will result in a larger load on the cooling system. Items such as stoves, dishwashers, clothes dryers, hot water, and incandescent lighting all add heat to the home. Low-power or insulated versions of these devices give off less heat for the air conditioning to remove. The air conditioning system can also improve efficiency by using a heat sink that is cooler than the standard air heat exchanger, such as geothermal or water. In cold climates, heating air and water is a major demand for household energy use. Significant energy reductions are possible by using different technologies. Heat pumps are a more efficient alternative to electrical resistance heaters for warming air or water. A variety of efficient clothes dryers are available, and the clothes lines requires no energy- only time. Natural-gas (or bio-gas) condensing boilers and hot-air furnaces increase efficiency over standard hot-flue models. Standard electric boilers can be made to run only at hours of the day when they are needed by means of a time switch. This decreases energy use vastly. In showers, a semi-closed-loop system could be used. New construction implementing heat exchangers can capture heat from wastewater or exhaust air in bathrooms, laundry, and kitchens. In both warm and cold climate extremes, airtight thermal insulated construction is the largest factor determining the efficiency of a home. Insulation is added to minimize the flow of heat to or from the home, but can be labor-intensive to retrofit to an existing home. == Energy conservation by countries == === Asia === Although energy efficiency is expected to play a vital role in cost-effectively cutting energy demand, only a small part of its economic potential is exploited in Asia. Governments have implemented a range of subsidies such as cash grants, cheap credit, tax exemptions, and co-financing with public-sector funds to encourage energy-efficiency initiatives across several sectors. Governments in the Asia-Pacific region have implemented a range of information provision and labeling programs for buildings, appliances, and the transportation and induel-economy labels, or actively seek to encourage behavioral changes, such as Japan's Cool Biz campaign that encourages setting air conditioners at 28-degrees Celsius and allowing employees to dress casually in the summer. China's government has launched a series of policies since 2005 to effectively promote the goal of reducing energy-saving emissions; however, road transportation, the fastest-growing energy-consuming sector in the transportation industry, lacks specific, operational, and systematic energy-saving plans. Road transportation is the highest priority to achieve energy conservation effectively and reduce emissions, particularly since social and economic development has entered the "new norm" period. Generally speaking, the government should make comprehensive plans for conservation and emissions reduction in the road transportation industry within the three dimensions of demand, structure, and technology. For example, encouraging trips using public transportation and new transportation modes such as car-sharing and increasing investment in new energy vehicles in structure reform, etc. === European Union === At the end of 2006, the European Union (EU) pledged to cut its annual consumption of primary energy by 20% by 2020. The EU Energy Efficiency Directive 2012 mandates energy efficiency improvements within the EU. As part of the EU's SAVE program, aimed at promoting energy efficiency and encouraging energy-saving behavior, the Boiler Efficiency Directive specifies minimum levels of efficiency for boilers using liquid or gaseous fuels. There is steady progress on energy regulation implementation in Europe, North America, and Asia, with the highest number of building energy standards being adopted and implemented. Moreover, the performance of Europe is highly encouraging concerning energy standard activities. They recorded the highest percentage of mandatory energy standards compared to the other five regions. In 2050, energy savings in Europe can reach 67% of the 2019 baseline scenario, amounting to a demand of 361 Mtoe in an "energy efficiency first" societal trend scenario. A condition is that there be no rebound effect, for otherwise the savings are 32% only or energy use may even increase by 42% if techno-economic potentials are not realized. Germany has reduced its primary energy consumption by 11% from 1990 to 2015 and set itself goals of reducing it by 30% by the year 2030 and by 50% by the year 2050 in comparison to the level of 2008. === India === The Petroleum Conservation Research Association (PCRA) is an Indian governmental body created in 1978 that engages in promoting energy efficiency and conservation in every walk of life. In the recent past, PCRA has organised mass media campaigns in television, radio, and print media. This is an impact-assessment survey by a third party that revealed that due to these larger campaigns by PCRA, the public's overall awareness level has gone up leading to the saving of fossil fuels worth crores of rupees, besides reducing pollution. The Bureau of Energy Efficiency is an Indian government organization created in 2001 that is responsible for promoting energy efficiency and conservation. Protection and Conservation of Natural Resources are done by Community Natural Resources Management (CNRM). === Iran === Supreme leader of Iran Ali Khamenei had regularly criticized energy administration and high fuel consumption. === Japan === Since the 1973 oil crisis, energy conservation has been an issue in Japan. All oil-based fuel is imported, so domestic sustainable energy is being developed. The Energy Conservation Center promotes energy efficiency in every aspect of Japan. Public entities are implementing the efficient use of energy for industries and research. It includes projects such as the Top Runner Program. In this project, new appliances are regularly tested on efficiency, and the most efficient ones are made the standard. === Middle East === The Middle East holds 40% of the world's crude oil reserves and 23% of its natural gas reserves. Conservation of domestic fossil fuels is, therefore, a legitimate priority for the Gulf countries, given domestic needs as well as the global market for these products. Energy subsidies are the chief barrier to conservation in the Gulf. Residential electricity prices can be a tenth of U.S. rates. As a result, increased tariff revenues from gas, electricity, and water sales would encourage investment in natural gas exploration and production and generation capacity, helping to alleviate future shortages. Households in the MENA region are responsible for 53% of energy use in Saudi Arabia and 57% of the UAE's ecological footprint. This is partially due to poorly designed and constructed buildings, mainly under a cheap energy model that has left them without contemporary control technology or even proper insulation and efficient appliances. Building energy consumption can be cut by 20% under a combination of insulation, efficient windows and appliances, shading, reflective roofing, and a host of automated controls that adjust energy use. Governments could also set minimum energy efficiency and water use standards on importing appliances sold inside their countries, effectively banning the sale of inefficient air conditioners, dishwashers, and washing machines. Administration of the laws would essentially be a function of national customs services. Governments could go further, offering incentives – or mandates – that air conditioners of a certain age be replaced. ==== Lebanon ==== In Lebanon and since 2002 The Lebanese Center for Energy Conservation (LCEC) has been promoting the development of efficient and rational uses of energy and the use of renewable energy at the consumer level. It was created as a project financed by the International Environment Facility (GEF) and the Ministry of Energy Water (MEW) under the management of the United Nations Development Programme (UNDP) and gradually established itself as an independent technical national center although it continues to be supported by the United Nations Development Programme (UNDP) as indicated in the Memorandum of Understanding (MoU) signed between MEW and UNDP on 18 June 2007. === Nepal === Until recently, Nepal has been focusing on the exploitation of its huge water resources to produce hydropower. Demand-side management and energy conservation were not in the focus of government action. In 2009, bilateral Development Cooperation between Nepal and the Federal Republic of Germany has agreed upon the joint implementation of the "Nepal Energy Efficiency Programme". The lead executing agencies for the implementation are the Water and Energy Commission Secretariat (WECS). The aim of the program is the promotion of energy efficiency in policymaking, in rural and urban households as well as in the industry. Due to the lack of a government organization that promotes energy efficiency in the country, the Federation of Nepalese Chambers of Commerce and Industry (FNCCI) has established the Energy Efficiency Centre under his roof to promote energy conservation in the private sector. The Energy Efficiency Centre is a non-profit initiative that is offering energy auditing services to the industries. The centre is also supported by Nepal Energy Efficiency Programme of Deutsche Gesellschaft für Internationale Zusammenarbeit. A study conducted in 2012 found out that Nepalese industries could save 160,000-megawatt hours of electricity and 8,000 terajoules of thermal energy (like diesel, furnace oil, and coal) every year. These savings are equivalent to annual energy cost cut of up to 6.4 Billion Nepalese Rupees. As a result of Nepal Economic Forum 2014, an economic reform agenda in the priority sectors was declared focusing on energy conservation among others. In the energy reform agenda, the government of Nepal gave the commitment to introduce incentive packages in the budget of the fiscal year 2015/16 for industries that practices energy efficiency or use efficient technologies (incl. cogeneration). === New Zealand === In New Zealand the Energy Efficiency and Conservation Authority is the Government Agency responsible for promoting energy efficiency and conservation. The Energy Management Association of New Zealand is a membership-based organization representing the New Zealand energy services sector, providing training and accreditation services with the aim of ensuring energy management services are credible and dependable. === Nigeria === In Nigeria, the Lagos State Government is encouraging Lagosians to imbibe an energy conservation culture. In 2013, the Lagos State Electricity Board (LSEB) ran an initiative tagged "Conserve Energy, Save Money" under the Ministry of Energy and Mineral Resources. The initiative is designed to sensitize Lagosians around the theme of energy conservation by influencing their behavior through do-it-yourself tips. In September 2013, Governor Babatunde Raji Fashola of Lagos State and the campaign ambassador, rapper Jude "MI" Abaga participated in the Governor's conference video call on the topic of energy conservation. In addition to this, during the month of October (the official energy conservation month in the state), LSEB hosted experience centers in malls around Lagos State where members of the public were encouraged to calculate their household energy consumption and discover ways to save money using a consumer-focused energy app. To get Lagosians started on energy conservation, solar lamps and energy-saving bulbs were also handed out. In Kaduna State, the Kaduna Power Supply Company (KAPSCO) ran a program to replace all light bulbs in Public Offices; fitting energy-saving bulbs in place of incandescent bulbs. KAPSCO is also embarking on an initiative to retrofit all conventional streetlights in the Kaduna Metropolis to LEDs which consume much less energy. === Sri Lanka === Sri Lanka currently consumes fossil fuels, hydro power, wind power, solar power and dendro power for their day to day power generation. The Sri Lanka Sustainable Energy Authority is playing a major role regarding energy management and energy conservation. Today, most industries are requested to reduce their energy consumption by using renewable energy sources and optimizing their energy usage. === Turkey === Turkey aims to decrease by at least 20% the amount of energy consumed per GDP of Turkey by 2023 (energy intensity). === United Kingdom === The Department for Business, Energy and Industrial Strategy is responsible for promoting energy efficiency in the United Kingdom. === United States === The United States is currently the second-largest single consumer of energy, following China. The U.S. Department of Energy categorizes national energy use in four broad sectors: transportation, residential, commercial, and industrial. About half of U.S. energy consumption in the transportation and residential sectors is primarily controlled by individual consumers. In the typical American home, space heating is the most significant energy use, followed by electrical technology (appliances, lighting, and electronics) and water heating. Commercial and industrial energy expenditures are determined by businesses entities and other facility managers. National energy policy has a significant effect on energy usage across all four sectors. Since the oil embargoes and price spikes of the 1970s, energy efficiency and conservation have been fundamental tenets of U.S. energy policy. The scope of energy conservation and efficiency measures has been broadened throughout time by U.S. energy policies and programs, including federal and state legislation and regulatory actions, to include all economic sectors and all geographical areas of the nation. Measurable energy conservation and efficiency gains in the 1980s led to the 1987 Energy Security Report to the President (DOE, 1987) that "the United States uses about 29 quads less energy in a year today than it would have if our economic growth since 1972 had been accompanied by the less- efficient trends in energy use we were following at that time" The DOE Strategy and the legislation included new strategies for strengthening conservation and efficiency in buildings, industry, and electric power, such as integrated resource planning for electric and natural gas utilities and efficiency and labeling standards for 13 residential appliances and equipment categories. Lack of a national consensus on how to proceed interfered with developing a consistent and comprehensive approach. Nevertheless, the Energy Policy Act of 2005 (EPAct05; 109th U.S. Congress, 2005) contained many new energy conservation and efficiency provisions in the transportation, buildings, and electric power sectors. The most recent federal law to increase and broaden U.S. energy conservation and efficiency laws, programs, and practices is the Energy Independence and Security Act of 2007 (EISA). Over the next few decades, it is anticipated that EISA will significantly reduce energy use because it has more standards and targets than previous legislation. Both acts reinforce the importance of lighting and appliance efficiency programs, targeting an additional 70% lighting efficiency by 2020, introducing 45 new standards for appliances, and setting up new standards for vehicle fuel economy. The Federal Government is also promoting a new 30% model code for efficient building practices in the construction industry. Additionally, according to the American Council for an Energy-Efficient Economy (ACEEE), the EISA's energy efficiency and conservation initiatives will cut carbon dioxide emissions by 9% in 2030. These requirements cover appliance and lighting efficiency, energy savings in homes, businesses, and public buildings, the effectiveness of industrial manufacturing facilities, and the efficiency of electricity supply and end use. Expectations are high for increased energy savings due to these initiatives, which have already started contributing to new federal, state, and local laws, programs, and practices across the U.S. The development and use of alternative transportation fuels (whose supply is expected to expand by 15% by 2022), renewable energy sources, and other clean energy technologies have also received more attention and financial incentives. Recent policies also emphasize growing the use of coal with carbon capture and sequestration, solar, wind, nuclear, and other clean energy sources. In February 2023 the United States Department of Energy proposed a set of new energy efficiency standards that, if implemented, will save to users of different electric machines in the United States around $3,500,000,000 per year and will reduce by the year 2050 carbon emissions by the same amount as emitted by 29,000,000 houses. == Mechanisms to promote conservation == === Governmental mechanisms === Governments at the national, regional, and local levels may implement policies to promote energy efficiency. Building energy rules can cover the energy consumption of an entire structure or specific building components, like heating and cooling systems. They represent some of the most frequently used instruments for energy efficiency improvements in buildings and can play an essential role in improving energy conservation in buildings. There are multiple reasons for the growth of these policies and programs since the 2000s, including cost savings as energy prices increased, growing concern about the environmental impacts of energy use, and public health concerns. The policies and programs related to energy conservation are critical to establishing safety and performance levels, assisting in consumer decision-making, and explicitly identifying energy-conserving and energy-efficient products. Recent policies include new programs and regulatory incentives that call for electric and natural gas utilities to increase their involvement in delivering energy-efficiency products and services to their customers. For example, the National Action Plan for Energy Efficiency (NAPEE) is a public-private partnership created in response to EPAct05 that brings together senior executives from electric and natural gas utilities, state public utility commissions, other state agencies, and environmental and consumer groups representing every region of the country. The success of building energy regulation in effectively controlling energy consumption in the building sector will be, to a great extent, associated with the adopted energy performance indicator and the promoted energy assessment tools. It can help overcome significant market barriers and ensure cost-effective energy efficiency opportunities are incorporated into new buildings. This is crucial in emerging nations where new constructions are rapidly developing, and market and energy prices sometimes discourage efficient technologies. The building energy standards development and adoption showed that 42% of emerging developing countries surveyed have no energy standard in place, 20% have mandatory, 22% have mixed, and 16% proposed. The major impediments to implementing building energy regulations for energy conservation and efficiency in the building sector are institutional barriers and market failures rather than technical problems, as pointed out by Nature Publishing Group (2008). Among these, Santamouris (2005) includes a lack of owners' awareness of energy conservation benefits, building energy regulations benefits, insufficient awareness and training of property managers, builders, and engineers, and a lack of specialized professionals to ensure compliance. Based on the above information, the development and adoption of building energy regulations, such as energy standards in developing countries, are still far behind compared to building energy regulation adoption and implementation in developed countries. Building energy standards are starting to appear in Africa, Latin America, and Middle East regions, even though this is a new development going to the result obtained in this study. The level of progress on energy regulation activities in Africa, Latin America, and the Middle East is increasing, given the higher number of energy standard proposals recorded in these regions. According to the Royal Institute of Chartered Surveyors, several codes are being developed in developing countries with UNDP and GEF support. These typically include elemental and integrated routes to compliance, such as a fundamental method defining the performance requirements of specific building elements. However, they are still far behind in building energy regulation development, implementation, and compliance compared to developed nations. Also, decision-making regarding energy regulations is still from the government only, with little or no input from non-governmental entities. As a result, lower energy regulation development is recorded in these regions compared to regions with integrated and consensus approaches. Additionally, there is growing government involvement in the development and implementation of energy standards; 62% of Middle Eastern respondents, 45% of African respondents, and 43% of Latin American respondents indicated that existing government agencies, such as building agencies and energy agencies, are involved in implementing building energy standards in their respective nations, as opposed to 20% of European respondents, 38% of Asian respondents, and 0% of North American respondents, who indicated the involvement of existing agencies. Several North African nations, like Tunisia and Egypt, have programs relating to building energy standards, while Algeria and Morocco are now seeking to establish building energy standards, according to the Royal Institute of Chartered Surveyors. Similarly, Egypt's residential energy standard became law in 2005, and their commercial standard was anticipated to follow. The standards provide minimal performance requirements for applications involving air conditioners and other appliances and elemental and integrated pathways. However, it was claimed that enforcement legislation was still required in 2005. Additionally, Morocco launched a program in 2005 to create thermal energy requirements for construction, concentrating on the hospitality, healthcare, and communal housing industries. ==== Mandatory energy standards ==== Energy standards are the primary way governments foster energy efficiency as a public good. A recognized standard-setting organization prepares a standard. Standards developed by recognized organizations are often used as the basis for the development and updating of building codes. They allow innovative approaches and techniques to achieve effective energy use and optimum building performance. Besides, it encourages cost-effective energy use of building components, including building envelope, lighting, HVAC, electrical installations, lift and escalator, and other equipment. Energy-efficiency standards have been expanded and strengthened for appliances, building equipment, and lighting. For example, appliances and equipment standards are being developed for a new range of devices, including reduction goals for "standby" power that keeps consumer electronic products in a ready-to-use mode. Some devices require certain levels of energy performance from a car, building, appliance, or other technical equipment. If the vehicle, building, appliance, or equipment does not meet these standards, there may be restrictions on its sale or rent. In the U.K., these are called "minimum energy efficiency standards" or MEES and were applied to privately rented accommodation in 2019. Energy codes and standards are vital in setting minimum energy-efficient design and construction requirements. Buildings should be developed following energy standards to save energy efficiently. They specify uniform requirements for new buildings, additions, and modifications. National organizations like the American Society of Heating, Refrigerating, and Air-Conditioning Engineers publish the standards (ASHRAE). State and municipal governments frequently use energy standards as the technical foundation for creating their energy regulations. Some energy standards are written in a mandatory and enforceable language, making it simple for governments to add the standards' provisions directly to their laws or regulations. The American Society of Heating, Refrigeration, and Air-Conditioning Engineers (ASHRAE) is a well-known example of a standard-making organization. This organization dates to the nineteenth century and is international in its membership (About ASHRAE 2018). Examples of ASHRAE standards that relate to energy conservation in the built environment are: Standard 62.1-2016 Ventilation for Acceptable Indoor Air Quality Standard 90.2-2007 Energy Efficient Design of Low-Rise Residential Buildings Standard 100-2018 Energy Efficiency in Existing Buildings Standard 189.1-2014 Standard for the Design of High-Performance Green Buildings The Residential Energy Services Network is a crucial benchmark for energy reduction (RESNET). The Home Energy Rating System (HERS) of RESNET, which is based on the International Code Council's (ICC) energy code, is used to rate home energy consumption with a standard numerical scale that examines factors in home energy use (About HERS 2018). The American National Standards Institute (ANSI) has acknowledged the HERS assessment system as a national benchmark for evaluating energy efficiency. The International Energy Conservation Code (IECC) of the ICC requires an energy rating index, and the main index used in the residential building sector is HERS. The mortgage financing sector makes substantial use of the HERS index. A home's expected energy usage may impact the available mortgage funds based on the HERS score, with more energy-efficient, lower energy-using homes potentially qualifying for a better mortgage rate or amount. ==== Mandatory energy labels ==== Many governments require that a car, building, or piece of equipment be labeled with its energy performance. This allows consumers and customers to see the energy implications of their choices, but does not restrict their choices or regulate which products are available to choose from. It also does not enable easily comparing options (such as being able to filter by energy-efficiency in online stores) or have the best energy-conserving options accessible (such as energy-conserving options being available in the frequented local store). (An analogy would be nutritional labeling on food.) A trial of estimated financial energy cost of refrigerators alongside EU energy-efficiency class (EEEC) labels online found that the approach of labels involves a trade-off between financial considerations and higher cost requirements in effort or time for the product-selection from the many available options which are often unlabelled and don't have any EEEC-requirement for being bought, used or sold within the EU. Moreover, in this one trial the labeling was ineffective in shifting purchases towards more sustainable options. ==== Energy taxes ==== Some countries employ energy or carbon taxes to motivate energy users to reduce their consumption. Carbon taxes can motivate consumption to shift to energy sources with fewer emissions of carbon dioxide, such as solar power, wind power, hydroelectricity or nuclear power while avoiding cars with combustion engines, jet fuel, oil, fossil gas and coal. On the other hand, taxes on all energy consumption can reduce energy use across the board while reducing a broader array of environmental consequences arising from energy production. The state of California employs a tiered energy tax whereby every consumer receives a baseline energy allowance that carries a low tax. As for usage increases above that baseline, the tax increases drastically. Such programs aim to protect poorer households while creating a larger tax burden for high energy consumers. Developing countries specifically are less likely to impose policy measures that slow carbon emissions as this would slow their economic development. These growing countries may be more likely to support their own economic growth and support their citizens rather than decreasing their carbon emissions. The following pros and cons of a carbon tax help one to see some of the potential effects of a carbon tax policy. Pros of Carbon Tax include: Making polluters pay the external cost of carbon emissions. Enables greater social efficiency as all citizens pay the full social cost. Raises revenue which can, in turn, be spent on mitigating the effects of pollution. Encourages firms and consumers to search for non-carbon producing alternatives (ex. solar power, wind power, hydroelectricity, or nuclear power). Reduces environmental costs associated with excess carbon pollution. Cons of Carbon Tax include: Businesses claim higher taxes which can discourage investment and economic growth. A carbon tax may encourage tax evasion as firms may pollute in secret to avoid a carbon tax. It may be difficult to measure external costs and how much the carbon tax should truly be. There are administration costs in measuring pollution and collecting the associated tax. Firms may move production to countries in which there is no carbon tax. === Non-governmental mechanisms === ==== Voluntary energy standards ==== Another aspect of promoting energy efficiency is using the Leadership in Energy and Environmental Design (LEED) voluntary building design standards. This program is supported by the US Green Building Council. The "Energy and Atmosphere" Prerequisite applies to energy issues, it focuses on energy performance, renewable energy, and other. See green building. == See also == == References == == Further reading == GA Mansoori, N Enayati, LB Agyarko (2016), Energy: Sources, Utilization, Legislation, Sustainability, Illinois as Model State, World Sci. Pub. Co., ISBN 978-981-4704-00-7 Alexeew, Johannes; Carolin Anders and Hina Zia (2015): Energy-efficient buildings – a business case for India? An analysis of incremental costs for four building projects of the Energy-Efficient Homes Programme. Berlin/New Delhi: Adelphi/TERI Gary Steffy, Architectural Lighting Design, John Wiley and Sons (2001) ISBN 0-471-38638-3 Lumina Technologies, Analysis of energy consumption in a San Francisco Bay Area research office complex, for the (confidential) owner, Santa Rosa, Ca. 17 May 1996 Robb, Drew (2 June 2007). "GSA paves way for IT-based buildings – Government Computer News". Gcn.com. Archived from the original on 25 December 2008. Retrieved 29 July 2010. == External links == bigEE – Your guide to energy efficiency in buildings Energy saving advice and grants for UK consumers Energy efficiency and renewable energy at the U.S. Department of Energy EnergyStar Archived 28 June 2013 at the Wayback Machine – for commercial buildings and plants Ulrich Hottelet: Want to Save the Earth? Pick a Clothesline, Atlantic Times, November 2007 Energy Efficiency in Asia and the Pacific Asian Development Bank Energy Saving Tips Save up to $100 on power bills per year by switching off any unused appliances.
Wikipedia/Energy_conservation
In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system. The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its sign indicates whether the process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy, it is not absolute but depends on the choice of a zero point. Therefore, only relative free energy values, or changes in free energy, are physically meaningful. The free energy is the portion of any first-law energy that is available to perform thermodynamic work at constant temperature, i.e., work mediated by thermal energy. Free energy is subject to irreversible loss in the course of such work. Since first-law energy is always conserved, it is evident that free energy is an expendable, second-law kind of energy. Several free energy functions may be formulated based on system criteria. Free energy functions are Legendre transforms of the internal energy. The Gibbs free energy is given by G = H − TS, where H is the enthalpy, T is the absolute temperature, and S is the entropy. H = U + pV, where U is the internal energy, p is the pressure, and V is the volume. G is the most useful for processes involving a system at constant pressure p and temperature T, because, in addition to subsuming any entropy change due merely to heat, a change in G also excludes the p dV work needed to "make space for additional molecules" produced by various processes. Gibbs free energy change therefore equals work not associated with system expansion or compression, at constant temperature and pressure, hence its utility to solution-phase chemists, including biochemists. The historically earlier Helmholtz free energy is defined in contrast as A = U − TS. Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation "work content", and the designation A (from German Arbeit 'work'). Since it makes no reference to any quantities involved in work (such as p and V), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by a system at constant temperature, and it can increase at most by the amount of work done on a system isothermally. The Helmholtz free energy has a special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore p dV work.) Historically, the term 'free energy' has been used for either quantity. In physics, free energy most often refers to the Helmholtz free energy, denoted by A (or F), while in chemistry, free energy most often refers to the Gibbs free energy. The values of the two free energies are usually quite similar and the intended free energy function is often implicit in manuscripts and presentations. == Meaning of "free" == The basic definition of "energy" is a measure of a body's (in thermodynamics, the system's) ability to cause change. For example, when a person pushes a heavy box a few metres forward, that person exerts mechanical energy, also known as work, on the box over a distance of a few meters forward. The mathematical definition of this form of energy is the product of the force exerted on the object and the distance by which the box moved (Work = Force × Distance). Because the person changed the stationary position of the box, that person exerted energy on that box. The work exerted can also be called "useful energy", because energy was converted from one form into the intended purpose, i.e. mechanical use. For the case of the person pushing the box, the energy in the form of internal (or potential) energy obtained through metabolism was converted into work to push the box. This energy conversion, however, was not straightforward: while some internal energy went into pushing the box, some was diverted away (lost) in the form of heat (transferred thermal energy). For a reversible process, heat is the product of the absolute temperature T {\displaystyle T} and the change in entropy S {\displaystyle S} of a body (entropy is a measure of disorder in a system). The difference between the change in internal energy, which is Δ U {\displaystyle \Delta U} , and the energy lost in the form of heat is what is called the "useful energy" of the body, or the work of the body performed on an object. In thermodynamics, this is what is known as "free energy". In other words, free energy is a measure of work (useful energy) a system can perform at constant temperature. Mathematically, free energy is expressed as A = U − T S {\displaystyle A=U-TS} This expression has commonly been interpreted to mean that work is extracted from the internal energy U {\displaystyle U} while T S {\displaystyle TS} represents energy not available to perform work. However, this is incorrect. For instance, in an isothermal expansion of an ideal gas, the internal energy change is Δ U = 0 {\displaystyle \Delta U=0} and the expansion work w = − T Δ S {\displaystyle w=-T\Delta S} is derived exclusively from the T S {\displaystyle TS} term supposedly not available to perform work. But it is noteworthy that the derivative form of the free energy: d A = − S d T − P d V {\displaystyle dA=-SdT-PdV} (for Helmholtz free energy) does indeed indicate that a spontaneous change in a non-reactive system's free energy (NOT the internal energy) comprises the available energy to do work (compression in this case) − P d V {\displaystyle -PdV} and the unavailable energy − S d T {\displaystyle -SdT} . Similar expression can be written for the Gibbs free energy change. In the 18th and 19th centuries, the theory of heat, i.e., that heat is a form of energy having relation to vibratory motion, was beginning to supplant both the caloric theory, i.e., that heat is a fluid, and the four element theory, in which heat was the lightest of the four elements. In a similar manner, during these years, heat was beginning to be distinguished into different classification categories, such as "free heat", "combined heat", "radiant heat", specific heat, heat capacity, "absolute heat", "latent caloric", "free" or "perceptible" caloric (calorique sensible), among others. In 1780, for example, Laplace and Lavoisier stated: “In general, one can change the first hypothesis into the second by changing the words ‘free heat, combined heat, and heat released’ into ‘vis viva, loss of vis viva, and increase of vis viva.’" In this manner, the total mass of caloric in a body, called absolute heat, was regarded as a mixture of two components; the free or perceptible caloric could affect a thermometer, whereas the other component, the latent caloric, could not. The use of the words "latent heat" implied a similarity to latent heat in the more usual sense; it was regarded as chemically bound to the molecules of the body. In the adiabatic compression of a gas, the absolute heat remained constant but the observed rise in temperature implied that some latent caloric had become "free" or perceptible. During the early 19th century, the concept of perceptible or free caloric began to be referred to as "free heat" or "heat set free". In 1824, for example, the French physicist Sadi Carnot, in his famous "Reflections on the Motive Power of Fire", speaks of quantities of heat ‘absorbed or set free’ in different transformations. In 1882, the German physicist and physiologist Hermann von Helmholtz coined the phrase ‘free energy’ for the expression A = U − T S {\displaystyle A=U-TS} , in which the change in A (or G) determines the amount of energy ‘free’ for work under the given conditions, specifically constant temperature.: 235  Thus, in traditional use, the term "free" was attached to Gibbs free energy for systems at constant pressure and temperature, or to Helmholtz free energy for systems at constant temperature, to mean ‘available in the form of useful work.’ With reference to the Gibbs free energy, we need to add the qualification that it is the energy free for non-volume work and compositional changes.: 77–79  An increasing number of books and journal articles do not include the attachment "free", referring to G as simply Gibbs energy (and likewise for the Helmholtz energy). This is the result of a 1988 IUPAC meeting to set unified terminologies for the international scientific community, in which the adjective ‘free’ was supposedly banished. This standard, however, has not yet been universally adopted, and many published articles and books still include the descriptive ‘free’. == Application == Just like the general concept of energy, free energy has a few definitions suitable for different conditions. In physics, chemistry, and biology, these conditions are thermodynamic parameters (temperature T {\displaystyle T} , volume V {\displaystyle V} , pressure p {\displaystyle p} , etc.). Scientists have come up with several ways to define free energy. The mathematical expression of Helmholtz free energy is: A = U − T S {\displaystyle A=U-TS} This definition of free energy is useful for gas-phase reactions or in physics when modeling the behavior of isolated systems kept at a constant volume. For example, if a researcher wanted to perform a combustion reaction in a bomb calorimeter, the volume is kept constant throughout the course of a reaction. Therefore, the heat of the reaction is a direct measure of the free energy change, q = Δ A {\displaystyle q=\Delta A} . In solution chemistry, on the other hand, most chemical reactions are kept at constant pressure. Under this condition, the heat q {\displaystyle q} of the reaction is equal to the enthalpy change Δ H {\displaystyle \Delta H} of the system. Under constant pressure and temperature, the free energy in a reaction is known as Gibbs free energy G {\displaystyle G} . G = H − T S {\displaystyle G=H-TS} These functions have a minimum in chemical equilibrium, as long as certain variables ( T {\displaystyle T} , and V {\displaystyle V} or p {\displaystyle p} ) are held constant. In addition, they also have theoretical importance in deriving Maxwell relations. Work other than p dV may be added, e.g., for electrochemical cells, or f dx work in elastic materials and in muscle contraction. Other forms of work which must sometimes be considered are stress-strain, magnetic, as in adiabatic demagnetization used in the approach to absolute zero, and work due to electric polarization. These are described by tensors. In most cases of interest there are internal degrees of freedom and processes, such as chemical reactions and phase transitions, which create entropy. Even for homogeneous "bulk" materials, the free energy functions depend on the (often suppressed) composition, as do all proper thermodynamic potentials (extensive functions), including the internal energy. N i {\displaystyle N_{i}} is the number of molecules (alternatively, moles) of type i {\displaystyle i} in the system. If these quantities do not appear, it is impossible to describe compositional changes. The differentials for processes at uniform pressure and temperature are (assuming only p V {\displaystyle pV} work): d A = − p d V − S d T + ∑ i μ i d N i {\displaystyle \mathrm {d} A=-p\,\mathrm {d} V-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,} d G = V d p − S d T + ∑ i μ i d N i {\displaystyle \mathrm {d} G=V\,\mathrm {d} p-S\,\mathrm {d} T+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,} where μi is the chemical potential for the ith component in the system. The second relation is especially useful at constant T {\displaystyle T} and p {\displaystyle p} , conditions which are easy to achieve experimentally, and which approximately characterize living creatures. Under these conditions, it simplifies to ( d G ) T , p = ∑ i μ i d N i {\displaystyle (\mathrm {d} G)_{T,p}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,} Any decrease in the Gibbs function of a system is the upper limit for any isothermal, isobaric work that can be captured in the surroundings, or it may simply be dissipated, appearing as T {\displaystyle T} times a corresponding increase in the entropy of the system and/or its surrounding. An example is surface free energy, the amount of increase of free energy when the area of surface increases by every unit area. The path integral Monte Carlo method is a numerical approach for determining the values of free energies, based on quantum dynamical principles. === Work and free energy change === For a reversible isothermal process, ΔS = qrev/T and therefore the definition of A results in Δ A = Δ U − T Δ S = Δ U − q rev = w rev {\displaystyle \Delta A=\Delta U-T\Delta S=\Delta U-q_{\text{rev}}=w_{\text{rev}}} (at constant temperature) This tells us that the change in free energy equals the reversible or maximum work for a process performed at constant temperature. Under other conditions, free-energy change is not equal to work; for instance, for a reversible adiabatic expansion of an ideal gas, Δ A = w rev − S Δ T {\displaystyle \Delta A=w_{\text{rev}}-S\Delta T} . Importantly, for a heat engine, including the Carnot cycle, the free-energy change after a full cycle is zero, Δ cyc A = 0 {\displaystyle \Delta _{\text{cyc}}A=0} , while the engine produces nonzero work. It is important to note that for heat engines and other thermal systems, the free energies do not offer convenient characterizations; internal energy and enthalpy are the preferred potentials for characterizing thermal systems. === Free energy change and spontaneous processes === According to the second law of thermodynamics, for any process that occurs in a closed system, the inequality of Clausius, ΔS > q/Tsurr, applies. For a process at constant temperature and pressure without non-PV work, this inequality transforms into Δ G < 0 {\displaystyle \Delta G<0} . Similarly, for a process at constant temperature and volume, Δ A < 0 {\displaystyle \Delta A<0} . Thus, a negative value of the change in free energy is a necessary condition for a process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0. == History == The quantity called "free energy" is a more advanced and accurate replacement for the outdated term affinity, which was used by chemists in previous years to describe the force that caused chemical reactions. The term affinity, as used in chemical relation, dates back to at least the time of Albertus Magnus. From the 1998 textbook Modern Thermodynamics by Nobel Laureate and chemistry professor Ilya Prigogine we find: "As motion was explained by the Newtonian concept of force, chemists wanted a similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked a clear definition." During the entire 18th century, the dominant view with regard to heat and light was that put forth by Isaac Newton, called the Newtonian hypothesis, which states that light and heat are forms of matter attracted or repelled by other forms of matter, with forces analogous to gravitation or to chemical affinity. In the 19th century, the French chemist Marcellin Berthelot and the Danish chemist Julius Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for a large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of a system of bodies which liberate heat. In addition to this, in 1780 Antoine Lavoisier and Pierre-Simon Laplace laid the foundations of thermochemistry by showing that the heat given out in a reaction is equal to the heat absorbed in the reverse reaction. They also investigated the specific heat and latent heat of a number of substances, and amounts of heat given out in combustion. In a similar manner, in 1840 Swiss chemist Germain Hess formulated the principle that the evolution of heat in a reaction is the same whether the process is accomplished in one-step process or in a number of stages. This is known as Hess' law. With the advent of the mechanical theory of heat in the early 19th century, Hess's law came to be viewed as a consequence of the law of conservation of energy. Based on these and other ideas, Berthelot and Thomsen, as well as others, considered the heat given out in the formation of a compound as a measure of the affinity, or the work done by the chemical forces. This view, however, was not entirely correct. In 1847, the English physicist James Joule showed that he could raise the temperature of water by turning a paddle wheel in it, thus showing that heat and mechanical work were equivalent or proportional to each other, i.e., approximately, dW ∝ dQ. This statement came to be known as the mechanical equivalent of heat and was a precursory form of the first law of thermodynamics. By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment. That is, one can use the heat derived from a combustion reaction in a coal furnace to boil water, and use this heat to vaporize steam, and then use the enhanced high-pressure energy of the vaporized steam to push a piston. Thus, we might naively reason that one can entirely convert the initial combustion heat of the chemical reaction into the work of pushing the piston. Clausius showed, however, that we must take into account the work that the molecules of the working body, i.e., the water molecules in the cylinder, do on each other as they pass or transform from one step of or state of the engine cycle to the next, e.g., from ( P 1 , V 1 {\displaystyle P_{1},V_{1}} ) to ( P 2 , V 2 {\displaystyle P_{2},V_{2}} ). Clausius originally called this the "transformation content" of the body, and then later changed the name to entropy. Thus, the heat used to transform the working body of molecules from one state to the next cannot be used to do external work, e.g., to push the piston. Clausius defined this transformation heat as d Q = T d S {\displaystyle dQ=TdS} . In 1873, Willard Gibbs published A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces, in which he introduced the preliminary outline of the principles of his new equation able to predict or estimate the tendencies of various natural processes to ensue when bodies or systems are brought into contact. By studying the interactions of homogeneous substances in contact, i.e., bodies, being in composition part solid, part liquid, and part vapor, and by using a three-dimensional volume-entropy-internal energy graph, Gibbs was able to determine three states of equilibrium, i.e., "necessarily stable", "neutral", and "unstable", and whether or not changes will ensue. In 1876, Gibbs built on this framework by introducing the concept of chemical potential so to take into account chemical reactions and states of bodies that are chemically different from each other. In his own words, to summarize his results in 1873, Gibbs states: If we wish to express in a single equation the necessary and sufficient condition of thermodynamic equilibrium for a substance when surrounded by a medium of constant pressure p and temperature T, this equation may be written: when δ refers to the variation produced by any variations in the state of the parts of the body, and (when different parts of the body are in different states) in the proportion in which the body is divided between the different states. The condition of stable equilibrium is that the value of the expression in the parenthesis shall be a minimum. In this description, as used by Gibbs, ε refers to the internal energy of the body, η refers to the entropy of the body, and ν is the volume of the body. Hence, in 1882, after the introduction of these arguments by Clausius and Gibbs, the German scientist Hermann von Helmholtz stated, in opposition to Berthelot and Thomas' hypothesis that chemical affinity is a measure of the heat of reaction of chemical reaction as based on the principle of maximal work, that affinity is not the heat given out in the formation of a compound but rather it is the largest quantity of work which can be gained when the reaction is carried out in a reversible manner, e.g., electrical work in a reversible cell. The maximum work is thus regarded as the diminution of the free, or available, energy of the system (Gibbs free energy G at T = constant, P = constant or Helmholtz free energy A at T = constant, V = constant), whilst the heat given out is usually a measure of the diminution of the total energy of the system (Internal energy). Thus, G or A is the amount of energy "free" for work under the given conditions. Up until this point, the general view had been such that: “all chemical reactions drive the system to a state of equilibrium in which the affinities of the reactions vanish”. Over the next 60 years, the term affinity came to be replaced with the term free energy. According to chemistry historian Henry Leicester, the influential 1923 textbook Thermodynamics and the Free Energy of Chemical Reactions by Gilbert N. Lewis and Merle Randall led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world. == See also == Energy Exergy Merle Randall Second law of thermodynamics Superconductivity == References ==
Wikipedia/Thermodynamic_free_energy
Waste-to-energy (WtE) or energy-from-waste (EfW) refers to a series of processes designed to convert waste materials into usable forms of energy, typically electricity or heat. As a form of energy recovery, WtE plays a crucial role in both waste management and sustainable energy production by reducing the volume of waste in landfills and providing an alternative energy source. The most common method of WtE is direct combustion of waste to produce heat, which can then be used to generate electricity via steam turbines. This method is widely employed in many countries and offers a dual benefit: it disposes of waste while generating energy, making it an efficient process for both waste reduction and energy production. In addition to combustion, other WtE technologies focus on converting waste into fuel sources. For example, gasification and pyrolysis are processes that thermochemically decompose organic materials in the absence of oxygen to produce syngas, a synthetic gas primarily composed of hydrogen, carbon monoxide, and small amounts of carbon dioxide. This syngas can be converted into methane, methanol, ethanol, or even synthetic fuels, which can be used in various industrial processes or as alternative fuels in transportation. Furthermore, anaerobic digestion, a biological process, converts organic waste into biogas (mainly methane and carbon dioxide) through microbial action. This biogas can be harnessed for energy production or processed into biomethane, which can serve as a substitute for natural gas. The WtE process contributes to circular economy principles by transforming waste products into valuable resources, reducing dependency on fossil fuels, and mitigating greenhouse gas emissions. However, challenges remain, particularly in ensuring that emissions from WtE plants, such as dioxins and furans, are properly managed to minimize environmental impact. Advanced pollution control technologies are essential to address these concerns and ensure WtE remains a viable, environmentally sound solution. WtE technologies present a significant opportunity to manage waste sustainably while contributing to global energy demands. They represent an essential component of integrated waste management strategies and a shift toward renewable energy systems. As technology advances, WtE may play an increasingly critical role in both reducing landfill use and enhancing energy security. == History == The first incinerator or "Destructor" was built in Nottingham, UK, in 1874 by Manlove, Alliott & Co. Ltd. to the design of Alfred Fryer. The USA's first incinerator was built in 1885 on Governors Island in New York, New York. In 1903 first waste-to-energy unit in Denmark was built in Frederiksberg, Copenhagen. The first facility in the Czech Republic was built in 1905 in Brno.Gasification and pyrolysis processes have been known and used for centuries and for coal as early as the 18th century.... Development technologies for processing [residual solid mixed waste] has only become a focus of attention in recent years stimulated by the search for more efficient energy recovery. (2004) == Methods == === Incineration === Incineration, the combustion of organic material such as waste with energy recovery, is the most common WtE implementation. All new WtE plants in OECD countries incinerating waste (residual MSW, commercial, industrial or RDF) must meet strict emission standards, including those on nitrogen oxides (NOx), sulphur dioxide (SO2), heavy metals and dioxins. Hence, modern incineration plants are vastly different from old types, some of which neither recovered energy nor materials. Modern incinerators reduce the volume of the original waste by 95-96 percent, depending upon composition and degree of recovery of materials such as metals from the ash for recycling. Incinerators may emit fine particulate, heavy metals, trace dioxin and acid gas, even though these emissions are relatively low from modern incinerators. Other concerns include proper management of residues: toxic fly ash, which must be handled in hazardous waste disposal installation as well as incinerator bottom ash (IBA), which must be reused properly. Critics argue that incinerators destroy valuable resources and they may reduce incentives for recycling. The question, however, is an open one, as European countries which recycle the most (up to 70%) also incinerate to avoid landfilling. Incinerators have electric efficiencies of 14-28%. In order to avoid losing the rest of the energy, it can be used for e.g. district heating (cogeneration). The total efficiencies of cogeneration incinerators are typically higher than 80% (based on the lower heating value of the waste). The method of incineration to convert municipal solid waste (MSW) is a relatively old method of WtE generation. Incineration generally entails burning waste (residual MSW, commercial, industrial and RDF) to boil water which powers steam generators that generate electric energy and heat to be used in homes, businesses, institutions and industries. One problem associated is the potential for pollutants to enter the atmosphere with the flue gases from the boiler. These pollutants can be acidic and in the 1980s were reported to cause environmental degradation by turning rain into acid rain. Modern incinerators incorporate carefully engineered primary and secondary burn chambers, and controlled burners designed to burn completely with the lowest possible emissions, eliminating, in some cases, the need for lime scrubbers and electro-static precipitators on smokestacks. By passing the smoke through the basic lime scrubbers, any acids that might be in the smoke are neutralized which prevents the acid from reaching the atmosphere and hurting the environment. Many other devices, such as fabric filters, reactors, and catalysts destroy or capture other regulated pollutants. According to the New York Times, modern incineration plants are so clean that "many times more dioxin is now released from home fireplaces and backyard barbecues than from incineration". According to the German Environmental Ministry, "because of stringent regulations, waste incineration plants are no longer significant in terms of emissions of dioxins, dust, and heavy metals". Compared with other waste to energy technologies, incineration seems to be the most attractive due to its higher power production efficiency, lower investment costs, and lower emission rates. Additionally, incineration yields the highest amount of electricity with the highest capacity to lessen pile of wastes in landfills through direct combustion. === Fuel from plastics === One process that is used to convert plastic into fuel is pyrolysis, the thermal decomposition of materials at high temperatures in an inert atmosphere. It involves change of chemical composition and is mainly used for treatment of organic materials. In large scale production, plastic waste is ground and melted and then pyrolyzed. Catalytic converters help in the process. The vapours are condensed with oil or fuel and accumulated in settling tanks and filtered. Fuel is obtained after homogenation and can be used for automobiles and machinery. It is commonly termed as thermofuel or energy from plastic. A new process uses a two-part catalyst, cobalt and zeolite, to convert plastics into propane. It works on polyethylene and polypropylene and the propane yield is approximately 80%. === Other === There are a number of other new and emerging technologies that are able to produce energy from waste and other fuels without direct combustion. Many of these technologies have the potential to produce more electric power from the same amount of fuel than would be possible by direct combustion. This is mainly due to the separation of corrosive components (ash) from the converted fuel, thereby allowing higher combustion temperatures in e.g. boilers, gas turbines, internal combustion engines, fuel cells. Some advanced technologies are able to efficiently convert the energy in the feedstocks into liquid or gaseous fuels, using heat but in the absence of oxygen, without actual combustion, by using a combination of thermal technologies. Typically, they are cleaner, as the feedstock is separated prior to treatment to remove the unwanted components: Thermal treatment technologies include: Gasification: produces combustible gas, hydrogen, synthetic fuels Thermal depolymerization: produces synthetic crude oil, which can be further refined Pyrolysis: produces combustible tar/bio-oil and chars Plasma arc gasification or plasma gasification process (PGP): produces rich syngas including hydrogen and carbon monoxide usable for fuel cells or generating electricity to drive the plasma arch, usable vitrified silicate and metal ingots, salt and sulphur Non-thermal technologies: Anaerobic digestion: Biogas rich in methane Fermentation production: examples are ethanol, lactic acid, hydrogen Mechanical biological treatment (MBT) MBT + Anaerobic digestion MBT to Refuse derived fuel == Global developments == During the 2001–2007 period, the waste-to-energy capacity increased by about four million metric tons per year. Japan and China each built several plants based on direct smelting or on fluidized bed combustion of solid waste. In China there were about 434 waste-to-energy plants in early 2016. Japan is the largest user in thermal treatment of municipal solid waste in the world, with 40 million tons annually. Some of the newest plants use stoker technology and others use the advanced oxygen enrichment technology. Several treatment plants exist worldwide using relatively novel processes such as direct smelting, the Ebara fluidization process and the Thermoselect JFE gasification and melting technology process. As of June 2014, Indonesia had a total of 93.5 MW installed capacity of waste-to-energy, with a pipeline of projects in different preparation phases together amounting to another 373MW of capacity. Biofuel Energy Corporation of Denver, Colorado, opened two new biofuel plants in Wood River, Nebraska, and Fairmont, Minnesota, in July 2008. These plants use distillation to make ethanol for use in motor vehicles and other engines. Both plants are currently reported to be working at over 90% capacity. Fulcrum BioEnergy, which started in 2007 in Pleasanton, California, built a WtE plant near Reno, NV to convert waste to sustainable aviation fuel (SAF). The plant was in commissioning from 2022 to May 2024 under the name Sierra BioFuels. Fulcrum predicted that the plant would produce approximately 10.5 million gallons per year of Fischer-Tropsch products from nearly 200,000 tons per year of MSW. The total exported product amounted to just 350 gallons of syncrude which were transported to Marathon Petroleum's refinery for conversion into jet fuel. The plant had issues including damage from unexpected generation of nitric acid and deposits of a concrete-like substance up to 10 feet thick in its gasification system. In 2024 Fulcrum BioEnergy ceased operations at the plant after defaulting on $290 million bonds issued through the Nevada Department of Business and Industry used to fund the plant's construction. Waste-to-energy technology includes fermentation, which can take biomass and create ethanol, using waste cellulosic or organic material. In the fermentation process, the sugar in the waste is converted to carbon dioxide and alcohol, in the same general process that is used to make wine. Normally fermentation occurs with no air present. Esterification can also be done using waste-to-energy technologies, and the result of this process is biodiesel. The cost-effectiveness of esterification will depend on the feedstock being used, and all the other relevant factors such as transportation distance, amount of oil present in the feedstock, and others. Gasification and pyrolysis by now can reach gross thermal conversion efficiencies (fuel to gas) up to 75%, however, a complete combustion is superior in terms of fuel conversion efficiency. Some pyrolysis processes need an outside heat source which may be supplied by the gasification process, making the combined process self-sustaining. == Carbon dioxide emissions == In thermal WtE technologies, nearly all of the carbon content in the waste is emitted as carbon dioxide (CO2) to the atmosphere (when including final combustion of the products from pyrolysis and gasification; except when producing biochar for fertilizer). Municipal solid waste (MSW) contain approximately the same mass fraction of carbon as CO2 itself (27%), so treatment of 1 metric ton (1.1 short tons) of MSW produce approximately 1 metric ton (1.1 short tons) of CO2. In the event that the waste was landfilled, 1 metric ton (1.1 short tons) of MSW would produce approximately 62 cubic metres (2,200 cu ft) methane via the anaerobic decomposition of the biodegradable part of the waste. This amount of methane has more than twice the global warming potential than the 1 metric ton (1.1 short tons) of CO2, which would have been produced by combustion. In some countries, large amounts of landfill gas are collected. However, there is still the global warming potential of the landfill gas being emitted to atmosphere. For example, in the US in 1999 landfill gas emission was approximately 32% higher than the amount of CO2 that would have been emitted by combustion. In addition, nearly all biodegradable waste is biomass. That is, it has biological origin. This material has been formed by plants using atmospheric CO2 typically within the last growing season. If these plants are regrown the CO2 emitted from their combustion will be taken out from the atmosphere once more. Such considerations are the main reason why several countries administrate WtE of the biomass part of waste as renewable energy. The rest—mainly plastics and other oil and gas derived products—is generally treated as non-renewables. The CO2 emissions from plastic waste-to-energy systems are higher than those from current fossil fuel-based power systems per unit of power generated, even after considering the contribution of carbon capture and storage. Power generation using plastic waste will significantly increase by 2050. Carbon must be separated during energy recovery processes. Otherwise, the fight against global warming would fail due to plastic waste. === Determination of the biomass fraction === MSW to a large extent is of biological origin (biogenic), e.g. paper, cardboard, wood, cloth, food scraps. Typically half of the energy content in MSW is from biogenic material. Consequently, this energy is often recognised as renewable energy according to the waste input. Several methods have been developed by the European CEN 343 working group to determine the biomass fraction of waste fuels, such as Refuse Derived Fuel/Solid Recovered Fuel. The initial two methods developed (CEN/TS 15440) were the manual sorting method and the selective dissolution method. A detailed systematic comparison of these two methods was published in 2010. Since each method suffered from limitations in properly characterizing the biomass fraction, two alternative methods have been developed. The first method uses the principles of radiocarbon dating. A technical review (CEN/TR 15591:2007) outlining the carbon 14 method was published in 2007. A technical standard of the carbon dating method (CEN/TS 15747:2008) was published in 2008. In the United States, there is already an equivalent carbon 14 method under the standard method ASTM D6866. The second method (so-called balance method) employs existing data on materials composition and operating conditions of the WtE plant and calculates the most probable result based on a mathematical-statistical model. Currently the balance method is installed at three Austrian and eight Danish incinerators. A comparison between both methods carried out at three full-scale incinerators in Switzerland showed that both methods came to the same results. Carbon 14 dating can determine with precision the biomass fraction of waste, and also determine the biomass calorific value. Determining the calorific value is important for green certificate programs such as the Renewable Obligation Certificate program in the United Kingdom. These programs award certificates based on the energy produced from biomass. Several research papers, including the one commissioned by the Renewable Energy Association in the UK, have been published that demonstrate how the carbon 14 result can be used to calculate the biomass calorific value. The UK gas and electricity markets authority, Ofgem, released a statement in 2011 accepting the use of Carbon 14 as a way to determine the biomass energy content of waste feedstock under their administration of the Renewables Obligation. Their Fuel Measurement and Sampling (FMS) questionnaire describes the information they look for when considering such proposals. == Physical location == A 2019 report commissioned by the Global Alliance for Incinerator Alternatives (GAIA), done by the Tishman Environment and Design Center at The New School, found that 79% of the then 73 operating waste-to-energy facilities in the U.S. are located in low-income communities and/or "communities of color", because "of historic residential, racial segregation and expulsive zoning laws that allowed whiter, wealthier communities to exclude industrial uses and people of color from their boundaries." In Chester, Pennsylvania, where a community group is actively opposing their local waste-to-energy facility, Sintana Vergara, an assistant professor in the Department of Environmental Resources Engineering at Humboldt State University in California, commented that community resistance is based on both the pollution and the fact that many of these facilities have been sited in communities without any community input, and without any benefits to the community. In other countries WtE facilities are located adjacent to residental housing without significant conflicts, also in high-income areas. One prominent example is Amager Bakke in central Copenhagen, Denmark == Notable examples == According to a 2019 United Nations Environment Programme report, there are 589 WtE plants in Europe and 82 in the United States. The following are some examples of WtE plants. === Waste incineration WtE plants === Essex County Resource Recovery Facility, Newark, New Jersey Harrisburg incinerator, Harrisburg, Pennsylvania Lee County Solid Waste Resource Recovery Facility, Fort Myers, Florida, USA (1994) Montgomery County Resource Recovery Facility in Dickerson, Maryland, USA (1995) Spittelau (1971), and Flötzersteig (1963), Vienna, Austria (Wien Energie) SYSAV waste-to-energy plant in Malmö (2003 and 2008), Sweden Algonquin Power, Brampton, Ontario, Canada Stoke Incinerator, Stoke-on-Trent, UK (1989) Delaware Valley Resource Recovery Facility, Chester, United States Teesside EfW plant near Middlesbrough, North East England (1998) Edmonton Incinerator in Greater London, England (1974) Burnaby Waste-to-Energy Facility, Metro Vancouver, Canada (1988) Timarpur-Okhla Waste to Energy Plant, New Delhi, India East Delhi Waste Processing Company Limited, New Delhi, India SELCHP, South Bermondsey in Greater London, England (1994) === Liquid fuel producing plants === No industrial liquid fuel producing gasification plants are currently operational, but two are under erection/commissioning in Varennes (CA) and Swindon (UK). === Plasma gasification waste-to-energy plants === The US Air Force once tested a Transportable Plasma Waste to Energy System (TPWES) facility (PyroGenesis technology) at Hurlburt Field, Florida. The plant, which cost $7.4 million to construct, was closed and sold at a government liquidation auction in May 2013, less than three years after its commissioning. The opening bid was $25. The winning bid was sealed. Besides large plants, domestic waste-to-energy incinerators also exist. For example, the Refuge de Sarenne has a domestic waste-to-energy plant. It is made by combining a wood-fired gasification boiler with a Stirling motor. === Australia === Renergi will scale up their system of converting waste organic materials into liquid fuels using a thermal treatment process in Collie, Western Australia. The system will process 1.5 tonnes of organic matter per hour. Annually the facility will divert 4000 tonnes of municipal waste from landfill and source an additional 8000 tonnes of organic waste from agricultural and forestry operations. Renergi’s patented “grinding pyrolysis” process aims to converts organic materials into biochar, bio-gases and bio-oil by applying heat in an environment with limited oxygen. Another project in the Rockingham Industrial Zone, roughly 45 kilometres south of Perth will see a 29 MW plant built with capacity to power 40,000 homes from an annual feedstock of 300,000 tonnes of municipal, industrial and commercial rubbish. As well as supplying electricity to the South West Interconnected System, 25 MW of the plant’s output has already been committed under a power purchase agreement. === Africa === The Reppie waste to energy plant in Ethiopia was the first such plant in Africa. The plant became operational in 2018. == See also == == References == == Further reading == Field, Christopher B. "Emissions pathways, climate change, and impacts." PNAS 101.34 (2004): 12422–12427. Sudarsan, K. G.; Anupama, Mary P. (October 2009). "The Relevance of Biofuels" (PDF). Current Science. 90 (6). Archived from the original (PDF) on 2015-09-24. Tilman, David. "Environmental, economic, and energetic costs." PNAS 103.30 (2006): 11206–11210. Rogoff, Marc Jay; Screve, Francois (2019). Waste-To-energy: Technologies and Project Implementation (3rd ed.). William Andrew. ISBN 978-0-12-816079-4. == External links == Waste-to-Energy Research and Technology Council Archived 2007-10-06 at the Wayback Machine Energy Recovery from the Combustion of Municipal Solid Waste - US EPA WtERT Germany Gasification Technologies Council Archived 2016-01-20 at the Wayback Machine
Wikipedia/Waste-to-energy
A waste-to-energy plant is a waste management facility that combusts wastes to produce electricity. This type of power plant is sometimes called a trash-to-energy, municipal waste incineration, energy recovery, or resource recovery plant. Modern waste-to-energy plants are very different from the trash incinerators that were commonly used until a few decades ago. Unlike modern ones, those plants usually did not remove hazardous or recyclable materials before burning. These incinerators endangered the health of the plant workers and the nearby residents, and most of them did not generate electricity. Waste-to-energy generation is being increasingly looked at as a potential energy diversification strategy, especially by Sweden, which has been a leader in waste-to-energy production over the past 20 years. The typical range of net electrical energy that can be produced is about 500 to 600 kWh of electricity per ton of waste incinerated. Thus, the incineration of about 2,200 tons per day of waste will produce about 1,200 MWh of electrical energy. == Operation == Most waste-to-energy plants burn municipal solid waste, but some burn industrial waste or hazardous waste. A modern, properly run waste-to-energy plant sorts material before burning it and can co-exist with recycling. The only items that are burned are not recyclable, by design or economically, and are not hazardous. Waste-to-energy plants are similar in their design and equipment with other steam-electric power plants, particularly biomass plants. First, the waste is brought to the facility. Then, the waste is sorted to remove recyclable and hazardous materials. The waste is then stored until it is time for burning. A few plants use gasification, but most combust the waste directly because it is a mature, efficient technology. The waste can be added to the boiler continuously or in batches, depending on the design of the plant. In terms of volume, waste-to-energy plants incinerate 80 to 90 percent of waste. Sometimes, the residue ash is clean enough to be used for some purposes such as raw materials for use in manufacturing cinder blocks or for road construction. In addition, the metals that may be burned are collected from the bottom of the furnace and sold to foundries. Some waste-to-energy plants convert salt water to potable fresh water as a by-product of cooling processes. == Cost == The typical plant with a capacity of 400 GWh energy production annually costs about 440 million dollars to build. Waste-to-energy plants may have a significant cost advantage over traditional power options, as the waste-to-energy operator may receive revenue for receiving waste as an alternative to the cost of disposing of waste in a landfill, typically referred to as a "tipping fee" per ton basis, versus having to pay for the cost of fuel, whereas fuel cost can account for as much as 45 percent of the cost to produce electricity in a coal-powered plant, and 75 percent or more of the cost in a natural gas-powered plant. The National Solid Waste Management Association estimates that the average United States tipping fee for 2002 was $33.70 per ton. == Pollution == Waste-to-energy plants cause less air pollution than coal plants, but more than natural gas plants. At the same time, it is carbon-negative: processing waste into fuel releases considerably less carbon and methane into the air than having waste decay away in landfills or bodies of water. Waste-to-energy plants are designed to reduce the emission of air pollutants in the flue gases exhausted to the atmosphere, such as nitrogen oxides, sulfur oxides and particulates, and to destroy pollutants already present in the waste, using pollution control measures such as baghouses, scrubbers, and electrostatic precipitators. High temperature, efficient combustion, and effective scrubbing and controls can significantly reduce air pollution outputs. Burning municipal waste does produce significant amounts of dioxins and dioxin-like compounds as compared to the smaller amounts produced by burning coal or natural gas. These compounds are considered by scientists to be serious health hazards. However, advances in emission control designs and very stringent new governmental regulations, as well as public opposition to municipal waste incinerators, have caused large reductions in emissions from waste-to-energy plants. Waste-to-energy plants produce fly ash and bottom ash just as is the case when coal is combusted. The total amount of ash produced by waste-to-energy plants ranges from 15% to 25% by weight of the original quantity of waste, and the fly ash amounts to about 10% to 20% of the total ash. The fly ash, by far, constitutes more of a potential health hazard than does the bottom ash because the fly ash contains toxic metals such as lead, cadmium, copper, and zinc as well as small amounts of dioxins and furans. The bottom ash may or may not contain significant levels of health hazardous materials. In the United States, and perhaps in other countries as well, the law requires that the ash be tested for toxicity before disposal in landfills. If the ash is found to be hazardous, it can only be disposed of in landfills which are carefully designed to prevent pollutants in the ash from leaching into underground aquifers. Odor can be a problem when the plant location is not isolated. Some plants store the waste in an enclosed area with a negative pressure, which prevents unpleasant odors from escaping, and the air drawn from the storage area is sent through the boiler or a filter. However, not all plants take steps to reduce the odor, resulting in complaints. An issue that affects community relationships is the increased road traffic of garbage trucks to transport municipal waste to the waste-to-energy facility. Due to this reason, most waste-to-energy plants are located in industrial areas. Landfill gas, which contains about 50% methane, and 50% carbon dioxide, is contaminated with a small amount of pollutants. Unlike at waste-to-energy plants, there are little or no pollution controls on the burning of landfill gas. The gas is usually flared or used to run a reciprocating engine or microturbine, especially in digester gas power plants. Cleaning up the landfill gas is usually not cost effective because natural gas, which it substitutes for, is relatively cheap. == See also == Incineration Waste management#Incineration == References == == External links == Waste-to-energy plants European Union Directive on waste incineration ISWA Working Group on thermal treatment of solid waste
Wikipedia/Waste-to-energy_plant
In information theory and statistics, negentropy is used as a measure of distance to normality. The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book What is Life? Later, French physicist Léon Brillouin shortened the phrase to néguentropie (negentropy). In 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common. In a note to What is Life? Schrödinger explained his use of this phrase. ... if I had been catering for them [physicists] alone I should have let the discussion turn on free energy instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to energy for making the average reader alive to the contrast between the two things. == Information theory == In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian. Negentropy is defined as J ( p x ) = S ( φ x ) − S ( p x ) {\displaystyle J(p_{x})=S(\varphi _{x})-S(p_{x})\,} where S ( φ x ) {\displaystyle S(\varphi _{x})} is the differential entropy of the Gaussian density with the same mean and variance as p x {\displaystyle p_{x}} and S ( p x ) {\displaystyle S(p_{x})} is the differential entropy of p x {\displaystyle p_{x}} : S ( p x ) = − ∫ p x ( u ) log ⁡ p x ( u ) d u {\displaystyle S(p_{x})=-\int p_{x}(u)\log p_{x}(u)\,du} Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis. The negentropy of a distribution is equal to the Kullback–Leibler divergence between p x {\displaystyle p_{x}} and a Gaussian distribution with the same mean and variance as p x {\displaystyle p_{x}} (see Differential entropy § Maximization in the normal distribution for a proof). In particular, it is always nonnegative. == Correlation between statistical negentropy and Gibbs' free energy == There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal process (both quantities differs just with a figure sign) and by then Planck for the isothermal-isobaric process. More recently, the Massieu–Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics, applied among the others in molecular biology and thermodynamic non-equilibrium processes. J = S max − S = − Φ = − k ln ⁡ Z {\displaystyle J=S_{\max }-S=-\Phi =-k\ln Z\,} where: S {\displaystyle S} is entropy J {\displaystyle J} is negentropy (Gibbs "capacity for entropy") Φ {\displaystyle \Phi } is the Massieu potential Z {\displaystyle Z} is the partition function k {\displaystyle k} the Boltzmann constant In particular, mathematically the negentropy (the negative entropy function, in physics interpreted as free entropy) is the convex conjugate of LogSumExp (in physics interpreted as the free energy). == Brillouin's negentropy principle of information == In 1953, Léon Brillouin derived a general equation stating that the changing of an information bit value requires at least k T ln ⁡ 2 {\displaystyle kT\ln 2} energy. This is the same energy as the work Leó Szilárd's engine produces in the idealistic case. In his book, he further explored this problem concluding that any cause of this bit value change (measurement, decision about a yes/no question, erasure, display, etc.) will require the same amount of energy. == See also == Exergy Free entropy Entropy in thermodynamics and information theory == Notes ==
Wikipedia/Negentropy
In surface science, surface energy (also interfacial free energy or surface free energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (that is, the atoms on the surface must have more energy than the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material by sublimation. The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the work required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces. There is "excess energy" as a result of the now-incomplete, unrealized bonding between the two created surfaces. Cutting a solid body into pieces disrupts its bonds and increases the surface area, and therefore increases surface energy. If the cutting is done reversibly, then conservation of energy means that the energy consumed by the cutting process will be equal to the energy inherent in the two new surfaces created. The unit surface energy of a material would therefore be half of its energy of cohesion, all other things being equal; in practice, this is true only for a surface freshly prepared in vacuum. Surfaces often change their form away from the simple "cleaved bond" model just implied above. They are found to be highly dynamic regions, which readily rearrange or react, so that energy is often reduced by such processes as passivation or adsorption. == Assessment == === Measurement === ==== Contact angle ==== The most common way to measure surface energy is through contact angle experiments. In this method, the contact angle of the surface is measured with several liquids, usually water and diiodomethane. Based on the contact angle results and knowing the surface tension of the liquids, the surface energy can be calculated. In practice, this analysis is done automatically by a contact angle meter. There are several different models for calculating the surface energy based on the contact angle readings. The most commonly used method is OWRK, which requires the use of two probe liquids and gives out as a result the total surface energy as well as divides it into polar and dispersive components. Contact angle method is the standard surface energy measurement method due to its simplicity, applicability to a wide range of surfaces and quickness. The measurement can be fully automated and is standardized. In general, as surface energy increases, the contact angle decreases because more of the liquid is being "grabbed" by the surface. Conversely, as surface energy decreases, the contact angle increases, because the surface doesn't want to interact with the liquid. ==== Other methods ==== The surface energy of a liquid may be measured by stretching a liquid membrane (which increases the surface area and hence the surface energy). In that case, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, γ δA, is needed (where γ is the surface energy density of the liquid). However, such a method cannot be used to measure the surface energy of a solid because stretching of a solid membrane induces elastic energy in the bulk in addition to increasing the surface energy. The surface energy of a solid is usually measured at high temperatures. At such temperatures the solid creeps and even though the surface area changes, the volume remains approximately constant. If γ is the surface energy density of a cylindrical rod of radius r and length l at high temperature and a constant uniaxial tension P, then at equilibrium, the variation of the total Helmholtz free energy vanishes and we have δ F = − P δ l + γ δ A = 0 ⟹ γ = P δ l δ A {\displaystyle \delta F=-P~\delta l+\gamma ~\delta A=0\quad \implies \quad \gamma =P{\frac {\delta l}{\delta A}}} where F is the Helmholtz free energy and A is the surface area of the rod: A = 2 π r 2 + 2 π r l ⟹ δ A = 4 π r δ r + 2 π l δ r + 2 π r δ l {\displaystyle A=2\pi r^{2}+2\pi rl\quad \implies \quad \delta A=4\pi r\delta r+2\pi l\delta r+2\pi r\delta l} Also, since the volume (V) of the rod remains constant, the variation (δV) of the volume is zero, that is, V = π r 2 l is constant ⟹ δ V = 2 π r l δ r + π r 2 δ l = 0 ⟹ δ r = − r 2 l δ l . {\displaystyle V=\pi r^{2}l{\text{ is constant}}\quad \implies \quad \delta V=2\pi rl\delta r+\pi r^{2}\delta l=0\quad \implies \quad \delta r=-{\frac {r}{2l}}\delta l~.} Therefore, the surface energy density can be expressed as γ = P l π r ( l − 2 r ) . {\displaystyle \gamma ={\frac {Pl}{\pi r(l-2r)}}~.} The surface energy density of the solid can be computed by measuring P, r, and l at equilibrium. This method is valid only if the solid is isotropic, meaning the surface energy is the same for all crystallographic orientations. While this is only strictly true for amorphous solids (glass) and liquids, isotropy is a good approximation for many other materials. In particular, if the sample is polygranular (most metals) or made by powder sintering (most ceramics) this is a good approximation. In the case of single-crystal materials, such as natural gemstones, anisotropy in the surface energy leads to faceting. The shape of the crystal (assuming equilibrium growth conditions) is related to the surface energy by the Wulff construction. The surface energy of the facets can thus be found to within a scaling constant by measuring the relative sizes of the facets. === Calculation === ==== Deformed solid ==== In the deformation of solids, surface energy can be treated as the "energy required to create one unit of surface area", and is a function of the difference between the total energies of the system before and after the deformation: γ = 1 A ( E 1 − E 0 ) {\displaystyle \gamma ={\frac {1}{A}}\left(E_{1}-E_{0}\right)} . Calculation of surface energy from first principles (for example, density functional theory) is an alternative approach to measurement. Surface energy is estimated from the following variables: width of the d-band, the number of valence d-electrons, and the coordination number of atoms at the surface and in the bulk of the solid. ==== Surface formation energy of a crystalline solid ==== In density functional theory, surface energy can be calculated from the following expression: γ = E slab − N E bulk 2 A {\displaystyle \gamma ={\frac {E_{\text{slab}}-NE_{\text{bulk}}}{2A}}} where Eslab is the total energy of surface slab obtained using density functional theory. N is the number of atoms in the surface slab. Ebulk is the bulk energy per atom. A is the surface area. For a slab, we have two surfaces and they are of the same type, which is reflected by the number 2 in the denominator. To guarantee this, we need to create the slab carefully to make sure that the upper and lower surfaces are of the same type. Strength of adhesive contacts is determined by the work of adhesion which is also called relative surface energy of two contacting bodies. The relative surface energy can be determined by detaching of bodies of well defined shape made of one material from the substrate made from the second material. For example, the relative surface energy of the interface "acrylic glass – gelatin" is equal to 0.03 N/m. Experimental setup for measuring relative surface energy and its function can be seen in the video. === Estimation from the heat of sublimation === To estimate the surface energy of a pure, uniform material, an individual region of the material can be modeled as a cube. In order to move a cube from the bulk of a material to the surface, energy is required. This energy cost is incorporated into the surface energy of the material, which is quantified by: γ = ( z σ − z β ) 1 2 W AA a 0 {\displaystyle \gamma ={\frac {\left(z_{\sigma }-z_{\beta }\right){\frac {1}{2}}W_{\text{AA}}}{a_{0}}}} where zσ and zβ are coordination numbers corresponding to the surface and the bulk regions of the material, and are equal to 5 and 6, respectively; a0 is the surface area of an individual molecule, and WAA is the pairwise intermolecular energy. Surface area can be determined by squaring the cube root of the volume of the molecule: a 0 = V molecule 2 3 = ( M ¯ ρ N A ) 2 3 {\displaystyle a_{0}=V_{\text{molecule}}^{\frac {2}{3}}=\left({\frac {\bar {M}}{\rho N_{\text{A}}}}\right)^{\frac {2}{3}}} Here, M̄ corresponds to the molar mass of the molecule, ρ corresponds to the density, and NA is the Avogadro constant. In order to determine the pairwise intermolecular energy, all intermolecular forces in the material must be broken. This allows thorough investigation of the interactions that occur for single molecules. During sublimation of a substance, intermolecular forces between molecules are broken, resulting in a change in the material from solid to gas. For this reason, considering the enthalpy of sublimation can be useful in determining the pairwise intermolecular energy. Enthalpy of sublimation can be calculated by the following equation: Δ sub H = − 1 2 W AA N A z b {\displaystyle \Delta _{\text{sub}}H=-{\frac {1}{2}}W_{\text{AA}}N_{\text{A}}z_{b}} Using empirically tabulated values for enthalpy of sublimation, it is possible to determine the pairwise intermolecular energy. Incorporating this value into the surface energy equation allows for the surface energy to be estimated. The following equation can be used as a reasonable estimate for surface energy: γ ≈ − Δ sub H ( z σ − z β ) a 0 N A z β {\displaystyle \gamma \approx {\frac {-\Delta _{\text{sub}}H\left(z_{\sigma }-z_{\beta }\right)}{a_{0}N_{\text{A}}z_{\beta }}}} == Interfacial energy == The presence of an interface influences generally all thermodynamic parameters of a system. There are two models that are commonly used to demonstrate interfacial phenomena: the Gibbs ideal interface model and the Guggenheim model. In order to demonstrate the thermodynamics of an interfacial system using the Gibbs model, the system can be divided into three parts: two immiscible liquids with volumes Vα and Vβ and an infinitesimally thin boundary layer known as the Gibbs dividing plane (σ) separating these two volumes. The total volume of the system is: V = V α + V β {\displaystyle V=V_{\alpha }+V_{\beta }} All extensive quantities of the system can be written as a sum of three components: bulk phase α, bulk phase β, and the interface σ. Some examples include internal energy U, the number of molecules of the ith substance ni, and the entropy S. U = U α + U β + U σ N i = N i α + N i β + N i σ S = S α + S β + S σ {\displaystyle {\begin{aligned}U&=U_{\alpha }+U_{\beta }+U_{\sigma }\\N_{i}&=N_{i\alpha }+N_{i\beta }+N_{i\sigma }\\S&=S_{\alpha }+S_{\beta }+S_{\sigma }\end{aligned}}} While these quantities can vary between each component, the sum within the system remains constant. At the interface, these values may deviate from those present within the bulk phases. The concentration of molecules present at the interface can be defined as: N i σ = N i − c i α V α − c i β V β {\displaystyle N_{i\sigma }=N_{i}-c_{i\alpha }V_{\alpha }-c_{i\beta }V_{\beta }} where ciα and ciβ represent the concentration of substance i in bulk phase α and β, respectively. It is beneficial to define a new term interfacial excess Γi which allows us to describe the number of molecules per unit area: Γ i = N i α A {\displaystyle \Gamma _{i}={\frac {N_{i\alpha }}{A}}} == Wetting == === Spreading parameter === Surface energy comes into play in wetting phenomena. To examine this, consider a drop of liquid on a solid substrate. If the surface energy of the substrate changes upon the addition of the drop, the substrate is said to be wetting. The spreading parameter can be used to mathematically determine this: S = γ s − γ l − γ s-l {\displaystyle S=\gamma _{\text{s}}-\gamma _{\text{l}}-\gamma _{\text{s-l}}} where S is the spreading parameter, γs the surface energy of the substrate, γl the surface energy of the liquid, and γs-l the interfacial energy between the substrate and the liquid. If S < 0, the liquid partially wets the substrate. If S > 0, the liquid completely wets the substrate. === Contact angle === A way to experimentally determine wetting is to look at the contact angle (θ), which is the angle connecting the solid–liquid interface and the liquid–gas interface (as in the figure). If θ = 0°, the liquid completely wets the substrate. If 0° < θ < 90°, high wetting occurs. If 90° < θ < 180°, low wetting occurs. If θ = 180°, the liquid does not wet the substrate at all. The Young equation relates the contact angle to interfacial energy: γ s-g = γ s-l + γ l-g cos ⁡ θ {\displaystyle \gamma _{\text{s-g}}=\gamma _{\text{s-l}}+\gamma _{\text{l-g}}\cos \theta } where γs-g is the interfacial energy between the solid and gas phases, γs-l the interfacial energy between the substrate and the liquid, γl-g is the interfacial energy between the liquid and gas phases, and θ is the contact angle between the solid–liquid and the liquid–gas interface. === Wetting of high- and low-energy substrates === The energy of the bulk component of a solid substrate is determined by the types of interactions that hold the substrate together. High-energy substrates are held together by bonds, while low-energy substrates are held together by forces. Covalent, ionic, and metallic bonds are much stronger than forces such as van der Waals and hydrogen bonding. High-energy substrates are more easily wetted than low-energy substrates. In addition, more complete wetting will occur if the substrate has a much higher surface energy than the liquid. == Modification techniques == The most commonly used surface modification protocols are plasma activation, wet chemical treatment, including grafting, and thin-film coating. Surface energy mimicking is a technique that enables merging the device manufacturing and surface modifications, including patterning, into a single processing step using a single device material. Many techniques can be used to enhance wetting. Surface treatments, such as corona treatment, plasma treatment and acid etching, can be used to increase the surface energy of the substrate. Additives can also be added to the liquid to decrease its surface tension. This technique is employed often in paint formulations to ensure that they will be evenly spread on a surface. == The Kelvin equation == As a result of the surface tension inherent to liquids, curved surfaces are formed in order to minimize the area. This phenomenon arises from the energetic cost of forming a surface. As such the Gibbs free energy of the system is minimized when the surface is curved. The Kelvin equation is based on thermodynamic principles and is used to describe changes in vapor pressure caused by liquids with curved surfaces. The cause for this change in vapor pressure is the Laplace pressure. The vapor pressure of a drop is higher than that of a planar surface because the increased Laplace pressure causes the molecules to evaporate more easily. Conversely, in liquids surrounding a bubble, the pressure with respect to the inner part of the bubble is reduced, thus making it more difficult for molecules to evaporate. The Kelvin equation can be stated as: R T ln ⁡ P 0 K P 0 = γ V m ( 1 R 1 + 1 R 2 ) {\displaystyle RT\ln {\frac {P_{0}^{K}}{P_{0}}}=\gamma V_{m}\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)} where PK0 is the vapor pressure of the curved surface, P0 is the vapor pressure of the flat surface, γ is the surface tension, Vm is the molar volume of the liquid, R is the universal gas constant, T is temperature (in kelvin), and R1 and R2 are the principal radii of curvature of the surface. == Surface modified pigments for coatings == Pigments offer great potential in modifying the application properties of a coating. Due to their fine particle size and inherently high surface energy, they often require a surface treatment in order to enhance their ease of dispersion in a liquid medium. A wide variety of surface treatments have been previously used, including the adsorption on the surface of a molecule in the presence of polar groups, monolayers of polymers, and layers of inorganic oxides on the surface of organic pigments. New surfaces are constantly being created as larger pigment particles get broken down into smaller subparticles. These newly-formed surfaces consequently contribute to larger surface energies, whereby the resulting particles often become cemented together into aggregates. Because particles dispersed in liquid media are in constant thermal or Brownian motion, they exhibit a strong affinity for other pigment particles nearby as they move through the medium and collide. This natural attraction is largely attributed to the powerful short-range van der Waals forces, as an effect of their surface energies. The chief purpose of pigment dispersion is to break down aggregates and form stable dispersions of optimally sized pigment particles. This process generally involves three distinct stages: wetting, deaggregation, and stabilization. A surface that is easy to wet is desirable when formulating a coating that requires good adhesion and appearance. This also minimizes the risks of surface tension related defects, such as crawling, cratering, and orange peel. This is an essential requirement for pigment dispersions; for wetting to be effective, the surface tension of the pigment's vehicle must be lower than the surface free energy of the pigment. This allows the vehicle to penetrate into the interstices of the pigment aggregates, thus ensuring complete wetting. Finally, the particles are subjected to a repulsive force in order to keep them separated from one another and lowers the likelihood of flocculation. Dispersions may become stable through two different phenomena: charge repulsion and steric or entropic repulsion. In charge repulsion, particles that possess the same like electrostatic charges repel each other. Alternatively, steric or entropic repulsion is a phenomenon used to describe the repelling effect when adsorbed layers of material (such as polymer molecules swollen with solvent) are present on the surface of the pigment particles in dispersion. Only certain portions (anchors) of the polymer molecules are adsorbed, with their corresponding loops and tails extending out into the solution. As the particles approach each other their adsorbed layers become crowded; this provides an effective steric barrier that prevents flocculation. This crowding effect is accompanied by a decrease in entropy, whereby the number of conformations possible for the polymer molecules is reduced in the adsorbed layer. As a result, energy is increased and often gives rise to repulsive forces that aid in keeping the particles separated from each other. == Surface energies of common materials == == See also == Contact angle Surface tension Sessile drop technique Capillary surface Wulff Construction == References == == External links == What is surface free energy? Surface Energy and Adhesion
Wikipedia/Surface_energy
In physical sciences, mechanical energy is the sum of macroscopic potential and kinetic energies. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is constant. If an object moves in the opposite direction of a conservative net force, the potential energy will increase; and if the speed (not the velocity) of the object changes, the kinetic energy of the object also changes. In all real systems, however, nonconservative forces, such as frictional forces, will be present, but if they are of negligible magnitude, the mechanical energy changes little and its conservation is a useful approximation. In elastic collisions, the kinetic energy is conserved, but in inelastic collisions some mechanical energy may be converted into thermal energy. The equivalence between lost mechanical energy and an increase in temperature was discovered by James Prescott Joule. Many devices are used to convert mechanical energy to or from other forms of energy, e.g. an electric motor converts electrical energy to mechanical energy, an electric generator converts mechanical energy into electrical energy and a heat engine converts heat to mechanical energy. == General == Energy is a scalar quantity, and the mechanical energy of a system is the sum of the potential energy (which is measured by the position of the parts of the system) and the kinetic energy (which is also called the energy of motion): E mechanical = U + K {\displaystyle E_{\text{mechanical}}=U+K} The potential energy, U, depends on the position of an object subjected to gravity or some other conservative force. The gravitational potential energy of an object is equal to the weight W of the object multiplied by the height h of the object's center of gravity relative to an arbitrary datum: U = W h {\displaystyle U=Wh} Potential energy is the energy stored in an object due to its position relative to a conservative force field, such as gravity or a spring. It increases when work is done against the force—meaning when the object is moved in the direction opposite to that of the force. If F represents the conservative force and x the position, the potential energy of the force between the two positions x1 and x2 is defined as the negative integral of F from x1 to x2: U = − ∫ x 1 x 2 F → ⋅ d x → {\displaystyle U=-\int _{x_{1}}^{x_{2}}{\vec {F}}\cdot d{\vec {x}}} The kinetic energy, K, depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects: K = 1 2 m v 2 {\displaystyle K={1 \over 2}mv^{2}} The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path. On the contrary, when a non-conservative force acts upon an object, the work done by the non-conservative force is dependent of the path. == Conservation of mechanical energy == According to the principle of conservation of mechanical energy, the mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces. In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. Though energy cannot be created or destroyed, it can be converted to another form of energy. === Swinging pendulum === In a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points. However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the negative work done on the pendulum by these non-conservative forces. === Irreversibilities === That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that comprise matter. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved – the sum of the mechanical energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the mechanical energy of the system will have changed. Usually, the mechanical energy before the collision is greater than the mechanical energy after the collision. In inelastic collisions, some of the mechanical energy of the colliding objects is transformed into kinetic energy of the constituent particles. This increase in kinetic energy of the constituent particles is perceived as an increase in temperature. The collision can be described by saying some of the mechanical energy of the colliding objects has been converted into an equal amount of heat. Thus, the total energy of the system remains unchanged though the mechanical energy of the system has reduced. === Satellite === A satellite of mass m {\displaystyle m} at a distance r {\displaystyle r} from the centre of Earth possesses both kinetic energy, K {\displaystyle K} , (by virtue of its motion) and gravitational potential energy, U {\displaystyle U} , (by virtue of its position within the Earth's gravitational field; Earth's mass is M {\displaystyle M} ). Hence, mechanical energy E mechanical {\displaystyle E_{\text{mechanical}}} of the satellite-Earth system is given by E mechanical = U + K {\displaystyle E_{\text{mechanical}}=U+K} E mechanical = − G M m r + 1 2 m v 2 {\displaystyle E_{\text{mechanical}}=-G{\frac {Mm}{r}}\ +{\frac {1}{2}}\,mv^{2}} If the satellite is in circular orbit, the energy conservation equation can be further simplified into E mechanical = − G M m 2 r {\displaystyle E_{\text{mechanical}}=-G{\frac {Mm}{2r}}} since in circular motion, Newton's 2nd Law of motion can be taken to be G M m r 2 = m v 2 r {\displaystyle G{\frac {Mm}{r^{2}}}\ ={\frac {mv^{2}}{r}}} == Conversion == Today, many technological devices convert mechanical energy into other forms of energy or vice versa. These devices can be placed in these categories: An electric motor converts electrical energy into mechanical energy. A generator converts mechanical energy into electrical energy. A hydroelectric powerplant converts the mechanical energy of water in a storage dam into electrical energy. An internal combustion engine is a heat engine that obtains mechanical energy from chemical energy by burning fuel. From this mechanical energy, the internal combustion engine often generates electricity. A steam engine converts the internal energy of steam into mechanical energy. A turbine converts the kinetic energy of a stream of gas or liquid into mechanical energy. == Distinction from other types == The classification of energy into different types often follows the boundaries of the fields of study in the natural sciences. Chemical energy is the kind of potential energy "stored" in chemical bonds and is studied in chemistry. Nuclear energy is energy stored in interactions between the particles in the atomic nucleus and is studied in nuclear physics. Electromagnetic energy is in the form of electric charges, magnetic fields, and photons. It is studied in electromagnetism. Various forms of energy in quantum mechanics; e.g., the energy levels of electrons in an atom. == References == Notes Citations Bibliography Brodie, David; Brown, Wendy; Heslop, Nigel; Ireson, Gren; Williams, Peter (1998). Terry Parkin (ed.). Physics. Addison Wesley Longman Limited. ISBN 978-0-582-28736-5. Jain, Mahesh C. (2009). Textbook of Engineering Physics, Part I. New Delhi: PHI Learning Pvt. Ltd. ISBN 978-81-203-3862-3. Retrieved 2011-08-25. Newton, Isaac (1999). I. Bernard Cohen; Anne Miller Whitman (eds.). The Principia: mathematical principles of natural philosophy. United States of America: University of California Press. ISBN 978-0-520-08816-0.
Wikipedia/Mechanical_energy
Primary energy (PE) is the energy found in nature that has not been subjected to any human engineered conversion process. It encompasses energy contained in raw fuels and other forms of energy, including waste, received as input to a system. Primary energy can be non-renewable or renewable. Total primary energy supply (TPES) is the sum of production and imports, plus or minus stock changes, minus exports and international bunker storage. The International Recommendations for Energy Statistics (IRES) prefers total energy supply (TES) to refer to this indicator. These expressions are often used to describe the total energy supply of a national territory. Secondary energy is a carrier of energy, such as electricity. These are produced by conversion from a primary energy source. Primary energy is used as a measure in energy statistics in the compilation of energy balances, as well as in the field of energetics. In energetics, a primary energy source (PES) refers to the energy forms required by the energy sector to generate the supply of energy carriers used by human society. Primary energy only counts raw energy and not usable energy and fails to account well for energy losses, particularly the large losses in thermal sources. It therefore generally grossly overcounts the usefulness of thermal renewable energy sources and by comparison undercounts sources like renewables that produce secondary energy. == Examples of sources == Primary energy sources should not be confused with the energy system components (or conversion processes) through which they are converted into energy carriers. == Usable energy == Primary energy sources are transformed in energy conversion processes to more convenient forms of energy that can directly be used by society, such as electrical energy, refined fuels, or synthetic fuels such as hydrogen fuel. In the field of energetics, these forms are called energy carriers and correspond to the concept of "secondary energy" in energy statistics. === Conversion to energy carriers (or secondary energy) === Energy carriers are energy forms which have been transformed from primary energy sources. Electricity is one of the most common energy carriers, being transformed from various primary energy sources such as coal, oil, natural gas, and wind. Electricity is particularly useful since it has low entropy (is highly ordered) and so can be converted into other forms of energy very efficiently. District heating is another example of secondary energy. According to the laws of thermodynamics, primary energy sources cannot be produced. They must be available to society to enable the production of energy carriers. Conversion efficiency varies. For thermal energy, electricity and mechanical energy production is limited by Carnot's theorem, and generates a lot of waste heat. Other non-thermal conversions can be more efficient. For example, while wind turbines do not capture all of the wind's energy, they have a high conversion efficiency and generate very little waste heat since wind energy is low entropy. In principle solar photovoltaic conversions could be very efficient, but current conversion can only be done well for narrow ranges of wavelength, whereas solar thermal is also subject to Carnot efficiency limits. Hydroelectric power is also very ordered, and converted very efficiently. The amount of usable energy is the exergy of a system. === Site and source energy === Site energy is the term used in North America for the amount of end-use energy of all forms consumed at a specified location. This can be a mix of primary energy (such as natural gas burned at the site) and secondary energy (such as electricity). Site energy is measured at the campus, building, or sub-building level and is the basis for energy charges on utility bills. Source energy, in contrast, is the term used in North America for the amount of primary energy consumed in order to provide a facility's site energy. It is always greater than the site energy, as it includes all site energy and adds to it the energy lost during transmission, delivery, and conversion. While source or primary energy provides a more complete picture of energy consumption, it cannot be measured directly and must be calculated using conversion factors from site energy measurements. For electricity, a typical value is three units of source energy for one unit of site energy. However, this can vary considerably depending on factors such as the primary energy source or fuel type, the type of power plant, and the transmission infrastructure. One full set of conversion factors is available as technical reference from Energy STAR. Either site or source energy can be an appropriate metric when comparing or analyzing energy use of different facilities. The U.S Energy Information Administration, for example, uses primary (source) energy for its energy overviews but site energy for its Commercial Building Energy Consumption Survey and Residential Building Energy Consumption Survey. The US Environmental Protection Agency's Energy STAR program recommends using source energy, and the US Department of Energy uses site energy in its definition of a zero net energy building. == Conversion factor conventions == Where primary energy is used to describe fossil fuels, the embodied energy of the fuel is available as thermal energy and around two thirds is typically lost in conversion to electrical or mechanical energy. There are very much less significant conversion losses when hydroelectricity, wind and solar power produce electricity, but today's UN conventions on energy statistics counts the electricity made from hydroelectricity, wind and solar as the primary energy itself for these sources. One consequence of employing primary energy as an energy metric is that the contribution of hydro, wind and solar energy is under reported compared to fossil energy sources, and there is hence an international debate on how to count energy from non-thermal renewables, with many estimates having them undercounted by a factor of about three. The false notion that all primary energy from thermal fossil fuel sources has to be replaced by an equivalent amount of non-thermal renewables (which is not necessary as conversion losses do not need to be replaced) has been termed the "primary energy fallacy". == See also == Energy industry Energy development Energy mix Energy system List of countries by total primary energy consumption and production == Notes == == References == == Further reading == Kydes, Andy (Lead Author); Cutler J. Cleveland (Topic Editor). 2007. "Primary energy." In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth June 1, 2006; Last revised August 14, 2007; Retrieved November 15, 2007. Øvergaard, Sara (September 2008). Definition of primary and secondary energy (PDF). Norway: Statistics Norway. Retrieved 2016-12-17. == External links == The Encyclopedia of Earth: Primary energy Our Energy Futures glossary: Primary Energy Sources
Wikipedia/Primary_energy
Energy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an accumulator or battery. Energy comes in multiple forms including radiation, chemical, gravitational potential, electrical potential, electricity, elevated temperature, latent heat and kinetic. Energy storage involves converting energy from forms that are difficult to store to more conveniently or economically storable forms. Some technologies provide short-term energy storage, while others can endure for much longer. Bulk energy storage is currently dominated by hydroelectric dams, both conventional as well as pumped. Grid energy storage is a collection of methods used for energy storage on a large scale within an electrical power grid. Common examples of energy storage are the rechargeable battery, which stores chemical energy readily convertible to electricity to operate a mobile phone; the hydroelectric dam, which stores energy in a reservoir as gravitational potential energy; and ice storage tanks, which store ice frozen by cheaper energy at night to meet peak daytime demand for cooling. Fossil fuels such as coal and gasoline store ancient energy derived from sunlight by organisms that later died, became buried and over time were then converted into these fuels. Food (which is made by the same process as fossil fuels) is a form of energy stored in chemical form. == History == In the 20th century grid, electrical power was largely generated by burning fossil fuel. When less power was required, less fuel was burned. Hydropower, a mechanical energy storage method, is the most widely adopted mechanical energy storage, and has been in use for centuries. Large hydropower dams have been energy storage sites for more than one hundred years. Concerns with air pollution, energy imports, and global warming have spawned the growth of renewable energy such as solar and wind power. Wind power is uncontrolled and may be generating at a time when no additional power is needed. Solar power varies with cloud cover and at best is only available during daylight hours, while demand often peaks after sunset (see duck curve). Interest in storing power from these intermittent sources grows as the renewable energy industry begins to generate a larger fraction of overall energy consumption. In 2023 BloombergNEF forecast total energy storage deployments to grow at a compound annual growth rate of 27 percent through 2030. Off grid electrical use was a niche market in the 20th century, but in the 21st century, it has expanded. Portable devices are in use all over the world. Solar panels are now common in the rural settings worldwide. Access to electricity is now a question of economics and financial viability, and not solely on technical aspects. Electric vehicles are gradually replacing combustion-engine vehicles. However, powering long-distance transportation without burning fuel remains in development. == Methods == === Outline === The following list includes a variety of types of energy storage: === Mechanical === Energy can be stored in water pumped to a higher elevation using pumped storage methods or by moving solid matter to higher locations (gravity batteries). Other commercial mechanical methods include compressing air and flywheels that convert electric energy into internal energy or kinetic energy and then back again when electrical demand peaks. ==== Hydroelectricity ==== Hydroelectric dams with reservoirs can be operated to provide electricity at times of peak demand. Water is stored in the reservoir during periods of low demand and released when demand is high. The net effect is similar to pumped storage, but without the pumping loss. While a hydroelectric dam does not directly store energy from other generating units, it behaves equivalently by lowering output in periods of excess electricity from other sources. In this mode, dams are one of the most efficient forms of energy storage, because only the timing of its generation changes. Hydroelectric turbines have a start-up time on the order of a few minutes. ==== Pumped hydro ==== Worldwide, pumped-storage hydroelectricity (PSH) is the largest-capacity form of active grid energy storage available, and, as of March 2012, the Electric Power Research Institute (EPRI) reports that PSH accounts for more than 99% of bulk storage capacity worldwide, representing around 127,000 MW. PSH energy efficiency varies in practice between 70% and 80%, with claims of up to 87%. At times of low electrical demand, excess generation capacity is used to pump water from a lower source into a higher reservoir. When demand grows, water is released back into a lower reservoir (or waterway or body of water) through a turbine, generating electricity. Reversible turbine-generator assemblies act as both a pump and turbine (usually a Francis turbine design). Nearly all facilities use the height difference between two water bodies. Pure pumped-storage plants shift the water between reservoirs, while the "pump-back" approach is a combination of pumped storage and conventional hydroelectric plants that use natural stream-flow. ==== Compressed air ==== Compressed-air energy storage (CAES) uses surplus energy to compress air for subsequent electricity generation. Small-scale systems have long been used in such applications as propulsion of mine locomotives. The compressed air is stored in an underground reservoir, such as a salt dome. Compressed-air energy storage (CAES) plants can bridge the gap between production volatility and load. CAES storage addresses the energy needs of consumers by effectively providing readily available energy to meet demand. Renewable energy sources like wind and solar energy vary. So at times when they provide little power, they need to be supplemented with other forms of energy to meet energy demand. Compressed-air energy storage plants can take in the surplus energy output of renewable energy sources during times of energy over-production. This stored energy can be used at a later time when demand for electricity increases or energy resource availability decreases. Compression of air creates heat; the air is warmer after compression. Expansion requires heat. If no extra heat is added, the air will be much colder after expansion. If the heat generated during compression can be stored and used during expansion, efficiency improves considerably. A CAES system can deal with the heat in three ways. Air storage can be adiabatic, diabatic, or isothermal. Another approach uses compressed air to power vehicles. ==== Flywheel ==== Flywheel energy storage (FES) works by accelerating a rotor (a flywheel) to a very high speed, holding energy as rotational energy. When energy is added the rotational speed of the flywheel increases, and when energy is extracted, the speed declines, due to conservation of energy. Most FES systems use electricity to accelerate and decelerate the flywheel, but devices that directly use mechanical energy are under consideration. FES systems have rotors made of high strength carbon-fiber composites, suspended by magnetic bearings and spinning at speeds from 20,000 to over 50,000 revolutions per minute (rpm) in a vacuum enclosure. Such flywheels can reach maximum speed ("charge") in a matter of minutes. The flywheel system is connected to a combination electric motor/generator. FES systems have relatively long lifetimes (lasting decades with little or no maintenance; full-cycle lifetimes quoted for flywheels range from in excess of 105, up to 107, cycles of use), high specific energy (100–130 W·h/kg, or 360–500 kJ/kg) and power density. ==== Solid mass gravitational ==== Changing the altitude of solid masses can store or release energy via an elevating system driven by an electric motor/generator. Studies suggest energy can begin to be released with as little as 1 second warning, making the method a useful supplemental feed into an electricity grid to balance load surges. Efficiencies can be as high as 85% recovery of stored energy. This can be achieved by siting the masses inside old vertical mine shafts or in specially constructed towers where the heavy weights are winched up to store energy and allowed a controlled descent to release it. At 2020 a prototype vertical store is being built in Edinburgh, Scotland Potential energy storage or gravity energy storage was under active development in 2013 in association with the California Independent System Operator. It examined the movement of earth-filled hopper rail cars driven by electric locomotives from lower to higher elevations. Other proposed methods include:- using rails, cranes, or elevators to move weights up and down; using high-altitude solar-powered balloon platforms supporting winches to raise and lower solid masses slung underneath them, using winches supported by an ocean barge to take advantage of a 4 km (13,000 ft) elevation difference between the sea surface and the seabed, === Thermal === Thermal energy storage (TES) is the temporary storage or removal of heat. ==== Sensible heat thermal ==== Sensible heat storage take advantage of sensible heat in a material to store energy. Seasonal thermal energy storage (STES) allows heat or cold to be used months after it was collected from waste energy or natural sources. The material can be stored in contained aquifers, clusters of boreholes in geological substrates such as sand or crystalline bedrock, in lined pits filled with gravel and water, or water-filled mines. Seasonal thermal energy storage (STES) projects often have paybacks in four to six years. An example is Drake Landing Solar Community in Canada, for which 97% of the year-round heat is provided by solar-thermal collectors on garage roofs, enabled by a borehole thermal energy store (BTES). In Braedstrup, Denmark, the community's solar district heating system also uses STES, at a temperature of 65 °C (149 °F). A heat pump, which runs only while surplus wind power is available. It is used to raise the temperature to 80 °C (176 °F) for distribution. When wind energy is not available, a gas-fired boiler is used. Twenty percent of Braedstrup's heat is solar. ==== Latent heat thermal (LHTES) ==== Latent heat thermal energy storage systems work by transferring heat to or from a material to change its phase. A phase-change is the melting, solidifying, vaporizing or liquifying. Such a material is called a phase change material (PCM). Materials used in LHTESs often have a high latent heat so that at their specific temperature, the phase change absorbs a large amount of energy, much more than sensible heat. A steam accumulator is a type of LHTES where the phase change is between liquid and gas and uses the latent heat of vaporization of water. Ice storage air conditioning systems use off-peak electricity to store cold by freezing water into ice. The stored cold in ice releases during melting process and can be used for cooling at peak hours. ==== Cryogenic thermal energy storage ==== Air can be liquefied by cooling using electricity and stored as a cryogen with existing technologies. The liquid air can then be expanded through a turbine and the energy recovered as electricity. The system was demonstrated at a pilot plant in the UK in 2012. In 2019, Highview announced plans to build a 50 MW in the North of England and northern Vermont, with the proposed facility able to store five to eight hours of energy, for a 250–400 MWh storage capacity. ==== Carnot battery ==== Electrical energy can be stored thermally by resistive heating or heat pumps, and the stored heat can be converted back to electricity via Rankine cycle or Brayton cycle. This technology has been studied to retrofit coal-fired power plants into fossil-fuel free generation systems. Coal-fired boilers are replaced by high-temperature heat storage charged by excess electricity from renewable energy sources. In 2020, German Aerospace Center started to construct the world's first large-scale Carnot battery system, which has 1,000 MWh storage capacity. === Electrochemical === ==== Rechargeable battery ==== A rechargeable battery comprises one or more electrochemical cells. It is known as a 'secondary cell' because its electrochemical reactions are electrically reversible. Rechargeable batteries come in many shapes and sizes, ranging from button cells to megawatt grid systems. Rechargeable batteries have lower total cost of use and environmental impact than non-rechargeable (disposable) batteries. Some rechargeable battery types are available in the same form factors as disposables. Rechargeable batteries have higher initial cost but can be recharged very cheaply and used many times. Common rechargeable battery chemistries include: Lead–acid battery: Lead acid batteries hold the largest market share of electric storage products. A single cell produces about 2V when charged. In the charged state the metallic lead negative electrode and the lead sulfate positive electrode are immersed in a dilute sulfuric acid (H2SO4) electrolyte. In the discharge process electrons are pushed out of the cell as lead sulfate is formed at the negative electrode while the electrolyte is reduced to water. Lead–acid battery technology has been developed extensively. Upkeep requires minimal labor and its cost is low. The battery's available energy capacity is subject to a quick discharge resulting in a low life span and low energy density. Nickel–cadmium battery (NiCd): Uses nickel oxide hydroxide and metallic cadmium as electrodes. Cadmium is a toxic element, and was banned for most uses by the European Union in 2004. Nickel–cadmium batteries have been almost completely replaced by nickel–metal hydride (NiMH) batteries. Nickel–metal hydride battery (NiMH): First commercial types were available in 1989. These are now a common consumer and industrial type. The battery has a hydrogen-absorbing alloy for the negative electrode instead of cadmium. Lithium-ion battery: The choice in many consumer electronics and have one of the best energy-to-mass ratios and a very slow self-discharge when not in use. Lithium-ion polymer battery: These batteries are light in weight and can be made in any shape desired. Aluminium-sulfur battery with rock salt crystals as electrolyte: aluminium and sulfur are Earth-abundant materials and are much more cheaper than traditional Lithium. ===== Flow battery ===== A flow battery works by passing a solution over a membrane where ions are exchanged to charge or discharge the cell. Cell voltage is chemically determined by the Nernst equation and ranges, in practical applications, from 1.0 V to 2.2 V. Storage capacity depends on the volume of solution. A flow battery is technically akin both to a fuel cell and an electrochemical accumulator cell. Commercial applications are for long half-cycle storage such as backup grid power. ==== Supercapacitor ==== Supercapacitors, also called electric double-layer capacitors (EDLC) or ultracapacitors, are a family of electrochemical capacitors that do not have conventional solid dielectrics. Capacitance is determined by two storage principles, double-layer capacitance and pseudocapacitance. Supercapacitors bridge the gap between conventional capacitors and rechargeable batteries. They store the most energy per unit volume or mass (energy density) among capacitors. They support up to 10,000 farads/1.2 Volt, up to 10,000 times that of electrolytic capacitors, but deliver or accept less than half as much power per unit time (power density). While supercapacitors have specific energy and energy densities that are approximately 10% of batteries, their power density is generally 10 to 100 times greater. This results in much shorter charge/discharge cycles. Also, they tolerate many more charge-discharge cycles than batteries. Supercapacitors have many applications, including: Low supply current for memory backup in static random-access memory (SRAM) Power for cars, buses, trains, cranes and elevators, including energy recovery from braking, short-term energy storage and burst-mode power delivery === Chemical === ==== Power-to-gas ==== Power-to-gas is the conversion of electricity to a gaseous fuel such as hydrogen or methane. The three commercial methods use electricity to reduce water into hydrogen and oxygen by means of electrolysis. In the first method, hydrogen is injected into the natural gas grid or is used for transportation. The second method is to combine the hydrogen with carbon dioxide to produce methane using a methanation reaction such as the Sabatier reaction, or biological methanation, resulting in an extra energy conversion loss of 8%. The methane may then be fed into the natural gas grid. The third method uses the output gas of a wood gas generator or a biogas plant, after the biogas upgrader is mixed with the hydrogen from the electrolyzer, to upgrade the quality of the biogas. ===== Hydrogen ===== The element hydrogen can be a form of stored energy. Hydrogen can produce electricity via a hydrogen fuel cell. At penetrations below 20% of the grid demand, renewables do not severely change the economics; but beyond about 20% of the total demand, external storage becomes important. If these sources are used to make ionic hydrogen, they can be freely expanded. A 5-year community-based pilot program using wind turbines and hydrogen generators began in 2007 in the remote community of Ramea, Newfoundland and Labrador. A similar project began in 2004 on Utsira, a small Norwegian island. Energy losses involved in the hydrogen storage cycle come from the electrolysis of water, liquification or compression of the hydrogen and conversion to electricity. Hydrogen can also be produced from aluminum and water by stripping aluminum's naturally-occurring aluminum oxide barrier and introducing it to water. This method is beneficial because recycled aluminum cans can be used to generate hydrogen, however systems to harness this option have not been commercially developed and are much more complex than electrolysis systems. Common methods to strip the oxide layer include caustic catalysts such as sodium hydroxide and alloys with gallium, mercury and other metals. Underground hydrogen storage is the practice of hydrogen storage in caverns, salt domes and depleted oil and gas fields. Large quantities of gaseous hydrogen have been stored in caverns by Imperial Chemical Industries for many years without any difficulties. The European Hyunder project indicated in 2013 that storage of wind and solar energy using underground hydrogen would require 85 caverns. Powerpaste is a magnesium and hydrogen -based fluid gel that releases hydrogen when reacting with water. It was invented, patented and is being developed by the Fraunhofer Institute for Manufacturing Technology and Advanced Materials (IFAM) of the Fraunhofer-Gesellschaft. Powerpaste is made by combining magnesium powder with hydrogen to form magnesium hydride in a process conducted at 350 °C and five to six times atmospheric pressure. An ester and a metal salt are then added to make the finished product. Fraunhofer states that they are building a production plant slated to start production in 2021, which will produce 4 tons of Powerpaste annually. Fraunhofer has patented their invention in the United States and EU. Fraunhofer claims that Powerpaste is able to store hydrogen energy at 10 times the energy density of a lithium battery of a similar dimension and is safe and convenient for automotive situations. ===== Methane ===== Methane is the simplest hydrocarbon with the molecular formula CH4. Methane is more easily stored and transported than hydrogen. Storage and combustion infrastructure (pipelines, gasometers, power plants) are mature. Synthetic natural gas (syngas or SNG) can be created in a multi-step process, starting with hydrogen and oxygen. Hydrogen is then reacted with carbon dioxide in a Sabatier process, producing methane and water. Methane can be stored and later used to produce electricity. The resulting water is recycled, reducing the need for water. In the electrolysis stage, oxygen is stored for methane combustion in a pure oxygen environment at an adjacent power plant, eliminating nitrogen oxides. Methane combustion produces carbon dioxide (CO2) and water. The carbon dioxide can be recycled to boost the Sabatier process and water can be recycled for further electrolysis. Methane production, storage and combustion recycles the reaction products. The CO2 has economic value as a component of an energy storage vector, not a cost as in carbon capture and storage. ==== Power-to-liquid ==== Power-to-liquid is similar to power to gas except that the hydrogen is converted into liquids such as methanol or ammonia. These are easier to handle than gases, and require fewer safety precautions than hydrogen. They can be used for transportation, including aircraft, but also for industrial purposes or in the power sector. ==== Biofuels ==== Various biofuels such as biodiesel, vegetable oil, alcohol fuels, or biomass can replace fossil fuels. Various chemical processes can convert the carbon and hydrogen in coal, natural gas, plant and animal biomass and organic wastes into short hydrocarbons suitable as replacements for existing hydrocarbon fuels. Examples are Fischer–Tropsch diesel, methanol, dimethyl ether and syngas. This diesel source was used extensively in World War II in Germany, which faced limited access to crude oil supplies. South Africa produces most of the country's diesel from coal for similar reasons. A long term oil price above US$35/bbl may make such large scale synthetic liquid fuels economical. ===== Aluminum ===== Aluminum has been proposed as an energy store by a number of researchers. Its electrochemical equivalent (8.04 Ah/cm3) is nearly four times greater than that of lithium (2.06 Ah/cm3). Energy can be extracted from aluminum by reacting it with water to generate hydrogen. However, it must first be stripped of its natural oxide layer, a process which requires pulverization, chemical reactions with caustic substances, or alloys. The byproduct of the reaction to create hydrogen is aluminum oxide, which can be recycled into aluminum with the Hall–Héroult process, making the reaction theoretically renewable. If the Hall-Heroult Process is run using solar or wind power, aluminum could be used to store the energy produced at higher efficiency than direct solar electrolysis. ==== Boron, silicon, and zinc ==== Boron, silicon, and zinc have been proposed as energy storage solutions. ==== Other chemical ==== The organic compound norbornadiene converts to quadricyclane upon exposure to light, storing solar energy as the energy of chemical bonds. A working system has been developed in Sweden as a molecular solar thermal system. === Electrical methods === ==== Capacitor ==== A capacitor (originally known as a 'condenser') is a passive two-terminal electrical component used to store energy electrostatically. Practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e., insulator). A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery, or like other types of rechargeable energy storage system. Capacitors are commonly used in electronic devices to maintain power supply while batteries change. (This prevents loss of information in volatile memory.) Conventional capacitors provide less than 360 joules per kilogram, while a conventional alkaline battery has a density of 590 kJ/kg. Capacitors store energy in an electrostatic field between their plates. Given a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge (+Q) to collect on one plate and negative charge (-Q) to collect on the other plate. If a battery is attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if an accelerating or alternating voltage is applied across the leads of the capacitor, a displacement current can flow. Besides capacitor plates, charge can also be stored in a dielectric layer. Capacitance is greater given a narrower separation between conductors and when the conductors have a larger surface area. In practice, the dielectric between the plates emits a small amount of leakage current and has an electric field strength limit, known as the breakdown voltage. However, the effect of recovery of a dielectric after a high-voltage breakdown holds promise for a new generation of self-healing capacitors. The conductors and leads introduce undesired inductance and resistance. Research is assessing the quantum effects of nanoscale capacitors for digital quantum batteries. ==== Superconducting magnetics ==== Superconducting magnetic energy storage (SMES) systems store energy in a magnetic field created by the flow of direct current in a superconducting coil that has been cooled to a temperature below its superconducting critical temperature. A typical SMES system includes a superconducting coil, power conditioning system and refrigerator. Once the superconducting coil is charged, the current does not decay and the magnetic energy can be stored indefinitely. The stored energy can be released to the network by discharging the coil. The associated inverter/rectifier accounts for about 2–3% energy loss in each direction. SMES loses the least amount of electricity in the energy storage process compared to other methods of storing energy. SMES systems offer round-trip efficiency greater than 95%. Due to the energy requirements of refrigeration and the cost of superconducting wire, SMES is used for short duration storage such as improving power quality. It also has applications in grid balancing. == Applications == === Mills === The classic application before the Industrial Revolution was the control of waterways to drive water mills for processing grain or powering machinery. Complex systems of reservoirs and dams were constructed to store and release water (and the potential energy it contained) when required. === Homes === Home energy storage is expected to become increasingly common given the growing importance of distributed generation of renewable energies (especially photovoltaics) and the important share of energy consumption in buildings. To exceed a self-sufficiency of 40% in a household equipped with photovoltaics, energy storage is needed. Multiple manufacturers produce rechargeable battery systems for storing energy, generally to hold surplus energy from home solar or wind generation. Today, for home energy storage, Li-ion batteries are preferable to lead-acid ones given their similar cost but much better performance. Tesla Motors produces two models of the Tesla Powerwall. One is a 10 kWh weekly cycle version for backup applications and the other is a 7 kWh version for daily cycle applications. In 2016, a limited version of the Tesla Powerpack 2 cost $398(US)/kWh to store electricity worth 12.5 cents/kWh (US average grid price) making a positive return on investment doubtful unless electricity prices are higher than 30 cents/kWh. RoseWater Energy produces two models of the "Energy & Storage System", the HUB 120 and SB20. Both versions provide 28.8 kWh of output, enabling it to run larger houses or light commercial premises, and protecting custom installations. The system provides five key elements into one system, including providing a clean 60 Hz Sine wave, zero transfer time, industrial-grade surge protection, renewable energy grid sell-back (optional), and battery backup. Enphase Energy announced an integrated system that allows home users to store, monitor and manage electricity. The system stores 1.2 kWh of energy and 275W/500W power output. Storing wind or solar energy using thermal energy storage though less flexible, is considerably cheaper than batteries. A simple 52-gallon electric water heater can store roughly 12 kWh of energy for supplementing hot water or space heating. For purely financial purposes in areas where net metering is available, home generated electricity may be sold to the grid through a grid-tie inverter without the use of batteries for storage. === Grid electricity and power stations === ==== Renewable energy ==== The largest source and the greatest store of renewable energy is provided by hydroelectric dams. A large reservoir behind a dam can store enough water to average the annual flow of a river between dry and wet seasons, and a very large reservoir can store enough water to average the flow of a river between dry and wet years. While a hydroelectric dam does not directly store energy from intermittent sources, it does balance the grid by lowering its output and retaining its water when power is generated by solar or wind. If wind or solar generation exceeds the region's hydroelectric capacity, then some additional source of energy is needed. Many renewable energy sources (notably solar and wind) produce variable power. Storage systems can level out the imbalances between supply and demand that this causes. Electricity must be used as it is generated or converted immediately into storable forms. The main method of electrical grid storage is pumped-storage hydroelectricity. Areas of the world such as Norway, Wales, Japan and the US have used elevated geographic features for reservoirs, using electrically powered pumps to fill them. When needed, the water passes through generators and converts the gravitational potential of the falling water into electricity. Pumped storage in Norway, which gets almost all its electricity from hydro, has currently a capacity of 1.4 GW but since the total installed capacity is nearly 32 GW and 75% of that is regulable, it can be expanded significantly. Some forms of storage that produce electricity include pumped-storage hydroelectric dams, rechargeable batteries, thermal storage including molten salts which can efficiently store and release very large quantities of heat energy, and compressed air energy storage, flywheels, cryogenic systems and superconducting magnetic coils. Surplus power can also be converted into methane (Sabatier process) with stockage in the natural gas network. In 2011, the Bonneville Power Administration in the northwestern United States created an experimental program to absorb excess wind and hydro power generated at night or during stormy periods that are accompanied by high winds. Under central control, home appliances absorb surplus energy by heating ceramic bricks in special space heaters to hundreds of degrees and by boosting the temperature of modified hot water heater tanks. After charging, the appliances provide home heating and hot water as needed. The experimental system was created as a result of a severe 2010 storm that overproduced renewable energy to the extent that all conventional power sources were shut down, or in the case of a nuclear power plant, reduced to its lowest possible operating level, leaving a large area running almost completely on renewable energy. Another advanced method used at the former Solar Two project in the United States and the Solar Tres Power Tower in Spain uses molten salt to store thermal energy captured from the sun and then convert it and dispatch it as electrical power. The system pumps molten salt through a tower or other special conduits to be heated by the sun. Insulated tanks store the solution. Electricity is produced by turning water to steam that is fed to turbines. Since the early 21st century batteries have been applied to utility scale load-leveling and frequency regulation capabilities. In vehicle-to-grid storage, electric vehicles that are plugged into the energy grid can deliver stored electrical energy from their batteries into the grid when needed. === Air conditioning === Thermal energy storage (TES) can be used for air conditioning. It is most widely used for cooling single large buildings and/or groups of smaller buildings. Commercial air conditioning systems are the biggest contributors to peak electrical loads. In 2009, thermal storage was used in over 3,300 buildings in over 35 countries. It works by chilling material at night and using the chilled material for cooling during the hotter daytime periods. The most popular technique is ice storage, which requires less space than water and is cheaper than fuel cells or flywheels. In this application, a standard chiller runs at night to produce an ice pile. Water circulates through the pile during the day to chill water that would normally be the chiller's daytime output. A partial storage system minimizes capital investment by running the chillers nearly 24 hours a day. At night, they produce ice for storage and during the day they chill water. Water circulating through the melting ice augments the production of chilled water. Such a system makes ice for 16 to 18 hours a day and melts ice for six hours a day. Capital expenditures are reduced because the chillers can be just 40% – 50% of the size needed for a conventional, no-storage design. Storage sufficient to store half a day's available heat is usually adequate. A full storage system shuts off the chillers during peak load hours. Capital costs are higher, as such a system requires larger chillers and a larger ice storage system. This ice is produced when electrical utility rates are lower. Off-peak cooling systems can lower energy costs. The U.S. Green Building Council has developed the Leadership in Energy and Environmental Design (LEED) program to encourage the design of reduced-environmental impact buildings. Off-peak cooling may help toward LEED Certification. Thermal storage for heating is less common than for cooling. An example of thermal storage is storing solar heat to be used for heating at night. Latent heat can also be stored in technical phase change materials (PCMs). These can be encapsulated in wall and ceiling panels, to moderate room temperatures. === Transport === Liquid hydrocarbon fuels are the most commonly used forms of energy storage for use in transportation, followed by a growing use of Battery Electric Vehicles and Hybrid Electric Vehicles. Other energy carriers such as hydrogen can be used to avoid producing greenhouse gases. Public transport systems like trams and trolleybuses require electricity, but due to their variability in movement, a steady supply of electricity via renewable energy is challenging. Photovoltaic systems installed on the roofs of buildings can be used to power public transportation systems during periods in which there is increased demand for electricity and access to other forms of energy are not readily available. Upcoming transitions in the transportation system also include e.g. ferries and airplanes, where electric power supply is investigated as an interesting alternative. === Electronics === Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems they stabilize voltage and power flow. == Use cases == The United States Department of Energy International Energy Storage Database (IESDB), is a free-access database of energy storage projects and policies funded by the United States Department of Energy Office of Electricity and Sandia National Labs. == Capacity == Storage capacity is the amount of energy extracted from an energy storage device or system; usually measured in joules or kilowatt-hours and their multiples, it may be given in number of hours of electricity production at power plant nameplate capacity; when storage is of primary type (i.e., thermal or pumped-water), output is sourced only with the power plant embedded storage system. == Economics == The economics of energy storage strictly depends on the reserve service requested, and several uncertainty factors affect the profitability of energy storage. Therefore, not every storage method is technically and economically suitable for the storage of several MWh, and the optimal size of the energy storage is market and location dependent. Moreover, ESS are affected by several risks, e.g.: Techno-economic risks, which are related to the specific technology; Market risks, which are the factors that affect the electricity supply system; Regulation and policy risks. Therefore, traditional techniques based on deterministic Discounted Cash Flow (DCF) for the investment appraisal are not fully adequate to evaluate these risks and uncertainties and the investor's flexibility to deal with them. Hence, the literature recommends to assess the value of risks and uncertainties through the Real Option Analysis (ROA), which is a valuable method in uncertain contexts. The economic valuation of large-scale applications (including pumped hydro storage and compressed air) considers benefits including: curtailment avoidance, grid congestion avoidance, price arbitrage and carbon-free energy delivery. In one technical assessment by the Carnegie Mellon Electricity Industry Centre, economic goals could be met using batteries if their capital cost was $30 to $50 per kilowatt-hour. A metric of energy efficiency of storage is energy storage on energy invested (ESOI), which is the amount of energy that can be stored by a technology, divided by the amount of energy required to build that technology. The higher the ESOI, the better the storage technology is energetically. For lithium-ion batteries this is around 10, and for lead acid batteries it is about 2. Other forms of storage such as pumped hydroelectric storage generally have higher ESOI, such as 210. Pumped-storage hydroelectricity is by far the largest storage technology used globally. However, the usage of conventional pumped-hydro storage is limited because it requires terrain with elevation differences and also has a very high land use for relatively small power. In locations without suitable natural geography, underground pumped-hydro storage could also be used. High costs and limited life still make batteries a "weak substitute" for dispatchable power sources, and are unable to cover for variable renewable power gaps lasting for days, weeks or months. In grid models with high VRE share, the excessive cost of storage tends to dominate the costs of the whole grid — for example, in California alone 80% share of VRE would require 9.6 TWh of storage but 100% would require 36.3 TWh. As of 2018 the state only had 150 GWh of storage, primarily in pumped storage and a small fraction in batteries. According to another study, supplying 80% of US demand from VRE would require a smart grid covering the whole country or battery storage capable to supply the whole system for 12 hours, both at cost estimated at $2.5 trillion. Similarly, several studies have found that relying only on VRE and energy storage would cost about 30–50% more than a comparable system that combines VRE with nuclear plants or plants with carbon capture and storage instead of energy storage. == Research == === Germany === In 2013, the German government allocated €200M (approximately US$270M) for research, and another €50M to subsidize battery storage in residential rooftop solar panels, according to a representative of the German Energy Storage Association. Siemens AG commissioned a production-research plant to open in 2015 at the Zentrum für Sonnenenergie und Wasserstoff (ZSW, the German Center for Solar Energy and Hydrogen Research in the State of Baden-Württemberg), a university/industry collaboration in Stuttgart, Ulm and Widderstall, staffed by approximately 350 scientists, researchers, engineers, and technicians. The plant develops new near-production manufacturing materials and processes (NPMM&P) using a computerized Supervisory Control and Data Acquisition (SCADA) system. It aims to enable the expansion of rechargeable battery production with increased quality and lower cost. From 2023 onwards, a new project by the German Research Foundation focuses on molecular photoswitches to store solar thermal energy. The spokesperson of these so-called molecular solar thermal (MOST) systems is Prof. Dr. Hermann A. Wegner. === United States === In 2014, research and test centers opened to evaluate energy storage technologies. Among them was the Advanced Systems Test Laboratory at the University of Wisconsin at Madison in Wisconsin State, which partnered with battery manufacturer Johnson Controls. The laboratory was created as part of the university's newly opened Wisconsin Energy Institute. Their goals include the evaluation of state-of-the-art and next generation electric vehicle batteries, including their use as grid supplements. The State of New York unveiled its New York Battery and Energy Storage Technology (NY-BEST) Test and Commercialization Center at Eastman Business Park in Rochester, New York, at a cost of $23 million for its almost 1,700 m2 laboratory. The center includes the Center for Future Energy Systems, a collaboration between Cornell University of Ithaca, New York and the Rensselaer Polytechnic Institute in Troy, New York. NY-BEST tests, validates and independently certifies diverse forms of energy storage intended for commercial use. On September 27, 2017, Senators Al Franken of Minnesota and Martin Heinrich of New Mexico introduced Advancing Grid Storage Act (AGSA), which would devote more than $1 billion in research, technical assistance and grants to encourage energy storage in the United States. In grid models with high VRE share, the excessive cost of storage tends to dominate the costs of the whole grid – for example, in California alone 80% share of VRE would require 9.6 TWh of storage but 100% would require 36.3 TWh. According to another study, supplying 80% of US demand from VRE would require a smart grid covering the whole country or battery storage capable to supply the whole system for 12 hours, both at cost estimated at $2.5 trillion. === United Kingdom === In the United Kingdom, some 14 industry and government agencies allied with seven British universities in May 2014 to create the SUPERGEN Energy Storage Hub in order to assist in the coordination of energy storage technology research and development. == See also == == References == == Further reading == Journals and papers Chen, Haisheng; Thang Ngoc Cong; Wei Yang; Chunqing Tan; Yongliang Li; Yulong Ding. Progress in electrical energy storage system: A critical review, Progress in Natural Science, accepted July 2, 2008, published in Vol. 19, 2009, pp. 291–312, doi: 10.1016/j.pnsc.2008.07.014. Sourced from the National Natural Science Foundation of China and the Chinese Academy of Sciences. Published by Elsevier and Science in China Press. Synopsis: a review of electrical energy storage technologies for stationary applications. Retrieved from ac.els-cdn.com on May 13, 2014. (PDF) Corum, Lyn. The New Core Technology: Energy storage is part of the smart grid evolution, The Journal of Energy Efficiency and Reliability, December 31, 2009. Discusses: Anaheim Public Utilities Department, lithium ion energy storage, iCel Systems, Beacon Power, Electric Power Research Institute (EPRI), ICEL, Self Generation Incentive Program, ICE Energy, vanadium redox flow, lithium Ion, regenerative fuel cell, ZBB, VRB, lead acid, CAES, and Thermal Energy Storage. (PDF) de Oliveira e Silva, G.; Hendrick, P. (2016). "Lead-acid batteries coupled with photovoltaics for increased electricity self-sufficiency in households". Applied Energy. 178: 856–867. Bibcode:2016ApEn..178..856D. doi:10.1016/j.apenergy.2016.06.003. Sahoo, Subrat; Timmann, Pascal (2023). "Energy Storage Technologies for Modern Power Systems: A Detailed Analysis of Functionalities, Potentials, and Impacts" (PDF). IEEE Access. 11: 49689–49729. Bibcode:2023IEEEA..1149689S. doi:10.1109/ACCESS.2023.3274504. ISSN 2169-3536. Retrieved December 14, 2024. Whittingham, M. Stanley. History, Evolution, and Future Status of Energy Storage, Proceedings of the IEEE, manuscript accepted February 20, 2012, date of publication April 16, 2012; date of current version May 10, 2012, published in Proceedings of the IEEE, Vol. 100, May 13, 2012, 0018–9219, pp. 1518–1534, doi: 10.1109/JPROC.2012.219017. Retrieved from ieeexplore.ieee.org May 13, 2014. Synopsis: A discussion of the important aspects of energy storage including emerging battery technologies and the importance of storage systems in key application areas, including electronic devices, transportation, and the utility grid. (PDF) Books GA Mansoori, N Enayati, LB Agyarko (2016), Energy: Sources, Utilization, Legislation, Sustainability, Illinois as Model State, World Sci. Pub. Co., ISBN 978-981-4704-00-7 Díaz-González, Franscisco (2016). Energy storage in power systems. United Kingdom: John Wiley & Sons. ISBN 9781118971321. == External links == U.S. Dept of Energy – Energy Storage Systems Government research center on energy storage technology. U.S. Dept of Energy – International Energy Storage Database Archived November 13, 2013, at the Wayback Machine The DOE International Energy Storage Database provides free, up-to-date information on grid-connected energy storage projects and relevant state and federal policies. IEEE Special Issue on Massive Energy Storage IEA-ECES – International Energy Agency – Energy Conservation through Energy Conservation programme. Energy Information Administration Glossary Energy Storage Project Regeneration.
Wikipedia/Energy_storage
Airborne wind energy (AWE) is the direct use or generation of wind energy by the use of aerodynamic or aerostatic lift devices. AWE technology is able to harvest high altitude winds, in contrast to wind turbines, which use a rotor mounted on a tower. The term high-altitude wind power (HAWP) has been used to refer to AWE systems. However, semantically HAWP might also include wind energy conversion systems that are somehow positioned at a large height from the ground or sea surface. Various mechanisms are proposed for capturing the kinetic energy of winds such as kites, kytoons, aerostats, gliders, gliders with turbines for regenerative soaring, sailplanes with turbines, or other airfoils, including multiple-point building- or terrain-enabled holdings. Once the mechanical energy is derived from the wind's kinetic energy, then many options are available for using that mechanical energy: direct traction, conversion to electricity aloft or at ground station, conversion to laser or microwave for power beaming to other aircraft or ground receivers. Energy generated by a high-altitude system may be used aloft or sent to the ground surface by conducting cables, mechanical force through a tether, rotation of endless line loop, movement of changed chemicals, flow of high-pressure gases, flow of low-pressure gases, or laser or microwave power beams. == High-altitude wind for power purposes == Winds at higher altitudes become steadier, more persistent, and of higher velocity. Because power available in wind increases as the cube of velocity (the velocity-cubed law), assuming other parameters remaining the same, doubling a wind's velocity gives 23=8 times the power; tripling the velocity gives 33=27 times the available power. With steadier and more predictable winds, high-altitude wind has an advantage over wind near the ground. Being able to locate HAWP to effective altitudes and using the vertical dimension of airspace for wind farming brings further advantage using high-altitude winds for generating energy. High-altitude wind generators can be adjusted in height and position to maximize energy return, which is impractical with fixed tower-mounted wind generators. In each range of altitudes there are altitude-specific concerns being addressed by researchers and developers. As altitude increases, tethers increase in length, the temperature of the air changes, and vulnerability to atmospheric lightning changes. With increasing altitude, exposure to liabilities increase, costs increase, turbulence exposure changes, likelihood of having the system fly in more than one directional strata of winds increases, and the costs of operation changes. HAWP systems that are flown must climb through all intermediate altitudes up to final working altitudes—being at first a low- and then a high- altitude device. An atlas of the high-altitude wind power resource has been prepared for all points on Earth. A similar atlas of global assessment was developed at Joby Energy. == Methods of capturing kinetic energy of high-altitude winds == Energy can be captured from the wind by kites, kytoons, tethered gliders, tethered sailplanes, aerostats (spherical as well as shaped kytoons), bladed turbines, airfoils, airfoil matrices, drogues, variable drogues, spiral airfoils, Darrieus turbines, Magnus-effect VAWT blimps, multiple-rotor complexes, fabric Jalbert-parafoil kites, uni-blade turbines, flipwings, tethers, bridles, string loops, wafting blades, undulating forms, and piezoelectric materials, and more. When a scheme's purpose is to propel ships and boats, the objects tether-placed in the wind will tend to have most of the captured energy be in useful tension in the main tether. The aloft working bodies will be operated to maintain useful tension even while the ship is moving. This is the method for powerkiting sports. This sector of HAWP is the most installed method. Folklore suggests that Benjamin Franklin used the traction method of HAWP. George Pocock was a pioneer in tugging vehicles by traction. === Controls === HAWP aircraft need to be controlled. Solutions in built systems have control mechanisms variously situated. Some systems are passive, or active, or a mix. When a kite steering unit (KSU) is lofted, the KSU may be robotic and self-contained; a KSU may be operated from the ground via radio-control by a live human operator or by smart computer programs. Some systems have built sensors in the aircraft body that report parameters like position, relative position to other parts. Kite control units (KCU) have involved more than steering; tether reeling speeds and directions can be adjusted in response to tether tensions and needs of the system during a power-generating phase or return-non-power-generating phase. Kite control parts vary widely. == Methods of converting the energy == The mechanical energy of the device may be converted to heat, sound, electricity, light, tension, pushes, pulls, laser, microwave, chemical changes, or compression of gases. Traction is a big direct use of the mechanical energy as in tugging cargo ships and kiteboarders. There are several methods of getting the mechanical energy from the wind's kinetic energy. Lighter-than-air (LTA) moored aerostats are employed as lifters of turbines. Heavier-than-air (HTA) tethered airfoils are being used as lifters or turbines themselves. Combinations of LTA and HTA devices in one system are being built and flown to capture HAWP. Even a family of free-flight airborne devices are represented in the literature that capture the kinetic energy of high-altitude winds (beginning with a description in 1967 by Richard Miller in his book Without Visible Means of Support) and a contemporary patent application by Dale C. Kramer, soaring sailplane competitor, inventor. A research on airborne wind turbine technology innovations reveals that the “Kite type AWTs” technique, the most common type, has high scope of growth in the future; it has contributed for about 44% of the total airborne wind energy during 2008–2012. The kite type AWTs extract energy through wind turbines suspended at high altitudes using kites such as multi-tethered kite, kite and dual purpose circular fan, rotary wing kites etc. === Electric generator position in a HAWP system === Electricity generation is just one of the options for capturing mechanical energy; however, this option dominates the focus of professionals aiming to supply large amounts of energy to commerce and utilities. A long array of secondary options include tugging water turbines, pumping of water, or compressing air or hydrogen. The position of the electric generator is a distinguishing feature among systems. Flying the generator aloft is done in a variety of ways. Keeping the generator at the mooring region is another large design option. The option in one system of a generator aloft and at the ground station has been used where a small generator operates electronic devices aloft while the ground generator is the big worker to make electricity for significant loads. === Carousel generator === The “Carousel” configuration several kites fly at a constant height and higher altitudes, pulling in rotation a generator that moves on a wide circular rail. For a large Carousel system, the power obtained can be calculated as of the order of GW, exposing a law that see the power attainable as a function of the diameter raised to the fifth power, while the increment of cost of the generator is linear. === Aerostat-based HAWP === One method of keeping working HAWP systems aloft is to use buoyant aerostats whether or not the electric generator is lifted or left on the ground. The aerostats are usually, but not always, shaped to achieve a kiting lifting effect. Recharging leaked lifting gas receives various solutions. In case of productive winds the aerostats are typically blown down by the aerodynamic drag applied on the wide and unavoidable Reynolds surface excluding them de facto from the HAWP category. W. R. Benoit US Patent 4350897 Lighter than air wind energy conversion system by William R. Benoit, filed Oct 24,1980, and issued: Sep 21, 1982. The TWIND system ( International patent application PCT/W02010/015720) is based on the use of a sail surface elevated by the climbing force of an aerostatic balloon connected to the ground by a cable used also for energy transmission. The wind present at high altitudes creates a horizontal push on the sail which in its movement transmits this energy to the ground via the connecting cable. At the end of its movement forward, the sail surface is reduced allowing it to move upwind with reduced energy waste. The Magenn aerostat is a vertical-axis wind turbine held with its axis horizontal by bridling the axis traverse to the wind so that Magnus-effect lift obtains during autorotation; the electricity is generated with end-hub generators. The LTA Windpower PowerShip uses lift from both an aerostat and wings. It operates close to neutral buoyancy and doesn't require a winch. Power is generated by turbines with the propellers on the trailing edge of the wings. The system is designed to be able to take off and land unattended. Airbine proposes to lift wind turbines into the air by use of aerostats; the electricity would return to ground loads by way of conductive tether. Airship power turbine by William J. Mouton, Jr., and David F. Thompson: Their system integrated the turbine within the central portion of a near-toroidal aerostat, like putting a turbine in the hole of an aerostat donut. The HAWE system is developed from Tiago Pardal's idea. This system consists of a pumping cycle similar to that of kite systems. In the generation phase, the pulling force increases 5–10 times due to the Magnus effect of a spinning cylinder (aerial platform). Like a kite, the pulling force produced by the aerial platform will unwind the cable and generate electricity on the ground. In the recovery phase it rewinds the cable with no Magnus effect in the aerial platform. Wind Fisher is developing cross-wind capable Magnus effect balloons which generate electricity with ground based generators operating a pumping cycle with a pair of helium inflated, lighter-than-air cylindrical wings. The company, based near Grenoble, is currently testing a 1.7m span heavier-than-air prototype. An open source concept, released in 2023, proposed a helium-filled balloon with attached sails, which create pressure and drive the rotation of the system around its horizontal axis. The kinetic energy is transferred to a generator on the ground through ropes in circular motion. == Non-airborne systems == Conceptually, two adjacent mountains (natural or terrain-enabled) or artificial buildings or towers (urban or artificial) could have a wind turbine suspended between them by use of cables. When HAWP is cabled between two mountain tops across a valley, the HAWP device is not airborne, but borne up by the cable system. No such systems are known to be in use, though patents teach these methods. When non-cabled bridges are the foundation for holding wind turbines high above the ground, then these are grouped with conventional towered turbines and are outside the intent of HAWP where the tethering an airborne system is foundational. == Safety == Lightning, aircraft traffic, emergency procedures, system inspections, visibility marking of system parts and its tethers, electrical safety, runaway-wing procedures, over-powering controls, appropriate mooring, and more form the safety environment for HAWP systems. == Challenges as an emerging industry == There have been several periods of high interest in HAWP before the contemporary activity. The first period had a high focus on pulling carriages over the lands and capturing atmospheric electricity and lightning for human use. The second period was in the 1970s and 1980s when research and investment flourished; a drop in oil price resulted in no significant installations of HAWP. Return on investment (ROI) has been the key parameter; that ROI remains in focus in the current development activity while in the background is the renewable and sustainable energy movement supporting wind power of any kind; but HAWP must compete on ROI with conventional towered solutions. A test center at Lista, Norway provides independent verification of research. == Early references to HAWP == Early centuries of kiting demonstrated that the kite is a rotary engine that rotates its tether part about its mooring point and causes hands and arms to move because of the energy captured from higher winds into the mechanical device. The tension in the lofted devices performs the work of lifting and pulling body parts and things. Airborne wind energy (AWE) for HAWP was birthed thousands of years ago; naming what happened and developing the implied potentials of tethered aircraft for doing special works is what is occurring in AWE HAWP. What is "low" for some workers is "high" for others. 1796 George Pocock used traction mode to travel in vehicles over land roads. 1827 George Pocock's book ‘The Aeropleustic Art’ or 'Navigation in the Air by the Use of Kites or Buoyant Sails' was published. Pocock described use of kites for land and sea travel. The book was republished several times. 1833 John Adolphus Etzler saw HAWP blossoming at least for traction. 1864? Book's chapter Kite-Ship well describes key dynamics of HAWP used for tugging ships by kites. John Gay's: or Work for Boys. Chapter XVIII in the Summer volume. 1935 Aloys van Gries stands as a strong early patentee of high-altitude wind power; he taught various kite systems for use in generating electricity in his DE 656194 C patent: Durch Drachen getragene Windkraftmaschine zur Nutzbarmachung von Hoehenwinden 1943 Stanley Biszak instructed using potential energy in free-flight for converting ambient winds impacting turbine to drive electric generator to charge batteries. 1967 Richard Miller, former editor of Soaring magazine, published book Without Visible Means of Support that describes the feasibility of free-flight coupled non-ground-moored kites to capture differences in wind strata to travel across continents; such HAWP is the subject of Dale C. Kramer's contemporary patent application. 1973? Hermann Oberth In the appendix of his book Primer for Those Who Would Govern there are sketches and a photograph of a model of the Kite Power Station from the Oberth Museum. 1977 April 3, 1977, invention declared. On September 21, 1979, Douglas Selsam notarized his kite-lifted endless chain of airfoils HAWP system, generic type that would later show in Dutch astronaut Wubbo Ockels' device called LadderMill described in a patent of 1997. Douglas Selsam conceived his Auto-oriented Wind Harnessing Buoyant Aerial Tramway on April 3, 1977. On the Selsam notarized disclosure of invention was placed a date of Sept. 20, while the notary placed the final signing on Sept. 21, 1979. notes and drawings. 1979 Professor Bryan Roberts begins giromill gyrocopter-type HAWP wind generator development. 1980 Miles Loyd publishes an article on the crosswind kite power. 1986 Bryan Roberts' AWE HAWP rotor generates electricity and lifts itself in tethered flight. 1992 Free Rotor WO/1992020917 Free Rotor by JACK, Colin, Humphry, Bruce (one man). Colin Jack. Colin Bruce. Multi-rotors are treated. Faired tethers are recognized. 1992. == Autorotation == Autorotation is the basis of a large sector of AWE technology. High altitude wind power research and development centers frequently are dependent on blade autorotation: SkyMill Energy, Joby Energy, Sky Windpower, BaseLoad Energy, Magenn Power, and Makani Power are making and testing airborne wind energy conversion systems (AWECS) that employ autorotation of blades to drive the shafts of generators to make electricity at altitude and send the electricity to earth via conductive tethers. == See also == Airborne Wind Energy Industry Association Airborne wind turbine Altitude Betz' law Crosswind kite power Kite applications KiteGen Kite types Laddermill Linear Generation system List of airborne wind energy organizations Tether Turbine Wind Wind farm Wind power Wind profile power law Wind resource assessment Wind turbine == References == == Bibliography == Vance, E. Wind power: High hopes. Nature 460, 564–566 (2009). https://doi.org/10.1038/460564a == External links == Airborne Wind Energy Participants List TU Delft kite power research group Archived 2013-04-03 at the Wayback Machine Energy Kite Systems a glossary of terms and links to HAWP systems AWESystems.info list of organizations Assessing the Viability of High Altitude Wind Resources in Ireland, Colm O’Gairbhith for Carbon Tracking
Wikipedia/Airborne_wind_energy
Power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. Power is a scalar quantity. Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the product of the aerodynamic drag plus traction force on the wheels, and the velocity of the vehicle. The output power of a motor is the product of the torque that the motor generates and the angular velocity of its output shaft. Likewise, the power dissipated in an electrical element of a circuit is the product of the current flowing through the element and of the voltage across the element. == Definition == Power is the rate with respect to time at which work is done or, more generally, the rate of change of total mechanical energy. It is given by: P = d E d t , {\displaystyle P={\frac {dE}{dt}},} where P is power, E is the total mechanical energy (sum of kinetic and potential energy), and t is time. For cases where only work is considered, power is also expressed as: P = d W d t , {\displaystyle P={\frac {dW}{dt}},} where W is the work done on the system. However, in systems where potential energy changes without explicit work being done (e.g., changing fields or conservative forces), the total energy definition is more general. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} } If a constant force F is applied throughout a distance x, the work done is defined as W = F ⋅ x {\displaystyle W=\mathbf {F} \cdot \mathbf {x} } . In this case, power can be written as: P = d W d t = d d t ( F ⋅ x ) = F ⋅ d x d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\left(\mathbf {F} \cdot \mathbf {x} \right)=\mathbf {F} \cdot {\frac {d\mathbf {x} }{dt}}=\mathbf {F} \cdot \mathbf {v} .} If instead the force is variable over a three-dimensional curve C, then the work is expressed in terms of the line integral: W = ∫ C F ⋅ d r = ∫ Δ t F ⋅ d r d t d t = ∫ Δ t F ⋅ v d t . {\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} =\int _{\Delta t}\mathbf {F} \cdot {\frac {d\mathbf {r} }{dt}}\ dt=\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt.} From the fundamental theorem of calculus, we know that P = d W d t = d d t ∫ Δ t F ⋅ v d t = F ⋅ v . {\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt=\mathbf {F} \cdot \mathbf {v} .} Hence the formula is valid for any general situation. In older works, power is sometimes called activity. == Units == The dimension of power is energy divided by time. In the International System of Units (SI), the unit of power is the watt (W), which is equal to one joule per second. Other common and traditional measures are horsepower (hp), comparing to the power of a horse; one mechanical horsepower equals about 745.7 watts. Other units of power include ergs per second (erg/s), foot-pounds per minute, dBm, a logarithmic measure relative to a reference of 1 milliwatt, calories per hour, BTU per hour (BTU/h), and tons of refrigeration. == Average power and instantaneous power == As a simple example, burning one kilogram of coal releases more energy than detonating a kilogram of TNT, but because the TNT reaction releases energy more quickly, it delivers more power than the coal. If ΔW is the amount of work performed during a period of time of duration Δt, the average power Pavg over that period is given by the formula P a v g = Δ W Δ t . {\displaystyle P_{\mathrm {avg} }={\frac {\Delta W}{\Delta t}}.} It is the average amount of work done or energy converted per unit of time. Average power is often called "power" when the context makes it clear. Instantaneous power is the limiting value of the average power as the time interval Δt approaches zero. P = lim Δ t → 0 P a v g = lim Δ t → 0 Δ W Δ t = d W d t . {\displaystyle P=\lim _{\Delta t\to 0}P_{\mathrm {avg} }=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {dW}{dt}}.} When power P is constant, the amount of work performed in time period t can be calculated as W = P t . {\displaystyle W=Pt.} In the context of energy conversion, it is more customary to use the symbol E rather than W. == Mechanical power == Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity. Mechanical power is also described as the time derivative of work. In mechanics, the work done by a force F on an object that travels along a curve C is given by the line integral: W C = ∫ C F ⋅ v d t = ∫ C F ⋅ d x , {\displaystyle W_{C}=\int _{C}\mathbf {F} \cdot \mathbf {v} \,dt=\int _{C}\mathbf {F} \cdot d\mathbf {x} ,} where x defines the path C and v is the velocity along this path. If the force F is derivable from a potential (conservative), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields: W C = U ( A ) − U ( B ) , {\displaystyle W_{C}=U(A)-U(B),} where A and B are the beginning and end of the path along which the work was done. The power at any point along the curve C is the time derivative: P ( t ) = d W d t = F ⋅ v = − d U d t . {\displaystyle P(t)={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} =-{\frac {dU}{dt}}.} In one dimension, this can be simplified to: P ( t ) = F ⋅ v . {\displaystyle P(t)=F\cdot v.} In rotational systems, power is the product of the torque τ and angular velocity ω, P ( t ) = τ ⋅ ω , {\displaystyle P(t)={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},} where ω is angular frequency, measured in radians per second. The ⋅ {\displaystyle \cdot } represents scalar product. In fluid power systems such as hydraulic actuators, power is given by P ( t ) = p Q , {\displaystyle P(t)=pQ,} where p is pressure in pascals or N/m2, and Q is volumetric flow rate in m3/s in SI units. === Mechanical advantage === If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the mechanical advantage of the system. Let the input power to a device be a force FA acting on a point that moves with velocity vA and the output power be a force FB acts on a point that moves with velocity vB. If there are no losses in the system, then P = F B v B = F A v A , {\displaystyle P=F_{\text{B}}v_{\text{B}}=F_{\text{A}}v_{\text{A}},} and the mechanical advantage of the system (output force per input force) is given by M A = F B F A = v A v B . {\displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}.} The similar relationship is obtained for rotating systems, where TA and ωA are the torque and angular velocity of the input and TB and ωB are the torque and angular velocity of the output. If there are no losses in the system, then P = T A ω A = T B ω B , {\displaystyle P=T_{\text{A}}\omega _{\text{A}}=T_{\text{B}}\omega _{\text{B}},} which yields the mechanical advantage M A = T B T A = ω A ω B . {\displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.} These relations are important because they define the maximum performance of a device in terms of velocity ratios determined by its physical dimensions. See for example gear ratios. == Electrical power == The instantaneous electrical power P delivered to a component is given by P ( t ) = I ( t ) ⋅ V ( t ) , {\displaystyle P(t)=I(t)\cdot V(t),} where P ( t ) {\displaystyle P(t)} is the instantaneous power, measured in watts (joules per second), V ( t ) {\displaystyle V(t)} is the potential difference (or voltage drop) across the component, measured in volts, and I ( t ) {\displaystyle I(t)} is the current through it, measured in amperes. If the component is a resistor with time-invariant voltage to current ratio, then: P = I ⋅ V = I 2 ⋅ R = V 2 R , {\displaystyle P=I\cdot V=I^{2}\cdot R={\frac {V^{2}}{R}},} where R = V I {\displaystyle R={\frac {V}{I}}} is the electrical resistance, measured in ohms. == Peak power and duty cycle == In the case of a periodic signal s ( t ) {\displaystyle s(t)} of period T {\displaystyle T} , like a train of identical pulses, the instantaneous power p ( t ) = | s ( t ) | 2 {\textstyle p(t)=|s(t)|^{2}} is also a periodic function of period T {\displaystyle T} . The peak power is simply defined by: P 0 = max [ p ( t ) ] . {\displaystyle P_{0}=\max[p(t)].} The peak power is not always readily measurable, however, and the measurement of the average power P a v g {\displaystyle P_{\mathrm {avg} }} is more commonly performed by an instrument. If one defines the energy per pulse as ε p u l s e = ∫ 0 T p ( t ) d t {\displaystyle \varepsilon _{\mathrm {pulse} }=\int _{0}^{T}p(t)\,dt} then the average power is P a v g = 1 T ∫ 0 T p ( t ) d t = ε p u l s e T . {\displaystyle P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}p(t)\,dt={\frac {\varepsilon _{\mathrm {pulse} }}{T}}.} One may define the pulse length τ {\displaystyle \tau } such that P 0 τ = ε p u l s e {\displaystyle P_{0}\tau =\varepsilon _{\mathrm {pulse} }} so that the ratios P a v g P 0 = τ T {\displaystyle {\frac {P_{\mathrm {avg} }}{P_{0}}}={\frac {\tau }{T}}} are equal. These ratios are called the duty cycle of the pulse train. == Radiant power == Power is related to intensity at a radius r {\displaystyle r} ; the power emitted by a source can be written as: P ( r ) = I ( 4 π r 2 ) . {\displaystyle P(r)=I(4\pi r^{2}).} == See also == Simple machines Orders of magnitude (power) Pulsed power Intensity – in the radiative sense, power per area Power gain – for linear, two-port networks Power density Signal strength Sound power == References ==
Wikipedia/Power_(physics)
In physics and chemistry, binding energy is the smallest amount of energy required to remove a particle from a system of particles or to disassemble a system of particles into individual parts. In the former meaning the term is predominantly used in condensed matter physics, atomic physics, and chemistry, whereas in nuclear physics the term separation energy is used. A bound system is typically at a lower energy level than its unbound constituents. According to relativity theory, a ΔE decrease in the total energy of a system is accompanied by a decrease Δm in the total mass, where Δmc2 = ΔE. == Types == There are several types of binding energy, each operating over a different distance and energy scale. The smaller the size of a bound system, the higher its associated binding energy. == Mass–energy relation == A bound system is typically at a lower energy level than its unbound constituents because its mass must be less than the total mass of its unbound constituents. For systems with low binding energies, this "lost" mass after binding may be fractionally small, whereas for systems with high binding energies, the missing mass may be an easily measurable fraction. This missing mass may be lost during the process of binding as energy in the form of heat or light, with the removed energy corresponding to the removed mass through Einstein's equation E = mc2. In the process of binding, the constituents of the system might enter higher energy states of the nucleus/atom/molecule while retaining their mass, and because of this, it is necessary that they are removed from the system before its mass can decrease. Once the system cools to normal temperatures and returns to ground states regarding energy levels, it will contain less mass than when it first combined and was at high energy. This loss of heat represents the "mass deficit", and the heat itself retains the mass that was lost (from the point of view of the initial system). This mass will appear in any other system that absorbs the heat and gains thermal energy. For example, if two objects are attracting each other in space through their gravitational field, the attraction force accelerates the objects, increasing their velocity, which converts their potential energy (gravity) into kinetic energy. When the particles either pass through each other without interaction or elastically repel during the collision, the gained kinetic energy (related to speed) begins to revert into potential energy, driving the collided particles apart. The decelerating particles will return to the initial distance and beyond into infinity, or stop and repeat the collision (oscillation takes place). This shows that the system, which loses no energy, does not combine (bind) into a solid object, parts of which oscillate at short distances. Therefore, to bind the particles, the kinetic energy gained due to the attraction must be dissipated by resistive force. Complex objects in collision ordinarily undergo inelastic collision, transforming some kinetic energy into internal energy (heat content, which is atomic movement), which is further radiated in the form of photons – the light and heat. Once the energy to escape the gravity is dissipated in the collision, the parts will oscillate at a closer, possibly atomic, distance, thus looking like one solid object. This lost energy, necessary to overcome the potential barrier to separate the objects, is the binding energy. If this binding energy were retained in the system as heat, its mass would not decrease, whereas binding energy lost from the system as heat radiation would itself have mass. It directly represents the "mass deficit" of the cold, bound system. Closely analogous considerations apply in chemical and nuclear reactions. Exothermic chemical reactions in closed systems do not change mass, but do become less massive once the heat of reaction is removed, though this mass change is too small to measure with standard equipment. In nuclear reactions, the fraction of mass that may be removed as light or heat, i.e. binding energy, is often a much larger fraction of the system mass. It may thus be measured directly as a mass difference between rest masses of reactants and (cooled) products. This is because nuclear forces are comparatively stronger than the Coulombic forces associated with the interactions between electrons and protons that generate heat in chemistry. === Mass change === Mass change (decrease) in bound systems, particularly atomic nuclei, has also been termed mass defect, mass deficit, or mass packing fraction. The difference between the unbound system calculated mass and experimentally measured mass of nucleus (mass change) is denoted as Δm. It can be calculated as follows: Mass change = (unbound system calculated mass) − (measured mass of system) e.g. (sum of masses of protons and neutrons) − (measured mass of nucleus) After a nuclear reaction occurs that results in an excited nucleus, the energy that must be radiated or otherwise removed as binding energy in order to decay to the unexcited state may be in one of several forms. This may be electromagnetic waves, such as gamma radiation; the kinetic energy of an ejected particle, such as an electron, in internal conversion decay; or partly as the rest mass of one or more emitted particles, such as the particles of beta decay. No mass deficit can appear, in theory, until this radiation or this energy has been emitted and is no longer part of the system. When nucleons bind together to form a nucleus, they must lose a small amount of mass, i.e. there is a change in mass to stay bound. This mass change must be released as various types of photon or other particle energy as above, according to the relation E = mc2. Thus, after the binding energy has been removed, binding energy = mass change × c2. This energy is a measure of the forces that hold the nucleons together. It represents energy that must be resupplied from the environment for the nucleus to be broken up into individual nucleons. For example, an atom of deuterium has a mass defect of 0.0023884 Da, and its binding energy is nearly equal to 2.23 MeV. This means that energy of 2.23 MeV is required to disintegrate an atom of deuterium. The energy given off during either nuclear fusion or nuclear fission is the difference of the binding energies of the "fuel", i.e. the initial nuclide(s), from that of the fission or fusion products. In practice, this energy may also be calculated from the substantial mass differences between the fuel and products, which uses previous measurements of the atomic masses of known nuclides, which always have the same mass for each species. This mass difference appears once evolved heat and radiation have been removed, which is required for measuring the (rest) masses of the (non-excited) nuclides involved in such calculations. == See also == Semi-empirical mass formula Separation energy (binding energy of one nucleon) Virial mass Prout's hypothesis, an early model of the atom that did not account for mass defect == References == == External links == Nuclear Binding Energy Mass and Nuclide Stability Experimental atomic mass data compiled Nov. 2003 Archived 2008-09-23 at the Wayback Machine
Wikipedia/Binding_energy
Chemical energy is the energy of chemical substances that is released when the substances undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, food, and gasoline (as well as oxygen gas, which is of high chemical energy due to its relatively weak double bond and indispensable for chemical-energy release in gasoline combustion). Breaking and re-making chemical bonds involves energy, which may be either absorbed by or evolved from a chemical system. If reactants with relatively weak electron-pair bonds convert to more strongly bonded products, energy is released. Therefore, relatively weakly bonded and unstable molecules store chemical energy. Energy that can be released or absorbed because of a reaction between chemical substances is equal to the difference between the energy content of the products and the reactants, if the initial and final temperature is the same. This change in energy can be estimated from the bond energies of the reactants and products. It can also be calculated from Δ U f ∘ r e a c t a n t s {\displaystyle \Delta {U_{f}^{\circ }}_{\mathrm {reactants} }} , the internal energy of formation of the reactant molecules, and Δ U f ∘ p r o d u c t s {\displaystyle \Delta {U_{f}^{\circ }}_{\mathrm {products} }} , the internal energy of formation of the product molecules. The internal energy change of a chemical process is equal to the heat exchanged if it is measured under conditions of constant volume and equal initial and final temperature, as in a closed container such as a bomb calorimeter. However, under conditions of constant pressure, as in reactions in vessels open to the atmosphere, the measured heat change is not always equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is equal to the enthalpy change, in this case the enthalpy of reaction, if initial and final temperatures are equal). A related term is the heat of combustion, which is the energy mostly of the weak double bonds of molecular oxygen released due to a combustion reaction and often applied in the study of fuels. Food is similar to hydrocarbon and carbohydrate fuels, and when it is oxidized to carbon dioxide and water, the energy released is analogous to the heat of combustion (though assessed differently than for a hydrocarbon fuel—see food energy). Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or interactions between them. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. For example, when a fuel is burned, the chemical energy of molecular oxygen and the fuel is converted to heat. Green plants transform solar energy to chemical energy (mostly of oxygen) through the process of photosynthesis, and electrical energy can be converted to chemical energy and vice versa through electrochemical reactions. The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc. It is not a form of potential energy itself, but is more closely related to free energy. The confusion in terminology arises from the fact that in other areas of physics not dominated by entropy, all potential energy is available to do useful work and drives the system to spontaneously undergo changes of configuration, and thus there is no distinction between "free" and "non-free" potential energy (hence the one word "potential"). However, in systems of large entropy such as chemical systems, the total amount of energy present (and conserved according to the first law of thermodynamics) of which this chemical potential energy is a part, is separated from the amount of that energy—thermodynamic free energy (from which chemical potential is derived)—which (appears to) drive the system forward spontaneously as the global entropy increases (in accordance with the second law). == References ==
Wikipedia/Chemical_energy
In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law. The physical region covered by a system may or may not coincide with a control volume used to analyze the system. == Overview == The volume of a thermodynamic system typically refers to the volume of the working fluid, such as, for example, the fluid within a piston. Changes to this volume may be made through an application of work, or may be used to produce work. An isochoric process however operates at a constant-volume, thus no work can be produced. Many other thermodynamic processes will result in a change in volume. A polytropic process, in particular, causes changes to the system so that the quantity p V n {\displaystyle pV^{n}} is constant (where p {\displaystyle p} is pressure, V {\displaystyle V} is volume, and n {\displaystyle n} is the polytropic index, a constant). Note that for specific polytropic indexes, a polytropic process will be equivalent to a constant-property process. For instance, for very large values of n {\displaystyle n} approaching infinity, the process becomes constant-volume. Gases are compressible, thus their volumes (and specific volumes) may be subject to change during thermodynamic processes. Liquids, however, are nearly incompressible, thus their volumes can be often taken as constant. In general, compressibility is defined as the relative volume change of a fluid or solid as a response to a pressure, and may be determined for substances in any phase. Similarly, thermal expansion is the tendency of matter to change in volume in response to a change in temperature. Many thermodynamic cycles are made up of varying processes, some which maintain a constant volume and some which do not. A vapor-compression refrigeration cycle, for example, follows a sequence where the refrigerant fluid transitions between the liquid and vapor states of matter. Typical units for volume are m 3 {\displaystyle \mathrm {m^{3}} } (cubic meters), l {\displaystyle \mathrm {l} } (liters), and f t 3 {\displaystyle \mathrm {ft} ^{3}} (cubic feet). == Heat and work == Mechanical work performed on a working fluid causes a change in the mechanical constraints of the system; in other words, for work to occur, the volume must be altered. Hence, volume is an important parameter in characterizing many thermodynamic processes where an exchange of energy in the form of work is involved. Volume is one of a pair of conjugate variables, the other being pressure. As with all conjugate pairs, the product is a form of energy. The product p V {\displaystyle pV} is the energy lost to a system due to mechanical work. This product is one term which makes up enthalpy H {\displaystyle H} : H = U + p V , {\displaystyle H=U+pV,\,} where U {\displaystyle U} is the internal energy of the system. The second law of thermodynamics describes constraints on the amount of useful work which can be extracted from a thermodynamic system. In thermodynamic systems where the temperature and volume are held constant, the measure of "useful" work attainable is the Helmholtz free energy; and in systems where the volume is not held constant, the measure of useful work attainable is the Gibbs free energy. Similarly, the appropriate value of heat capacity to use in a given process depends on whether the process produces a change in volume. The heat capacity is a function of the amount of heat added to a system. In the case of a constant-volume process, all the heat affects the internal energy of the system (i.e., there is no pV-work, and all the heat affects the temperature). However, in a process without a constant volume, the heat addition affects both the internal energy and the work (i.e., the enthalpy); thus the temperature changes by a different amount than in the constant-volume case and a different heat capacity value is required. == Specific volume == Specific volume ( ν {\displaystyle \nu } ) is the volume occupied by a unit of mass of a material. In many cases, the specific volume is a useful quantity to determine because, as an intensive property, it can be used to determine the complete state of a system in conjunction with another independent intensive variable. The specific volume also allows systems to be studied without reference to an exact operating volume, which may not be known (nor significant) at some stages of analysis. The specific volume of a substance is equal to the reciprocal of its mass density. Specific volume may be expressed in m 3 k g {\displaystyle {\frac {\mathrm {m^{3}} }{\mathrm {kg} }}} , f t 3 l b {\displaystyle {\frac {\mathrm {ft^{3}} }{\mathrm {lb} }}} , f t 3 s l u g {\displaystyle {\frac {\mathrm {ft^{3}} }{\mathrm {slug} }}} , or m L g {\displaystyle {\frac {\mathrm {mL} }{\mathrm {g} }}} . ν = V m = 1 ρ {\displaystyle \nu ={\frac {V}{m}}={\frac {1}{\rho }}} where, V {\displaystyle V} is the volume, m {\displaystyle m} is the mass and ρ {\displaystyle \rho } is the density of the material. For an ideal gas, ν = R ¯ T P {\displaystyle \nu ={\frac {{\bar {R}}T}{P}}} where, R ¯ {\displaystyle {\bar {R}}} is the specific gas constant, T {\displaystyle T} is the temperature and P {\displaystyle P} is the pressure of the gas. Specific volume may also refer to molar volume. == Gas volume == === Dependence on pressure and temperature === The volume of gas increases proportionally to absolute temperature and decreases inversely proportionally to pressure, approximately according to the ideal gas law: V = n R T p {\displaystyle V={\frac {nRT}{p}}} where: p is the pressure V is the volume n is the amount of substance of gas (moles) R is the gas constant, 8.314 J·K−1mol−1 T is the absolute temperature To simplify, a volume of gas may be expressed as the volume it would have in standard conditions for temperature and pressure, which are 0 °C (32 °F) and 100 kPa. === Humidity exclusion === In contrast to other gas components, water content in air, or humidity, to a higher degree depends on vaporization and condensation from or into water, which, in turn, mainly depends on temperature. Therefore, when applying more pressure to a gas saturated with water, all components will initially decrease in volume approximately according to the ideal gas law. However, some of the water will condense until returning to almost the same humidity as before, giving the resulting total volume deviating from what the ideal gas law predicted. Conversely, decreasing temperature would also make some water condense, again making the final volume deviating from predicted by the ideal gas law. Therefore, gas volume may alternatively be expressed excluding the humidity content: Vd (volume dry). This fraction more accurately follows the ideal gas law. On the contrary, Vs (volume saturated) is the volume a gas mixture would have if humidity was added to it until saturation (or 100% relative humidity). === General conversion === To compare gas volume between two conditions of different temperature or pressure (1 and 2), assuming nR are the same, the following equation uses humidity exclusion in addition to the ideal gas law: V 2 = V 1 × T 2 T 1 × p 1 − p w , 1 p 2 − p w , 2 {\displaystyle V_{2}=V_{1}\times {\frac {T_{2}}{T_{1}}}\times {\frac {p_{1}-p_{w,1}}{p_{2}-p_{w,2}}}} Where, in addition to terms used in the ideal gas law: pw is the partial pressure of gaseous water during condition 1 and 2, respectively For example, calculating how much 1 liter of air (a) at 0 °C, 100 kPa, pw = 0 kPa (known as STPD, see below) would fill when breathed into the lungs where it is mixed with water vapor (l), where it quickly becomes 37 °C (99 °F), 100 kPa, pw = 6.2 kPa (BTPS): V l = 1 l × 310 K 273 K × 100 k P a − 0 k P a 100 k P a − 6.2 k P a = 1.21 l {\displaystyle V_{l}=1\ \mathrm {l} \times {\frac {310\ \mathrm {K} }{273\ \mathrm {K} }}\times {\frac {100\ \mathrm {kPa} -0\ \mathrm {kPa} }{100\ \mathrm {kPa} -6.2\ \mathrm {kPa} }}=1.21\ \mathrm {l} } === Common conditions === Some common expressions of gas volume with defined or variable temperature, pressure and humidity inclusion are: ATPS: Ambient temperature (variable) and pressure (variable), saturated (humidity depends on temperature) ATPD: Ambient temperature (variable) and pressure (variable), dry (no humidity) BTPS: Body temperature (37 °C or 310 K) and pressure (generally same as ambient), saturated (47 mmHg or 6.2 kPa) STPD: Standard temperature (0 °C or 273 K) and pressure (760 mmHg (101.33 kPa) or 100 kPa (750.06 mmHg)), dry (no humidity) === Conversion factors === The following conversion factors can be used to convert between expressions for volume of a gas: === Partial volume === The partial volume of a particular gas is a fraction of the total volume occupied by the gas mixture, with unchanged pressure and temperature. In gas mixtures, e.g. air, the partial volume allows focusing on one particular gas component, e.g. oxygen. It can be approximated both from partial pressure and molar fraction: V X = V t o t × P X P t o t = V t o t × n X n t o t {\displaystyle V_{\rm {X}}=V_{\rm {tot}}\times {\frac {P_{\rm {X}}}{P_{\rm {tot}}}}=V_{\rm {tot}}\times {\frac {n_{\rm {X}}}{n_{\rm {tot}}}}} VX is the partial volume of any individual gas component (X) Vtot is the total volume in gas mixture PX is the partial pressure of gas X Ptot is the total pressure in gas mixture nX is the amount of substance of a gas (X) ntot is the total amount of substance in gas mixture == See also == Volumetric flow rate == References ==
Wikipedia/Volume_(thermodynamics)
In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale. == Mathematical formulation == In the canonical ensemble, the entropic force F {\displaystyle \mathbf {F} } associated to a macrostate partition { X } {\displaystyle \{\mathbf {X} \}} is given by F ( X 0 ) = T ∇ X S ( X ) | X 0 , {\displaystyle \mathbf {F} (\mathbf {X} _{0})=T\nabla _{\mathbf {X} }S(\mathbf {X} )|_{\mathbf {X} _{0}},} where T {\displaystyle T} is the temperature, S ( X ) {\displaystyle S(\mathbf {X} )} is the entropy associated to the macrostate X {\displaystyle \mathbf {X} } , and X 0 {\displaystyle \mathbf {X} _{0}} is the present macrostate. == Examples == === Pressure of an ideal gas === The internal energy of an ideal gas depends only on its temperature, and not on the volume of its containing box, so it is not an energy effect that tends to increase the volume of the box as gas pressure does. This implies that the pressure of an ideal gas has an entropic origin. What is the origin of such an entropic force? The most general answer is that the effect of thermal fluctuations tends to bring a thermodynamic system toward a macroscopic state that corresponds to a maximum in the number of microscopic states (or micro-states) that are compatible with this macroscopic state. In other words, thermal fluctuations tend to bring a system toward its macroscopic state of maximum entropy. === Brownian motion === The entropic approach to Brownian movement was initially proposed by R. M. Neumann. Neumann derived the entropic force for a particle undergoing three-dimensional Brownian motion using the Boltzmann equation, denoting this force as a diffusional driving force or radial force. In the paper, three example systems are shown to exhibit such a force: electrostatic system of molten salt, surface tension and, elasticity of rubber. === Polymers === A standard example of an entropic force is the elasticity of a freely jointed polymer molecule. For an ideal chain, maximizing its entropy means reducing the distance between its two free ends. Consequently, a force that tends to collapse the chain is exerted by the ideal chain between its two free ends. This entropic force is proportional to the distance between the two ends. The entropic force by a freely jointed chain has a clear mechanical origin and can be computed using constrained Lagrangian dynamics. With regards to biological polymers, there appears to be an intricate link between the entropic force and function. For example, disordered polypeptide segments – in the context of the folded regions of the same polypeptide chain – have been shown to generate an entropic force that has functional implications. === Hydrophobic force === Another example of an entropic force is the hydrophobic force. At room temperature, it partly originates from the loss of entropy by the 3D network of water molecules when they interact with molecules of dissolved substance. Each water molecule is capable of donating two hydrogen bonds through the two protons, accepting two more hydrogen bonds through the two sp3-hybridized lone pairs. Therefore, water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to hydrogen fluoride (which can accept 3 but donate only 1) or ammonia (which can donate 3 but accept only 1), which mainly form linear chains. If the introduced surface had an ionic or polar nature, there would be water molecules standing upright on 1 (along the axis of an orbital for ionic bond) or 2 (along a resultant polarity axis) of the four sp3 orbitals. These orientations allow easy movement, i.e. degrees of freedom, and thus lowers entropy minimally. But a non-hydrogen-bonding surface with a moderate curvature forces the water molecule to sit tight on the surface, spreading 3 hydrogen bonds tangential to the surface, which then become locked in a clathrate-like basket shape. Water molecules involved in this clathrate-like basket around the non-hydrogen-bonding surface are constrained in their orientation. Thus, any event that would minimize such a surface is entropically favored. For example, when two such hydrophobic particles come very close, the clathrate-like baskets surrounding them merge. This releases some of the water molecules into the bulk of the water, leading to an increase in entropy. Another related and counter-intuitive example of entropic force is protein folding, which is a spontaneous process and where hydrophobic effect also plays a role. Structures of water-soluble proteins typically have a core in which hydrophobic side chains are buried from water, which stabilizes the folded state. Charged and polar side chains are situated on the solvent-exposed surface where they interact with surrounding water molecules. Minimizing the number of hydrophobic side chains exposed to water is the principal driving force behind the folding process, although formation of hydrogen bonds within the protein also stabilizes protein structure. === Colloids === Entropic forces are important and widespread in the physics of colloids, where they are responsible for the depletion force, and the ordering of hard particles, such as the crystallization of hard spheres, the isotropic-nematic transition in liquid crystal phases of hard rods, and the ordering of hard polyhedra. Because of this, entropic forces can be an important driver of self-assembly Entropic forces arise in colloidal systems due to the osmotic pressure that comes from particle crowding. This was first discovered in, and is most intuitive for, colloid-polymer mixtures described by the Asakura–Oosawa model. In this model, polymers are approximated as finite-sized spheres that can penetrate one another, but cannot penetrate the colloidal particles. The inability of the polymers to penetrate the colloids leads to a region around the colloids in which the polymer density is reduced. If the regions of reduced polymer density around two colloids overlap with one another, by means of the colloids approaching one another, the polymers in the system gain an additional free volume that is equal to the volume of the intersection of the reduced density regions. The additional free volume causes an increase in the entropy of the polymers, and drives them to form locally dense-packed aggregates. A similar effect occurs in sufficiently dense colloidal systems without polymers, where osmotic pressure also drives the local dense packing of colloids into a diverse array of structures that can be rationally designed by modifying the shape of the particles. These effects are for anisotropic particles referred to as directional entropic forces. === Cytoskeleton === Contractile forces in biological cells are typically driven by molecular motors associated with the cytoskeleton. However, a growing body of evidence shows that contractile forces may also be of entropic origin. The foundational example is the action of microtubule crosslinker Ase1, which localizes to microtubule overlaps in the mitotic spindle. Molecules of Ase1 are confined to the microtubule overlap, where they are free to diffuse one-dimensionally. Analogically to an ideal gas in a container, molecules of Ase1 generate pressure on the overlap ends. This pressure drives the overlap expansion, which results in the contractile sliding of the microtubules. An analogous example was found in the actin cytoskeleton. Here, the actin-bundling protein anillin drives actin contractility in cytokinetic rings. == Controversial examples == Some forces that are generally regarded as conventional forces have been argued to be actually entropic in nature. These theories remain controversial and are the subject of ongoing work. Matt Visser, professor of mathematics at Victoria University of Wellington, NZ in "Conservative Entropic Forces" criticizes selected approaches but generally concludes: There is no reasonable doubt concerning the physical reality of entropic forces, and no reasonable doubt that classical (and semi-classical) general relativity is closely related to thermodynamics. Based on the work of Jacobson, Thanu Padmanabhan, and others, there are also good reasons to suspect a thermodynamic interpretation of the fully relativistic Einstein equations might be possible. === Gravity === In 2009, Erik Verlinde argued that gravity can be explained as an entropic force. It claimed (similar to Jacobson's result) that gravity is a consequence of the "information associated with the positions of material bodies". This model combines the thermodynamic approach to gravity with Gerard 't Hooft's holographic principle. It implies that gravity is not a fundamental interaction, but an emergent phenomenon. === Other forces === In the wake of the discussion started by Verlinde, entropic explanations for other fundamental forces have been suggested, including Coulomb's law. The same approach was argued to explain dark matter, dark energy and Pioneer effect. == Links to adaptive behavior == It was argued that causal entropic forces lead to spontaneous emergence of tool use and social cooperation. Causal entropic forces by definition maximize entropy production between the present and future time horizon, rather than just greedily maximizing instantaneous entropy production like typical entropic forces. A formal simultaneous connection between the mathematical structure of the discovered laws of nature, intelligence and the entropy-like measures of complexity was previously noted in 2000 by Andrei Soklakov in the context of Occam's razor principle. == See also == == References ==
Wikipedia/Entropic_force
Elastic energy is the mechanical potential energy stored in the configuration of a material or physical system as it is subjected to elastic deformation by work performed upon it. Elastic energy occurs when objects are impermanently compressed, stretched or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. (Note however, the work done by a stretched rubber band is not an example of elastic energy. It is an example of entropic elasticity.) The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The energy is potential as it will be converted into other forms of energy, such as kinetic energy and sound energy, when the object is allowed to return to its original shape (reformation) by its elasticity. U = 1 2 k Δ x 2 {\displaystyle U={\frac {1}{2}}k\,\Delta x^{2}} The essence of elasticity is reversibility. Forces applied to an elastic material transfer energy into the material which, upon yielding that energy to its surroundings, can recover its original shape. However, all materials have limits to the degree of distortion they can endure without breaking or irreversibly altering their internal structure. Hence, the characterizations of solid materials include specification, usually in terms of strains, of its elastic limits. Beyond the elastic limit, a material is no longer storing all of the energy from mechanical work performed on it in the form of elastic energy. Elastic energy of or within a substance is static energy of configuration. It corresponds to energy stored principally by changing the interatomic distances between nuclei. Thermal energy is the randomized distribution of kinetic energy within the material, resulting in statistical fluctuations of the material about the equilibrium configuration. There is some interaction, however. For example, for some solid objects, twisting, bending, and other distortions may generate thermal energy, causing the material's temperature to rise. Thermal energy in solids is often carried by internal elastic waves, called phonons. Elastic waves that are large on the scale of an isolated object usually produce macroscopic vibrations . Although elasticity is most commonly associated with the mechanics of solid bodies or materials, even the early literature on classical thermodynamics defines and uses "elasticity of a fluid" in ways compatible with the broad definition provided in the Introduction above.: 107 et seq.  Solids include complex crystalline materials with sometimes complicated behavior. By contrast, the behavior of compressible fluids, and especially gases, demonstrates the essence of elastic energy with negligible complication. The simple thermodynamic formula: d U = − P d V , {\displaystyle dU=-P\,dV\ ,} where dU is an infinitesimal change in recoverable internal energy U, P is the uniform pressure (a force per unit area) applied to the material sample of interest, and dV is the infinitesimal change in volume that corresponds to the change in internal energy. The minus sign appears because dV is negative under compression by a positive applied pressure which also increases the internal energy. Upon reversal, the work that is done by a system is the negative of the change in its internal energy corresponding to the positive dV of an increasing volume. The system loses stored internal energy when doing work on its surroundings. Pressure is stress and volumetric change corresponds to changing the relative spacing of points within the material. The stress-strain-internal energy relationship of the foregoing formula is repeated in formulations for elastic energy of solid materials with complicated crystalline structure. == Elastic potential energy in mechanical systems == Components of mechanical systems store elastic potential energy if they are deformed when forces are applied to the system. Energy is transferred to an object by work when an external force displaces or deforms the object. The quantity of energy transferred is the vector dot product of the force and the displacement of the object. As forces are applied to the system they are distributed internally to its component parts. While some of the energy transferred can end up stored as the kinetic energy of acquired velocity, the deformation of component objects results in stored elastic energy. A prototypical elastic component is a coiled spring. The linear elastic performance of a spring is parametrized by a constant of proportionality, called the spring constant. This constant is usually denoted as k (see also Hooke's law) and depends on the geometry, cross-sectional area, undeformed length and nature of the material from which the coil is fashioned. Within a certain range of deformation, k remains constant and is defined as the negative ratio of displacement to the magnitude of the restoring force produced by the spring at that displacement. k = − F r L − L o {\displaystyle k=-{\frac {F_{r}}{L-L_{o}}}} The deformed length, L, can be larger or smaller than Lo, the undeformed length, so to keep k positive, Fr must be given as a vector component of the restoring force whose sign is negative for L>Lo and positive for L< Lo. If the displacement is abbreviated as L − L o = x , {\displaystyle L-L_{o}=x,} then Hooke's law can be written in the usual form F r = − k x . {\displaystyle F_{r}=-k\,x.} Energy absorbed and held in the spring can be derived using Hooke's law to compute the restoring force as a measure of the applied force. This requires the assumption, sufficiently correct in most circumstances, that at a given moment, the magnitude of applied force. For each infinitesimal displacement dx, the applied force is simply k x and the product of these is the infinitesimal transfer of energy into the spring dU. The total elastic energy placed into the spring from zero displacement to final length L is thus the integral U = ∫ 0 L − L o k x d x = 1 2 k ( L − L o ) 2 {\displaystyle U=\int _{0}^{L-L_{o}}k\,x\,dx={\tfrac {1}{2}}k(L-L_{o})^{2}} For a material of Young's modulus, Y (same as modulus of elasticity λ), cross sectional area, A0, initial length, l0, which is stretched by a length, Δ l {\displaystyle \Delta l} : U e = ∫ Y A 0 Δ l l 0 d ( Δ l ) = Y A 0 Δ l 2 2 l 0 {\displaystyle U_{e}=\int {\frac {YA_{0}\Delta l}{l_{0}}}\,d\left(\Delta l\right)={\frac {YA_{0}{\Delta l}^{2}}{2l_{0}}}} where Ue is the elastic potential energy. The elastic potential energy per unit volume is given by: U e A 0 l 0 = Y Δ l 2 2 l 0 2 = 1 2 Y ε 2 {\displaystyle {\frac {U_{e}}{A_{0}l_{0}}}={\frac {Y{\Delta l}^{2}}{2l_{0}^{2}}}={\frac {1}{2}}Y{\varepsilon }^{2}} where ε = Δ l l 0 {\displaystyle \varepsilon ={\frac {\Delta l}{l_{0}}}} is the strain in the material. In the general case, elastic energy is given by the free energy per unit of volume f as a function of the strain tensor components εij f ( ε i j ) = 1 2 λ ε i i 2 + μ ε i j 2 {\displaystyle f(\varepsilon _{ij})={\frac {1}{2}}\lambda \varepsilon _{ii}^{2}+\mu \varepsilon _{ij}^{2}} where λ and μ are the Lamé elastic coefficients and we use Einstein summation convention. Noting the thermodynamic connection between stress tensor components and strain tensor components, σ i j = ( ∂ f ∂ ε i j ) T , {\displaystyle \sigma _{ij}=\left({\frac {\partial f}{\partial \varepsilon _{ij}}}\right)_{T},} where the subscript T denotes that temperature is held constant, then we find that if Hooke's law is valid, we can write the elastic energy density as f = 1 2 ε i j σ i j . {\displaystyle f={\frac {1}{2}}\varepsilon _{ij}\sigma _{ij}.} == Continuum systems == Matter in bulk can be distorted in many different ways: stretching, shearing, bending, twisting, etc. Each kind of distortion contributes to the elastic energy of a deformed material. In orthogonal coordinates, the elastic energy per unit volume due to strain is thus a sum of contributions: U = 1 2 C i j k l ε i j ε k l , {\displaystyle U={\frac {1}{2}}C_{ijkl}\varepsilon _{ij}\varepsilon _{kl},} where C i j k l {\displaystyle C_{ijkl}} is a 4th rank tensor, called the elastic tensor or stiffness tensor which is a generalization of the elastic moduli of mechanical systems, and ε i j {\displaystyle \varepsilon _{ij}} is the strain tensor (Einstein summation notation has been used to imply summation over repeated indices). The values of C i j k l {\displaystyle C_{ijkl}} depend upon the crystal structure of the material: in the general case, due to symmetric nature of σ {\displaystyle \sigma } and ε {\displaystyle \varepsilon } , the elastic tensor consists of 21 independent elastic coefficients. This number can be further reduced by the symmetry of the material: 9 for an orthorhombic crystal, 5 for an hexagonal structure, and 3 for a cubic symmetry. Finally, for an isotropic material, there are only two independent parameters, with C i j k l = λ δ i j δ k l + μ ( δ i k δ j l + δ i l δ j k ) {\displaystyle C_{ijkl}=\lambda \delta _{ij}\delta _{kl}+\mu \left(\delta _{ik}\delta _{jl}+\delta _{il}\delta _{jk}\right)} , where λ {\displaystyle \lambda } and μ {\displaystyle \mu } are the Lamé constants, and δ i j {\displaystyle \delta _{ij}} is the Kronecker delta. The strain tensor itself can be defined to reflect distortion in any way that results in invariance under total rotation, but the most common definition with regard to which elastic tensors are usually expressed defines strain as the symmetric part of the gradient of displacement with all nonlinear terms suppressed: ε i j = 1 2 ( ∂ i u j + ∂ j u i ) {\displaystyle \varepsilon _{ij}={\frac {1}{2}}\left(\partial _{i}u_{j}+\partial _{j}u_{i}\right)} where u i {\displaystyle u_{i}} is the displacement at a point in the i {\displaystyle i} -th direction and ∂ j {\displaystyle \partial _{j}} is the partial derivative in the j {\displaystyle j} -th direction. Note that: ε j j = ∂ j u j {\displaystyle \varepsilon _{jj}=\partial _{j}u_{j}} where no summation is intended. Although full Einstein notation sums over raised and lowered pairs of indices, the values of elastic and strain tensor components are usually expressed with all indices lowered. Thus beware (as here) that in some contexts a repeated index does not imply a sum overvalues of that index ( j {\displaystyle j} in this case), but merely a single component of a tensor. == See also == Clockwork Elasto-capillarity Rubber elasticity == References == == Sources == Eshelby, J.D (November 1975). "The elastic energy-momentum tensor". Journal of Elasticity. 5 (3–4): 321–335. doi:10.1007/BF00126994. S2CID 121320629.
Wikipedia/Elastic_energy
Energy efficiency in agriculture refers to reducing the amount of energy required to provide agricultural products and services. The European Commission has policies related to energy efficiency, including in agriculture. The European Union has established measures to promote energy efficiency, including setting targets for energy savings, and requiring energy audits and management plans for large companies. The AGREE project conducted studies on energy efficiency in different agricultural production systems and proposed measures for improvement. The results of the project were summarized in reports that highlighted the opportunities and drawbacks for energy efficiency in agriculture in different European countries. Improving energy efficiency in agriculture contributes to reducing greenhouse gas emissions. == European Commission definitions == === Energy in general === European Commission definitions of energy efficiency, are given below: Energy efficiency — a ratio between an output of performance, service, goods or energy, and an input of energy; Energy efficiency improvement — an increase in energy end-use efficiency as a result of technological, behavioural and/or economic changes; Energy savings — an amount of saved energy determined by measuring and/or estimating consumption before and after implementation of one or more energy efficiency improvement measures, whilst ensuring normalization for external conditions that affect energy consumption; According to article 2(d) of the Regulation (EC) No1099/2008 on energy statistics: Energy — means all forms of energy products (combustible fuels, heat, renewable energy, electricity, or any other form of energy) Primary energy consumption — means gross inland consumption, excluding non-energy uses Final energy consumption — means all energy supplied to industry, transport, households, services and agriculture. It excludes deliveries to the energy transformation sector and the energy industries themselves. === Energy in agriculture === Primary energy consumption (PEC) in agriculture is the energy consumed in an agricultural production system (within the farm limits) including the energy for the production of all indirect inputs. Energy efficiency in agriculture improvement is defined as the decrease of primary energy consumption for the production of a unit of agricultural product (expressed in weight or volume units), within the farm boundaries. == European Union policies == European Commission requirements regarding energy use across the EU (Directive 2012/27/EU) establish a common framework of measures for the promotion of energy efficiency within the European Union to: Ensure the achievement of the Union’s 2020 20% headline target on energy efficiency Pave the way for further energy efficiency improvements beyond that date The directive also: Lays down rules designed to remove barriers in the energy market and overcome market failures that impede efficiency in the supply and use of energy. Provides for the establishment of indicative national energy efficiency targets for 2020Key measures with implications for the agricultural sector: Energy companies are requested to reduce energy sales by 1.5% every year among their customers. This can be achieved via improved heating systems, fitting double-glazed windows or insulating roofs. Measures to achieve higher energy efficiency should be applied in agricultural buildings too (e.g. greenhouses, animal housing, etc.). The public sector is required to renovate 3% of buildings "owned and occupied" by the central government in each country. Buildings need to have a useful area larger than 500 m2 in order to be covered by this requirement (lowered to 250 m2 as of July 2015). In many EU member states there are public sector (general government or regional or municipal) agricultural buildings (e.g. in some countries for agricultural product storage) that could be included in the measures taken by the national government. EU countries are requested to draw up a roadmap to make the entire buildings sector more energy efficient by 2050 (commercial, public and private households included). Making farm buildings more energy efficient contributes to this aim. Measures regarding existing agricultural buildings should be carried out and new legislation regarding new installations need to be adopted in the direction of improving their energy efficiency. Energy audits and management plans are required for large companies, with cost-benefit analyses for the deployment of combined heat and power generation (CHP) and public procurement. This has implications for large farm companies and large farmers associations and their buildings, storage rooms and greenhouses. Each country has to present national indicative targets by April 2013. If the European Commission estimates that those are insufficient to meet the EU's overall 2020 goal, then it can request member states to re-assess their plans. In the first semester of 2014, the Commission will review the progress towards the 20% energy-efficiency target, report on it and assess whether further measures are needed. If Europe is off track, the Commission intends to come back with a proposal for further legislation. Including agricultural activities in the general planning of each member state would help in covering the targets and avoid re-assessing on behalf of the European Commission. This comment applies to the last 3 remarks of the Directive. == Recent developments and trends == In the framework of the AGREE project [3], studies on the energy efficiency of specific agricultural production systems of different types (arable crops, agro-forest, greenhouses, and animal husbandry) were executed in 2012-13 in Europe based on existing data from six countries and were combined in one report. Energy efficiency measures were proposed for each agricultural system and presented in an overview report. A synthesis and summary report on drivers and stakeholders of energy efficiency in agriculture, and potential of energy saving hours was produced. The most directly effective measures were taken into account in reporting their effect on energy consumption per unit of product in certain case studies in all seven countries taking into account trade-offs regarding GHG emissions and final farm cost. The results are presented in a report named Economic and environmental analysis of energy efficiency measures in agriculture – Case Studies and trade-offs. An intensive stakeholder process, by organising national stakeholders meetings in six countries, revealed the opportunities and drawbacks for a future energy efficient agriculture in Europe. The results of this process are presented for six countries at special reports, one for each country (Finland, Germany, Greece, Netherlands, Poland, Portugal). The results of all reports are summarized in a synthesis report on transnational value of national stakeholders meetings. The integration of the perspectives of representatives of different EU regions to achieve a future energy efficient agriculture in Europe, an output of a European transnational stakeholder meeting, is summarized in the Agenda for transnational collaboration. This represents the shared views on how to improve energy efficiency in European agriculture. == 2013 perspective == According to the work done in AGREE, suggestions were given on the definition of energy efficiency in agriculture Energy efficiency is the goal of efforts to reduce the amount of energy required to provide products and services. The general term "energy efficiency in agriculture" reflects changes in technology, government policies, weather patterns, and farming management practices. There is not a single measure to describe, ensure, and improve energy efficiency in agriculture. Instead, in the energy balance for a given production process, different indicators may serve and support energy efficiency analysis. The AGREE results are based on the specific input of primary energy per cultivation area (GJ/ha) and on the specific input of primary energy per tonne of agricultural product (GJ/t). All measures that are suitable to reduce the specific energy input per unit of product improve energy efficiency (energy efficiency improvement measures). Improving energy efficiency of agricultural production contributes directly to the reduction of greenhouse gas (GHG) emissions. == References ==
Wikipedia/Energy_efficiency_in_agriculture
Energy recovery includes any technique or method of minimizing the input of energy to an overall system by the exchange of energy from one sub-system of the overall system with another. The energy can be in any form in either subsystem, but most energy recovery systems exchange thermal energy in either sensible or latent form. In some circumstances the use of an enabling technology, either daily thermal energy storage or seasonal thermal energy storage (STES, which allows heat or cold storage between opposing seasons), is necessary to make energy recovery practicable. One example is waste heat from air conditioning machinery stored in a buffer tank to aid in night time heating. == Principle == A common application of this principle is in systems which have an exhaust stream or waste stream which is transferred from the system to its surroundings. Some of the energy in that flow of material (often gaseous or liquid) may be transferred to the make-up or input material flow. This input mass flow often comes from the system's surroundings, which, being at ambient conditions, are at a lower temperature than the waste stream. This temperature differential allows heat transfer and thus energy transfer, or in this case, recovery. Thermal energy is often recovered from liquid or gaseous waste streams to fresh make-up air and water intakes in buildings, such as for the HVAC systems, or process systems. == System approach == Energy consumption is a key part of most human activities. This consumption involves converting one energy system to another, for example: The conversion of mechanical energy to electrical energy, which can then power computers, light, motors etc. The input energy propels the work and is mostly converted to heat or follows the product in the process as output energy. Energy recovery systems harvest the output power and provide this as input power to the same or another process. An energy recovery system will close this energy cycle to prevent the input power from being released back to nature and rather be used in other forms of desired work. == Examples == Heat recovery is implemented in heat sources like e.g. a steel mill. Heated cooling water from the process is sold for heating of homes, shops and offices in the surrounding area. Regenerative braking is used in electric cars, trains, heavy cranes etc. where the energy consumed when elevating the potential is returned to the electric supplier when released. Active pressure reduction systems where the differential pressure in a pressurized fluid flow is recovered rather than converted to heat in a pressure reduction valve and released. Energy recovery ventilation Energy recycling Water heat recycling Heat recovery ventilation Heat recovery steam generator Cyclone Waste Heat Engine Hydrogen turboexpander-generator Thermal diode Thermal oxidizer Thermoelectric Modules Waste heat recovery units === Electric Turbo Compound (ETC) === Electric Turbo Compounding (ETC) is a technology solution to the challenge of improving the fuel efficiency of gas and diesel engines by recovering waste energy from the exhaust gases. === STES === At a foundry in Sweden waste heat is recovered and stored in a large mass of native bedrock which is penetrated by a cluster of 140 heat exchanger equipped boreholes (155mm diameter) that are 150m deep. This store is used for heating an adjacent factory as needed, even months later. The Drake Landing Solar Community in Alberta, Canada uses STES to recover and utilize natural heat that otherwise would be wasted. The community uses a cluster of boreholes in bedrock for interseasonal heat storage, and this enables obtaining 97 percent of the year-round space heating from solar thermal collectors on the garage roofs. Cold winter temperatures can be recovered by circulating water through a dry cooling tower and using that to chill a deep aquifer or borehole cluster. The chill is later recovered from the storage for summer air conditioning. With a coefficient of performance (COP) of 20 to 40, this method of cooling can be ten times more efficient than conventional air conditioning. == Environmental impact == There is a large potential for energy recovery in compact systems like large industries and utilities. Together with energy conservation, it should be possible to dramatically reduce world energy consumption. The effect of this will then be: Reduced number of coal-fired power plants Reduced airborne particles, NOx and CO2 – improved air quality Slowing or reducing climate change Lower fuel bills on transport Longer availability of crude oil Change of industries and economies not fully researched In 2008 Tom Casten, chairman of Recycled Energy Development, said that "We think we could make about 19 to 20 percent of U.S. electricity with heat that is currently thrown away by industry." A 2007 Department of Energy study found the potential for 135,000 megawatts of combined heat and power (which uses energy recovery) in the U.S., and a Lawrence Berkley National Laboratory study identified about 64,000 megawatts that could be obtained from industrial waste energy, not counting CHP. These studies suggest that about 200,000 megawatts, or 20%, of total power capacity could come from energy recycling in the U.S. Widespread use of energy recycling could therefore reduce global warming emissions by an estimated 20 percent. Indeed, as of 2005, about 42% of U.S. greenhouse gas pollution came from the production of electricity and 27% from the production of heat. It is difficult to quantify the environmental impact of a global energy recovery implementation in some sectors. The main impediments are: Lack of efficient technologies for private homes. Heat recovery systems in private homes can have an efficiency as low as 30% or less. It may be more realistic to use energy conservation like thermal insulation or improved buildings. Many areas are more dependent on forced cooling and a system for extracting heat from dwellings to be used for other uses are not widely available. Ineffective infrastructure. Heat recovery in particular need a short distance from producer to consumer to be viable. A solution may be to move a large consumer to the vicinity of the producer. This may have other complications. Transport sector is not ready. With the transport sector using about 20% of the energy supply, most of the energy is spent on overcoming gravity and friction. Electric cars with regenerative braking seem to be the best candidate for energy recovery. Wind systems on ships are under development. Very little work on the airline industry is known in this field. == See also == Efficient energy use Energy conservation Energy recycling DWEER List of energy storage projects Mechanical vapor recompression Pinch analysis Waste-to-energy == References == == External links == Energy Recovery from the Combustion of Municipal Solid Waste -EPA 26 Projects Funded: Energy Recovery Methods Studied with ASHRAE Undergraduate Grants Heat Recovery in Industry
Wikipedia/Energy_recovery
Energy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an accumulator or battery. Energy comes in multiple forms including radiation, chemical, gravitational potential, electrical potential, electricity, elevated temperature, latent heat and kinetic. Energy storage involves converting energy from forms that are difficult to store to more conveniently or economically storable forms. Some technologies provide short-term energy storage, while others can endure for much longer. Bulk energy storage is currently dominated by hydroelectric dams, both conventional as well as pumped. Grid energy storage is a collection of methods used for energy storage on a large scale within an electrical power grid. Common examples of energy storage are the rechargeable battery, which stores chemical energy readily convertible to electricity to operate a mobile phone; the hydroelectric dam, which stores energy in a reservoir as gravitational potential energy; and ice storage tanks, which store ice frozen by cheaper energy at night to meet peak daytime demand for cooling. Fossil fuels such as coal and gasoline store ancient energy derived from sunlight by organisms that later died, became buried and over time were then converted into these fuels. Food (which is made by the same process as fossil fuels) is a form of energy stored in chemical form. == History == In the 20th century grid, electrical power was largely generated by burning fossil fuel. When less power was required, less fuel was burned. Hydropower, a mechanical energy storage method, is the most widely adopted mechanical energy storage, and has been in use for centuries. Large hydropower dams have been energy storage sites for more than one hundred years. Concerns with air pollution, energy imports, and global warming have spawned the growth of renewable energy such as solar and wind power. Wind power is uncontrolled and may be generating at a time when no additional power is needed. Solar power varies with cloud cover and at best is only available during daylight hours, while demand often peaks after sunset (see duck curve). Interest in storing power from these intermittent sources grows as the renewable energy industry begins to generate a larger fraction of overall energy consumption. In 2023 BloombergNEF forecast total energy storage deployments to grow at a compound annual growth rate of 27 percent through 2030. Off grid electrical use was a niche market in the 20th century, but in the 21st century, it has expanded. Portable devices are in use all over the world. Solar panels are now common in the rural settings worldwide. Access to electricity is now a question of economics and financial viability, and not solely on technical aspects. Electric vehicles are gradually replacing combustion-engine vehicles. However, powering long-distance transportation without burning fuel remains in development. == Methods == === Outline === The following list includes a variety of types of energy storage: === Mechanical === Energy can be stored in water pumped to a higher elevation using pumped storage methods or by moving solid matter to higher locations (gravity batteries). Other commercial mechanical methods include compressing air and flywheels that convert electric energy into internal energy or kinetic energy and then back again when electrical demand peaks. ==== Hydroelectricity ==== Hydroelectric dams with reservoirs can be operated to provide electricity at times of peak demand. Water is stored in the reservoir during periods of low demand and released when demand is high. The net effect is similar to pumped storage, but without the pumping loss. While a hydroelectric dam does not directly store energy from other generating units, it behaves equivalently by lowering output in periods of excess electricity from other sources. In this mode, dams are one of the most efficient forms of energy storage, because only the timing of its generation changes. Hydroelectric turbines have a start-up time on the order of a few minutes. ==== Pumped hydro ==== Worldwide, pumped-storage hydroelectricity (PSH) is the largest-capacity form of active grid energy storage available, and, as of March 2012, the Electric Power Research Institute (EPRI) reports that PSH accounts for more than 99% of bulk storage capacity worldwide, representing around 127,000 MW. PSH energy efficiency varies in practice between 70% and 80%, with claims of up to 87%. At times of low electrical demand, excess generation capacity is used to pump water from a lower source into a higher reservoir. When demand grows, water is released back into a lower reservoir (or waterway or body of water) through a turbine, generating electricity. Reversible turbine-generator assemblies act as both a pump and turbine (usually a Francis turbine design). Nearly all facilities use the height difference between two water bodies. Pure pumped-storage plants shift the water between reservoirs, while the "pump-back" approach is a combination of pumped storage and conventional hydroelectric plants that use natural stream-flow. ==== Compressed air ==== Compressed-air energy storage (CAES) uses surplus energy to compress air for subsequent electricity generation. Small-scale systems have long been used in such applications as propulsion of mine locomotives. The compressed air is stored in an underground reservoir, such as a salt dome. Compressed-air energy storage (CAES) plants can bridge the gap between production volatility and load. CAES storage addresses the energy needs of consumers by effectively providing readily available energy to meet demand. Renewable energy sources like wind and solar energy vary. So at times when they provide little power, they need to be supplemented with other forms of energy to meet energy demand. Compressed-air energy storage plants can take in the surplus energy output of renewable energy sources during times of energy over-production. This stored energy can be used at a later time when demand for electricity increases or energy resource availability decreases. Compression of air creates heat; the air is warmer after compression. Expansion requires heat. If no extra heat is added, the air will be much colder after expansion. If the heat generated during compression can be stored and used during expansion, efficiency improves considerably. A CAES system can deal with the heat in three ways. Air storage can be adiabatic, diabatic, or isothermal. Another approach uses compressed air to power vehicles. ==== Flywheel ==== Flywheel energy storage (FES) works by accelerating a rotor (a flywheel) to a very high speed, holding energy as rotational energy. When energy is added the rotational speed of the flywheel increases, and when energy is extracted, the speed declines, due to conservation of energy. Most FES systems use electricity to accelerate and decelerate the flywheel, but devices that directly use mechanical energy are under consideration. FES systems have rotors made of high strength carbon-fiber composites, suspended by magnetic bearings and spinning at speeds from 20,000 to over 50,000 revolutions per minute (rpm) in a vacuum enclosure. Such flywheels can reach maximum speed ("charge") in a matter of minutes. The flywheel system is connected to a combination electric motor/generator. FES systems have relatively long lifetimes (lasting decades with little or no maintenance; full-cycle lifetimes quoted for flywheels range from in excess of 105, up to 107, cycles of use), high specific energy (100–130 W·h/kg, or 360–500 kJ/kg) and power density. ==== Solid mass gravitational ==== Changing the altitude of solid masses can store or release energy via an elevating system driven by an electric motor/generator. Studies suggest energy can begin to be released with as little as 1 second warning, making the method a useful supplemental feed into an electricity grid to balance load surges. Efficiencies can be as high as 85% recovery of stored energy. This can be achieved by siting the masses inside old vertical mine shafts or in specially constructed towers where the heavy weights are winched up to store energy and allowed a controlled descent to release it. At 2020 a prototype vertical store is being built in Edinburgh, Scotland Potential energy storage or gravity energy storage was under active development in 2013 in association with the California Independent System Operator. It examined the movement of earth-filled hopper rail cars driven by electric locomotives from lower to higher elevations. Other proposed methods include:- using rails, cranes, or elevators to move weights up and down; using high-altitude solar-powered balloon platforms supporting winches to raise and lower solid masses slung underneath them, using winches supported by an ocean barge to take advantage of a 4 km (13,000 ft) elevation difference between the sea surface and the seabed, === Thermal === Thermal energy storage (TES) is the temporary storage or removal of heat. ==== Sensible heat thermal ==== Sensible heat storage take advantage of sensible heat in a material to store energy. Seasonal thermal energy storage (STES) allows heat or cold to be used months after it was collected from waste energy or natural sources. The material can be stored in contained aquifers, clusters of boreholes in geological substrates such as sand or crystalline bedrock, in lined pits filled with gravel and water, or water-filled mines. Seasonal thermal energy storage (STES) projects often have paybacks in four to six years. An example is Drake Landing Solar Community in Canada, for which 97% of the year-round heat is provided by solar-thermal collectors on garage roofs, enabled by a borehole thermal energy store (BTES). In Braedstrup, Denmark, the community's solar district heating system also uses STES, at a temperature of 65 °C (149 °F). A heat pump, which runs only while surplus wind power is available. It is used to raise the temperature to 80 °C (176 °F) for distribution. When wind energy is not available, a gas-fired boiler is used. Twenty percent of Braedstrup's heat is solar. ==== Latent heat thermal (LHTES) ==== Latent heat thermal energy storage systems work by transferring heat to or from a material to change its phase. A phase-change is the melting, solidifying, vaporizing or liquifying. Such a material is called a phase change material (PCM). Materials used in LHTESs often have a high latent heat so that at their specific temperature, the phase change absorbs a large amount of energy, much more than sensible heat. A steam accumulator is a type of LHTES where the phase change is between liquid and gas and uses the latent heat of vaporization of water. Ice storage air conditioning systems use off-peak electricity to store cold by freezing water into ice. The stored cold in ice releases during melting process and can be used for cooling at peak hours. ==== Cryogenic thermal energy storage ==== Air can be liquefied by cooling using electricity and stored as a cryogen with existing technologies. The liquid air can then be expanded through a turbine and the energy recovered as electricity. The system was demonstrated at a pilot plant in the UK in 2012. In 2019, Highview announced plans to build a 50 MW in the North of England and northern Vermont, with the proposed facility able to store five to eight hours of energy, for a 250–400 MWh storage capacity. ==== Carnot battery ==== Electrical energy can be stored thermally by resistive heating or heat pumps, and the stored heat can be converted back to electricity via Rankine cycle or Brayton cycle. This technology has been studied to retrofit coal-fired power plants into fossil-fuel free generation systems. Coal-fired boilers are replaced by high-temperature heat storage charged by excess electricity from renewable energy sources. In 2020, German Aerospace Center started to construct the world's first large-scale Carnot battery system, which has 1,000 MWh storage capacity. === Electrochemical === ==== Rechargeable battery ==== A rechargeable battery comprises one or more electrochemical cells. It is known as a 'secondary cell' because its electrochemical reactions are electrically reversible. Rechargeable batteries come in many shapes and sizes, ranging from button cells to megawatt grid systems. Rechargeable batteries have lower total cost of use and environmental impact than non-rechargeable (disposable) batteries. Some rechargeable battery types are available in the same form factors as disposables. Rechargeable batteries have higher initial cost but can be recharged very cheaply and used many times. Common rechargeable battery chemistries include: Lead–acid battery: Lead acid batteries hold the largest market share of electric storage products. A single cell produces about 2V when charged. In the charged state the metallic lead negative electrode and the lead sulfate positive electrode are immersed in a dilute sulfuric acid (H2SO4) electrolyte. In the discharge process electrons are pushed out of the cell as lead sulfate is formed at the negative electrode while the electrolyte is reduced to water. Lead–acid battery technology has been developed extensively. Upkeep requires minimal labor and its cost is low. The battery's available energy capacity is subject to a quick discharge resulting in a low life span and low energy density. Nickel–cadmium battery (NiCd): Uses nickel oxide hydroxide and metallic cadmium as electrodes. Cadmium is a toxic element, and was banned for most uses by the European Union in 2004. Nickel–cadmium batteries have been almost completely replaced by nickel–metal hydride (NiMH) batteries. Nickel–metal hydride battery (NiMH): First commercial types were available in 1989. These are now a common consumer and industrial type. The battery has a hydrogen-absorbing alloy for the negative electrode instead of cadmium. Lithium-ion battery: The choice in many consumer electronics and have one of the best energy-to-mass ratios and a very slow self-discharge when not in use. Lithium-ion polymer battery: These batteries are light in weight and can be made in any shape desired. Aluminium-sulfur battery with rock salt crystals as electrolyte: aluminium and sulfur are Earth-abundant materials and are much more cheaper than traditional Lithium. ===== Flow battery ===== A flow battery works by passing a solution over a membrane where ions are exchanged to charge or discharge the cell. Cell voltage is chemically determined by the Nernst equation and ranges, in practical applications, from 1.0 V to 2.2 V. Storage capacity depends on the volume of solution. A flow battery is technically akin both to a fuel cell and an electrochemical accumulator cell. Commercial applications are for long half-cycle storage such as backup grid power. ==== Supercapacitor ==== Supercapacitors, also called electric double-layer capacitors (EDLC) or ultracapacitors, are a family of electrochemical capacitors that do not have conventional solid dielectrics. Capacitance is determined by two storage principles, double-layer capacitance and pseudocapacitance. Supercapacitors bridge the gap between conventional capacitors and rechargeable batteries. They store the most energy per unit volume or mass (energy density) among capacitors. They support up to 10,000 farads/1.2 Volt, up to 10,000 times that of electrolytic capacitors, but deliver or accept less than half as much power per unit time (power density). While supercapacitors have specific energy and energy densities that are approximately 10% of batteries, their power density is generally 10 to 100 times greater. This results in much shorter charge/discharge cycles. Also, they tolerate many more charge-discharge cycles than batteries. Supercapacitors have many applications, including: Low supply current for memory backup in static random-access memory (SRAM) Power for cars, buses, trains, cranes and elevators, including energy recovery from braking, short-term energy storage and burst-mode power delivery === Chemical === ==== Power-to-gas ==== Power-to-gas is the conversion of electricity to a gaseous fuel such as hydrogen or methane. The three commercial methods use electricity to reduce water into hydrogen and oxygen by means of electrolysis. In the first method, hydrogen is injected into the natural gas grid or is used for transportation. The second method is to combine the hydrogen with carbon dioxide to produce methane using a methanation reaction such as the Sabatier reaction, or biological methanation, resulting in an extra energy conversion loss of 8%. The methane may then be fed into the natural gas grid. The third method uses the output gas of a wood gas generator or a biogas plant, after the biogas upgrader is mixed with the hydrogen from the electrolyzer, to upgrade the quality of the biogas. ===== Hydrogen ===== The element hydrogen can be a form of stored energy. Hydrogen can produce electricity via a hydrogen fuel cell. At penetrations below 20% of the grid demand, renewables do not severely change the economics; but beyond about 20% of the total demand, external storage becomes important. If these sources are used to make ionic hydrogen, they can be freely expanded. A 5-year community-based pilot program using wind turbines and hydrogen generators began in 2007 in the remote community of Ramea, Newfoundland and Labrador. A similar project began in 2004 on Utsira, a small Norwegian island. Energy losses involved in the hydrogen storage cycle come from the electrolysis of water, liquification or compression of the hydrogen and conversion to electricity. Hydrogen can also be produced from aluminum and water by stripping aluminum's naturally-occurring aluminum oxide barrier and introducing it to water. This method is beneficial because recycled aluminum cans can be used to generate hydrogen, however systems to harness this option have not been commercially developed and are much more complex than electrolysis systems. Common methods to strip the oxide layer include caustic catalysts such as sodium hydroxide and alloys with gallium, mercury and other metals. Underground hydrogen storage is the practice of hydrogen storage in caverns, salt domes and depleted oil and gas fields. Large quantities of gaseous hydrogen have been stored in caverns by Imperial Chemical Industries for many years without any difficulties. The European Hyunder project indicated in 2013 that storage of wind and solar energy using underground hydrogen would require 85 caverns. Powerpaste is a magnesium and hydrogen -based fluid gel that releases hydrogen when reacting with water. It was invented, patented and is being developed by the Fraunhofer Institute for Manufacturing Technology and Advanced Materials (IFAM) of the Fraunhofer-Gesellschaft. Powerpaste is made by combining magnesium powder with hydrogen to form magnesium hydride in a process conducted at 350 °C and five to six times atmospheric pressure. An ester and a metal salt are then added to make the finished product. Fraunhofer states that they are building a production plant slated to start production in 2021, which will produce 4 tons of Powerpaste annually. Fraunhofer has patented their invention in the United States and EU. Fraunhofer claims that Powerpaste is able to store hydrogen energy at 10 times the energy density of a lithium battery of a similar dimension and is safe and convenient for automotive situations. ===== Methane ===== Methane is the simplest hydrocarbon with the molecular formula CH4. Methane is more easily stored and transported than hydrogen. Storage and combustion infrastructure (pipelines, gasometers, power plants) are mature. Synthetic natural gas (syngas or SNG) can be created in a multi-step process, starting with hydrogen and oxygen. Hydrogen is then reacted with carbon dioxide in a Sabatier process, producing methane and water. Methane can be stored and later used to produce electricity. The resulting water is recycled, reducing the need for water. In the electrolysis stage, oxygen is stored for methane combustion in a pure oxygen environment at an adjacent power plant, eliminating nitrogen oxides. Methane combustion produces carbon dioxide (CO2) and water. The carbon dioxide can be recycled to boost the Sabatier process and water can be recycled for further electrolysis. Methane production, storage and combustion recycles the reaction products. The CO2 has economic value as a component of an energy storage vector, not a cost as in carbon capture and storage. ==== Power-to-liquid ==== Power-to-liquid is similar to power to gas except that the hydrogen is converted into liquids such as methanol or ammonia. These are easier to handle than gases, and require fewer safety precautions than hydrogen. They can be used for transportation, including aircraft, but also for industrial purposes or in the power sector. ==== Biofuels ==== Various biofuels such as biodiesel, vegetable oil, alcohol fuels, or biomass can replace fossil fuels. Various chemical processes can convert the carbon and hydrogen in coal, natural gas, plant and animal biomass and organic wastes into short hydrocarbons suitable as replacements for existing hydrocarbon fuels. Examples are Fischer–Tropsch diesel, methanol, dimethyl ether and syngas. This diesel source was used extensively in World War II in Germany, which faced limited access to crude oil supplies. South Africa produces most of the country's diesel from coal for similar reasons. A long term oil price above US$35/bbl may make such large scale synthetic liquid fuels economical. ===== Aluminum ===== Aluminum has been proposed as an energy store by a number of researchers. Its electrochemical equivalent (8.04 Ah/cm3) is nearly four times greater than that of lithium (2.06 Ah/cm3). Energy can be extracted from aluminum by reacting it with water to generate hydrogen. However, it must first be stripped of its natural oxide layer, a process which requires pulverization, chemical reactions with caustic substances, or alloys. The byproduct of the reaction to create hydrogen is aluminum oxide, which can be recycled into aluminum with the Hall–Héroult process, making the reaction theoretically renewable. If the Hall-Heroult Process is run using solar or wind power, aluminum could be used to store the energy produced at higher efficiency than direct solar electrolysis. ==== Boron, silicon, and zinc ==== Boron, silicon, and zinc have been proposed as energy storage solutions. ==== Other chemical ==== The organic compound norbornadiene converts to quadricyclane upon exposure to light, storing solar energy as the energy of chemical bonds. A working system has been developed in Sweden as a molecular solar thermal system. === Electrical methods === ==== Capacitor ==== A capacitor (originally known as a 'condenser') is a passive two-terminal electrical component used to store energy electrostatically. Practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e., insulator). A capacitor can store electric energy when disconnected from its charging circuit, so it can be used like a temporary battery, or like other types of rechargeable energy storage system. Capacitors are commonly used in electronic devices to maintain power supply while batteries change. (This prevents loss of information in volatile memory.) Conventional capacitors provide less than 360 joules per kilogram, while a conventional alkaline battery has a density of 590 kJ/kg. Capacitors store energy in an electrostatic field between their plates. Given a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge (+Q) to collect on one plate and negative charge (-Q) to collect on the other plate. If a battery is attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if an accelerating or alternating voltage is applied across the leads of the capacitor, a displacement current can flow. Besides capacitor plates, charge can also be stored in a dielectric layer. Capacitance is greater given a narrower separation between conductors and when the conductors have a larger surface area. In practice, the dielectric between the plates emits a small amount of leakage current and has an electric field strength limit, known as the breakdown voltage. However, the effect of recovery of a dielectric after a high-voltage breakdown holds promise for a new generation of self-healing capacitors. The conductors and leads introduce undesired inductance and resistance. Research is assessing the quantum effects of nanoscale capacitors for digital quantum batteries. ==== Superconducting magnetics ==== Superconducting magnetic energy storage (SMES) systems store energy in a magnetic field created by the flow of direct current in a superconducting coil that has been cooled to a temperature below its superconducting critical temperature. A typical SMES system includes a superconducting coil, power conditioning system and refrigerator. Once the superconducting coil is charged, the current does not decay and the magnetic energy can be stored indefinitely. The stored energy can be released to the network by discharging the coil. The associated inverter/rectifier accounts for about 2–3% energy loss in each direction. SMES loses the least amount of electricity in the energy storage process compared to other methods of storing energy. SMES systems offer round-trip efficiency greater than 95%. Due to the energy requirements of refrigeration and the cost of superconducting wire, SMES is used for short duration storage such as improving power quality. It also has applications in grid balancing. == Applications == === Mills === The classic application before the Industrial Revolution was the control of waterways to drive water mills for processing grain or powering machinery. Complex systems of reservoirs and dams were constructed to store and release water (and the potential energy it contained) when required. === Homes === Home energy storage is expected to become increasingly common given the growing importance of distributed generation of renewable energies (especially photovoltaics) and the important share of energy consumption in buildings. To exceed a self-sufficiency of 40% in a household equipped with photovoltaics, energy storage is needed. Multiple manufacturers produce rechargeable battery systems for storing energy, generally to hold surplus energy from home solar or wind generation. Today, for home energy storage, Li-ion batteries are preferable to lead-acid ones given their similar cost but much better performance. Tesla Motors produces two models of the Tesla Powerwall. One is a 10 kWh weekly cycle version for backup applications and the other is a 7 kWh version for daily cycle applications. In 2016, a limited version of the Tesla Powerpack 2 cost $398(US)/kWh to store electricity worth 12.5 cents/kWh (US average grid price) making a positive return on investment doubtful unless electricity prices are higher than 30 cents/kWh. RoseWater Energy produces two models of the "Energy & Storage System", the HUB 120 and SB20. Both versions provide 28.8 kWh of output, enabling it to run larger houses or light commercial premises, and protecting custom installations. The system provides five key elements into one system, including providing a clean 60 Hz Sine wave, zero transfer time, industrial-grade surge protection, renewable energy grid sell-back (optional), and battery backup. Enphase Energy announced an integrated system that allows home users to store, monitor and manage electricity. The system stores 1.2 kWh of energy and 275W/500W power output. Storing wind or solar energy using thermal energy storage though less flexible, is considerably cheaper than batteries. A simple 52-gallon electric water heater can store roughly 12 kWh of energy for supplementing hot water or space heating. For purely financial purposes in areas where net metering is available, home generated electricity may be sold to the grid through a grid-tie inverter without the use of batteries for storage. === Grid electricity and power stations === ==== Renewable energy ==== The largest source and the greatest store of renewable energy is provided by hydroelectric dams. A large reservoir behind a dam can store enough water to average the annual flow of a river between dry and wet seasons, and a very large reservoir can store enough water to average the flow of a river between dry and wet years. While a hydroelectric dam does not directly store energy from intermittent sources, it does balance the grid by lowering its output and retaining its water when power is generated by solar or wind. If wind or solar generation exceeds the region's hydroelectric capacity, then some additional source of energy is needed. Many renewable energy sources (notably solar and wind) produce variable power. Storage systems can level out the imbalances between supply and demand that this causes. Electricity must be used as it is generated or converted immediately into storable forms. The main method of electrical grid storage is pumped-storage hydroelectricity. Areas of the world such as Norway, Wales, Japan and the US have used elevated geographic features for reservoirs, using electrically powered pumps to fill them. When needed, the water passes through generators and converts the gravitational potential of the falling water into electricity. Pumped storage in Norway, which gets almost all its electricity from hydro, has currently a capacity of 1.4 GW but since the total installed capacity is nearly 32 GW and 75% of that is regulable, it can be expanded significantly. Some forms of storage that produce electricity include pumped-storage hydroelectric dams, rechargeable batteries, thermal storage including molten salts which can efficiently store and release very large quantities of heat energy, and compressed air energy storage, flywheels, cryogenic systems and superconducting magnetic coils. Surplus power can also be converted into methane (Sabatier process) with stockage in the natural gas network. In 2011, the Bonneville Power Administration in the northwestern United States created an experimental program to absorb excess wind and hydro power generated at night or during stormy periods that are accompanied by high winds. Under central control, home appliances absorb surplus energy by heating ceramic bricks in special space heaters to hundreds of degrees and by boosting the temperature of modified hot water heater tanks. After charging, the appliances provide home heating and hot water as needed. The experimental system was created as a result of a severe 2010 storm that overproduced renewable energy to the extent that all conventional power sources were shut down, or in the case of a nuclear power plant, reduced to its lowest possible operating level, leaving a large area running almost completely on renewable energy. Another advanced method used at the former Solar Two project in the United States and the Solar Tres Power Tower in Spain uses molten salt to store thermal energy captured from the sun and then convert it and dispatch it as electrical power. The system pumps molten salt through a tower or other special conduits to be heated by the sun. Insulated tanks store the solution. Electricity is produced by turning water to steam that is fed to turbines. Since the early 21st century batteries have been applied to utility scale load-leveling and frequency regulation capabilities. In vehicle-to-grid storage, electric vehicles that are plugged into the energy grid can deliver stored electrical energy from their batteries into the grid when needed. === Air conditioning === Thermal energy storage (TES) can be used for air conditioning. It is most widely used for cooling single large buildings and/or groups of smaller buildings. Commercial air conditioning systems are the biggest contributors to peak electrical loads. In 2009, thermal storage was used in over 3,300 buildings in over 35 countries. It works by chilling material at night and using the chilled material for cooling during the hotter daytime periods. The most popular technique is ice storage, which requires less space than water and is cheaper than fuel cells or flywheels. In this application, a standard chiller runs at night to produce an ice pile. Water circulates through the pile during the day to chill water that would normally be the chiller's daytime output. A partial storage system minimizes capital investment by running the chillers nearly 24 hours a day. At night, they produce ice for storage and during the day they chill water. Water circulating through the melting ice augments the production of chilled water. Such a system makes ice for 16 to 18 hours a day and melts ice for six hours a day. Capital expenditures are reduced because the chillers can be just 40% – 50% of the size needed for a conventional, no-storage design. Storage sufficient to store half a day's available heat is usually adequate. A full storage system shuts off the chillers during peak load hours. Capital costs are higher, as such a system requires larger chillers and a larger ice storage system. This ice is produced when electrical utility rates are lower. Off-peak cooling systems can lower energy costs. The U.S. Green Building Council has developed the Leadership in Energy and Environmental Design (LEED) program to encourage the design of reduced-environmental impact buildings. Off-peak cooling may help toward LEED Certification. Thermal storage for heating is less common than for cooling. An example of thermal storage is storing solar heat to be used for heating at night. Latent heat can also be stored in technical phase change materials (PCMs). These can be encapsulated in wall and ceiling panels, to moderate room temperatures. === Transport === Liquid hydrocarbon fuels are the most commonly used forms of energy storage for use in transportation, followed by a growing use of Battery Electric Vehicles and Hybrid Electric Vehicles. Other energy carriers such as hydrogen can be used to avoid producing greenhouse gases. Public transport systems like trams and trolleybuses require electricity, but due to their variability in movement, a steady supply of electricity via renewable energy is challenging. Photovoltaic systems installed on the roofs of buildings can be used to power public transportation systems during periods in which there is increased demand for electricity and access to other forms of energy are not readily available. Upcoming transitions in the transportation system also include e.g. ferries and airplanes, where electric power supply is investigated as an interesting alternative. === Electronics === Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems they stabilize voltage and power flow. == Use cases == The United States Department of Energy International Energy Storage Database (IESDB), is a free-access database of energy storage projects and policies funded by the United States Department of Energy Office of Electricity and Sandia National Labs. == Capacity == Storage capacity is the amount of energy extracted from an energy storage device or system; usually measured in joules or kilowatt-hours and their multiples, it may be given in number of hours of electricity production at power plant nameplate capacity; when storage is of primary type (i.e., thermal or pumped-water), output is sourced only with the power plant embedded storage system. == Economics == The economics of energy storage strictly depends on the reserve service requested, and several uncertainty factors affect the profitability of energy storage. Therefore, not every storage method is technically and economically suitable for the storage of several MWh, and the optimal size of the energy storage is market and location dependent. Moreover, ESS are affected by several risks, e.g.: Techno-economic risks, which are related to the specific technology; Market risks, which are the factors that affect the electricity supply system; Regulation and policy risks. Therefore, traditional techniques based on deterministic Discounted Cash Flow (DCF) for the investment appraisal are not fully adequate to evaluate these risks and uncertainties and the investor's flexibility to deal with them. Hence, the literature recommends to assess the value of risks and uncertainties through the Real Option Analysis (ROA), which is a valuable method in uncertain contexts. The economic valuation of large-scale applications (including pumped hydro storage and compressed air) considers benefits including: curtailment avoidance, grid congestion avoidance, price arbitrage and carbon-free energy delivery. In one technical assessment by the Carnegie Mellon Electricity Industry Centre, economic goals could be met using batteries if their capital cost was $30 to $50 per kilowatt-hour. A metric of energy efficiency of storage is energy storage on energy invested (ESOI), which is the amount of energy that can be stored by a technology, divided by the amount of energy required to build that technology. The higher the ESOI, the better the storage technology is energetically. For lithium-ion batteries this is around 10, and for lead acid batteries it is about 2. Other forms of storage such as pumped hydroelectric storage generally have higher ESOI, such as 210. Pumped-storage hydroelectricity is by far the largest storage technology used globally. However, the usage of conventional pumped-hydro storage is limited because it requires terrain with elevation differences and also has a very high land use for relatively small power. In locations without suitable natural geography, underground pumped-hydro storage could also be used. High costs and limited life still make batteries a "weak substitute" for dispatchable power sources, and are unable to cover for variable renewable power gaps lasting for days, weeks or months. In grid models with high VRE share, the excessive cost of storage tends to dominate the costs of the whole grid — for example, in California alone 80% share of VRE would require 9.6 TWh of storage but 100% would require 36.3 TWh. As of 2018 the state only had 150 GWh of storage, primarily in pumped storage and a small fraction in batteries. According to another study, supplying 80% of US demand from VRE would require a smart grid covering the whole country or battery storage capable to supply the whole system for 12 hours, both at cost estimated at $2.5 trillion. Similarly, several studies have found that relying only on VRE and energy storage would cost about 30–50% more than a comparable system that combines VRE with nuclear plants or plants with carbon capture and storage instead of energy storage. == Research == === Germany === In 2013, the German government allocated €200M (approximately US$270M) for research, and another €50M to subsidize battery storage in residential rooftop solar panels, according to a representative of the German Energy Storage Association. Siemens AG commissioned a production-research plant to open in 2015 at the Zentrum für Sonnenenergie und Wasserstoff (ZSW, the German Center for Solar Energy and Hydrogen Research in the State of Baden-Württemberg), a university/industry collaboration in Stuttgart, Ulm and Widderstall, staffed by approximately 350 scientists, researchers, engineers, and technicians. The plant develops new near-production manufacturing materials and processes (NPMM&P) using a computerized Supervisory Control and Data Acquisition (SCADA) system. It aims to enable the expansion of rechargeable battery production with increased quality and lower cost. From 2023 onwards, a new project by the German Research Foundation focuses on molecular photoswitches to store solar thermal energy. The spokesperson of these so-called molecular solar thermal (MOST) systems is Prof. Dr. Hermann A. Wegner. === United States === In 2014, research and test centers opened to evaluate energy storage technologies. Among them was the Advanced Systems Test Laboratory at the University of Wisconsin at Madison in Wisconsin State, which partnered with battery manufacturer Johnson Controls. The laboratory was created as part of the university's newly opened Wisconsin Energy Institute. Their goals include the evaluation of state-of-the-art and next generation electric vehicle batteries, including their use as grid supplements. The State of New York unveiled its New York Battery and Energy Storage Technology (NY-BEST) Test and Commercialization Center at Eastman Business Park in Rochester, New York, at a cost of $23 million for its almost 1,700 m2 laboratory. The center includes the Center for Future Energy Systems, a collaboration between Cornell University of Ithaca, New York and the Rensselaer Polytechnic Institute in Troy, New York. NY-BEST tests, validates and independently certifies diverse forms of energy storage intended for commercial use. On September 27, 2017, Senators Al Franken of Minnesota and Martin Heinrich of New Mexico introduced Advancing Grid Storage Act (AGSA), which would devote more than $1 billion in research, technical assistance and grants to encourage energy storage in the United States. In grid models with high VRE share, the excessive cost of storage tends to dominate the costs of the whole grid – for example, in California alone 80% share of VRE would require 9.6 TWh of storage but 100% would require 36.3 TWh. According to another study, supplying 80% of US demand from VRE would require a smart grid covering the whole country or battery storage capable to supply the whole system for 12 hours, both at cost estimated at $2.5 trillion. === United Kingdom === In the United Kingdom, some 14 industry and government agencies allied with seven British universities in May 2014 to create the SUPERGEN Energy Storage Hub in order to assist in the coordination of energy storage technology research and development. == See also == == References == == Further reading == Journals and papers Chen, Haisheng; Thang Ngoc Cong; Wei Yang; Chunqing Tan; Yongliang Li; Yulong Ding. Progress in electrical energy storage system: A critical review, Progress in Natural Science, accepted July 2, 2008, published in Vol. 19, 2009, pp. 291–312, doi: 10.1016/j.pnsc.2008.07.014. Sourced from the National Natural Science Foundation of China and the Chinese Academy of Sciences. Published by Elsevier and Science in China Press. Synopsis: a review of electrical energy storage technologies for stationary applications. Retrieved from ac.els-cdn.com on May 13, 2014. (PDF) Corum, Lyn. The New Core Technology: Energy storage is part of the smart grid evolution, The Journal of Energy Efficiency and Reliability, December 31, 2009. Discusses: Anaheim Public Utilities Department, lithium ion energy storage, iCel Systems, Beacon Power, Electric Power Research Institute (EPRI), ICEL, Self Generation Incentive Program, ICE Energy, vanadium redox flow, lithium Ion, regenerative fuel cell, ZBB, VRB, lead acid, CAES, and Thermal Energy Storage. (PDF) de Oliveira e Silva, G.; Hendrick, P. (2016). "Lead-acid batteries coupled with photovoltaics for increased electricity self-sufficiency in households". Applied Energy. 178: 856–867. Bibcode:2016ApEn..178..856D. doi:10.1016/j.apenergy.2016.06.003. Sahoo, Subrat; Timmann, Pascal (2023). "Energy Storage Technologies for Modern Power Systems: A Detailed Analysis of Functionalities, Potentials, and Impacts" (PDF). IEEE Access. 11: 49689–49729. Bibcode:2023IEEEA..1149689S. doi:10.1109/ACCESS.2023.3274504. ISSN 2169-3536. Retrieved December 14, 2024. Whittingham, M. Stanley. History, Evolution, and Future Status of Energy Storage, Proceedings of the IEEE, manuscript accepted February 20, 2012, date of publication April 16, 2012; date of current version May 10, 2012, published in Proceedings of the IEEE, Vol. 100, May 13, 2012, 0018–9219, pp. 1518–1534, doi: 10.1109/JPROC.2012.219017. Retrieved from ieeexplore.ieee.org May 13, 2014. Synopsis: A discussion of the important aspects of energy storage including emerging battery technologies and the importance of storage systems in key application areas, including electronic devices, transportation, and the utility grid. (PDF) Books GA Mansoori, N Enayati, LB Agyarko (2016), Energy: Sources, Utilization, Legislation, Sustainability, Illinois as Model State, World Sci. Pub. Co., ISBN 978-981-4704-00-7 Díaz-González, Franscisco (2016). Energy storage in power systems. United Kingdom: John Wiley & Sons. ISBN 9781118971321. == External links == U.S. Dept of Energy – Energy Storage Systems Government research center on energy storage technology. U.S. Dept of Energy – International Energy Storage Database Archived November 13, 2013, at the Wayback Machine The DOE International Energy Storage Database provides free, up-to-date information on grid-connected energy storage projects and relevant state and federal policies. IEEE Special Issue on Massive Energy Storage IEA-ECES – International Energy Agency – Energy Conservation through Energy Conservation programme. Energy Information Administration Glossary Energy Storage Project Regeneration.
Wikipedia/Gravitational_potential_energy_storage