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the time interval of two events being different for two observers moving with respect to each other. In summary: Two events are defined to be simultaneous if an observer measures them as occurring at the same time (such as by receiving light from the events). Two events are not necessarily simultaneous to all observers. Access for free at openstax.org. 10.1 • Postulates of Special Relativity 311 The discrepancies between Newtonian mechanics and relativity theory illustrate an important point about how science advances. Einstein’s theory did not replace Newton’s but rather extended it. It is not unusual that a new theory must be developed to account for new information. In most cases, the new theory is built on the foundation of older theory. It is rare that old theories are completely replaced. In this chapter, you will learn about the theory of special relativity, but, as mentioned in the introduction, Einstein developed two relativity theories: special and general. Table 10.1 summarizes the differences between the two theories. Special Relativity General Relativity Published in 1905 Final form published in 1916 A theory of space-time A theory of gravity Applies to observers moving at constant speed Applies to observers that are accelerating Most useful in the field of nuclear physics Most useful in the field of astrophysics Accepted quickly and put to practical use by nuclear physicists and quantum chemists Largely ignored until 1960 when new mathematical techniques made the theory more accessible and astronomers found some important applications Also note that the theory of general relativity includes the theory of special relativity. Table 10.1 Comparing Special Relativity and General Relativity WORKED EXAMPLE Calculating the Time it Takes Light to Travel a Given Distance The sun is 1.50 × 108 km from Earth. How long does it take light to travel from the sun to Earth in minutes and seconds? Strategy Identify knowns. Identify unknowns. Time Find the equation that relates knowns and unknowns. Be sure to use consistent units. Solution 10.1 10.2 Discussion The answer is written as 5.00 × 102 rather than 500 in order to show that there are three significant figures. When astronomers witness an event on the sun, such as a sunspot, it actually happened minutes earlier. Compare 8 light minutesto the distance to stars, which are light yearsaway. Any events on other stars happened years ago. 312 Chapter 10 • Special Relativity Practice Problems 1. Light travels through 1.00 m of water in 4.42×10-9 s. What is the speed
of light in water? a. 4.42×10-9 m/s b. 4.42×109 m/s c. 2.26×108 m/s d. 226×108 m/s 2. An astronaut on the moon receives a message from mission control on Earth. The signal is sent by a form of electromagnetic radiation and takes 1.28 s to travel the distance between Earth and the moon. What is the distance from Earth to the moon? a. 2.34×105 km b. 2.34×108 km 3.84×105 km c. 3.84×108 km d. Check Your Understanding 3. Explain what is meant by a frame of reference. a. A frame of reference is a graph plotted between distance and time. b. A frame of reference is a graph plotted between speed and time. c. A frame of reference is the velocity of an object through empty space without regard to its surroundings. d. A frame of reference is an arbitrarily fixed point with respect to which motion of other points is measured. 4. Two people swim away from a raft that is floating downstream. One swims upstream and returns, and the other swims across the current and back. If this scenario represents the Michelson–Morley experiment, what do (i) the water, (ii) the swimmers, and (iii) the raft represent? the ether rays of light Earth a. rays of light the ether Earth b. c. the ether Earth rays of light d. Earth rays of light the ether 5. If Michelson and Morley had observed the interference pattern shift in their interferometer, what would that have indicated? a. The speed of light is the same in all frames of reference. b. The speed of light depends on the motion relative to the ether. c. The speed of light changes upon reflection from a surface. d. The speed of light in vacuum is less than 3.00×108 m/s. 6. If you designate a point as being fixed and use that point to measure the motion of surrounding objects, what is the point called? a. An origin b. A frame of reference c. A moving frame d. A coordinate system 10.2 Consequences of Special Relativity Section Learning Objectives By the end of this section, you will be able to do the following: • Describe the relativistic effects seen in time dilation, length contraction, and conservation of relativistic momentum • Explain and perform
calculations involving mass-energy equivalence Section Key Terms binding energy length contraction mass defect time dilation Access for free at openstax.org. 10.2 • Consequences of Special Relativity 313 proper length relativistic relativistic momentum relativistic energy relativistic factor rest mass Relativistic Effects on Time, Distance, and Momentum Consideration of the measurement of elapsed time and simultaneity leads to an important relativistic effect. Time dilation is the phenomenon of time passing more slowly for an observer who is moving relative to another observer. For example, suppose an astronaut measures the time it takes for light to travel from the light source, cross her ship, bounce off a mirror, and return. (See Figure 10.5.) How does the elapsed time the astronaut measures compare with the elapsed time measured for the same event by a person on the earth? Asking this question (another thought experiment) produces a profound result. We find that the elapsed time for a process depends on who is measuring it. In this case, the time measured by the astronaut is smaller than the time measured by the earth bound observer. The passage of time is different for the two observers because the distance the light travels in the astronaut’s frame is smaller than in the earth bound frame. Light travels at the same speed in each frame, and so it will take longer to travel the greater distance in the earth bound frame. Figure 10.5 (a) An astronaut measures the time for light to cross her ship using an electronic timer. Light travels a distance in the astronaut’s frame. (b) A person on the earth sees the light follow the longer path and take a longer time The relationship between Δtand Δto is given by where is the relativistic factor given by and vand care the speeds of the moving observer and light, respectively. 314 Chapter 10 • Special Relativity TIPS FOR SUCCESS Try putting some values for vinto the expression for the relativistic factor ( a difference and when is so close to 1 that it can be ignored. Try 225 m/s, the speed of an airliner; 2.98 × 104 m/s, the speed of Earth in its orbit; and 2.990 × 108 m/s, the speed of a particle in an accelerator. ). Observe at which speeds this factor will make Notice that when the velocity vis small compared to the speed of light c, then v/cbecomes small, and becomes close to 1.
When this happens, time measurements are the same in both frames of reference. Relativistic effects, meaning those that have to do with special relativity, usually become significant when speeds become comparable to the speed of light. This is seen to be the case for time dilation. You may have seen science fiction movies in which space travelers return to Earth after a long trip to find that the planet and everyone on it has aged much more than they have. This type of scenario is a based on a thought experiment, known as the twin paradox, which imagines a pair of twins, one of whom goes on a trip into space while the other stays home. When the space traveler returns, she finds her twin has aged much more than she. This happens because the traveling twin has been in two frames of reference, one leaving Earth and one returning. Time dilation has been confirmed by comparing the time recorded by an atomic clock sent into orbit to the time recorded by a clock that remained on Earth. GPS satellites must also be adjusted to compensate for time dilation in order to give accurate positioning. Have you ever driven on a road, like that shown in Figure 10.6, that seems like it goes on forever? If you look ahead, you might say you have about 10 km left to go. Another traveler might say the road ahead looks like it is about 15 km long. If you both measured the road, however, you would agree. Traveling at everyday speeds, the distance you both measure would be the same. You will read in this section, however, that this is not true at relativistic speeds. Close to the speed of light, distances measured are not the same when measured by different observers moving with respect to one other. Figure 10.6 People might describe distances differently, but at relativistic speeds, the distances really are different. (Corey Leopold, Flickr) One thing all observers agree upon is their relative speed. When one observer is traveling away from another, they both see the other receding at the same speed, regardless of whose frame of reference is chosen. Remember that speed equals distance divided by time: v = d/t. If the observers experience a difference in elapsed time, they must also observe a difference in distance traversed. This is because the ratio d/tmust be the same for both observers. The shortening of distance experienced by an observer moving with respect to the points whose distance apart is measured is called length contraction. Proper length, L0, is the distance between
two points measured in the reference frame where the observer and the points are at rest. The observer in motion with respect to the points measures L. These two lengths are related by the equation Because is the same expression used in the time dilation equation above, the equation becomes Access for free at openstax.org. 10.2 • Consequences of Special Relativity 315 To see how length contraction is seen by a moving observer, go to this simulation (http://openstax.org/l/28simultaneity). Here you can also see that simultaneity, time dilation, and length contraction are interrelated phenomena. This link is to a simulation that illustrates the relativity of simultaneous events. In classical physics, momentum is a simple product of mass and velocity. When special relativity is taken into account, objects that have mass have a speed limit. What effect do you think mass and velocity have on the momentum of objects moving at relativistic speeds; i.e., speeds close to the speed of light? Momentum is one of the most important concepts in physics. The broadest form of Newton’s second law is stated in terms of momentum. Momentum is conserved in classical mechanics whenever the net external force on a system is zero. This makes momentum conservation a fundamental tool for analyzing collisions. We will see that momentum has the same importance in modern physics. Relativistic momentum is conserved, and much of what we know about subatomic structure comes from the analysis of collisions of accelerator-produced relativistic particles. One of the postulates of special relativity states that the laws of physics are the same in all inertial frames. Does the law of conservation of momentum survive this requirement at high velocities? The answer is yes, provided that the momentum is defined as follows. Relativistic momentum, p, is classical momentum multiplied by the relativistic factor is the rest mass of the object (that is, the mass measured at rest, without any as before, is the relativistic factor. We use the mass of the object as measured at rest because we cannot where to an observer, and determine its mass while it is moving. factor involved), is its velocity relative 10.3 for velocity here to distinguish it from relative velocity between observers. Only one observer is being Note that we use considered here. With defined in this way, Again we see that the relativistic quantity becomes virtually the same as the classical at low velocities. That is, relativistic
momentum is conserved whenever the net external force is zero, just as in classical physics. is very nearly equal to 1 at low velocities. at low velocities, because becomes the classical Relativistic momentum has the same intuitive feel as classical momentum. It is greatest for large masses moving at high velocities. Because of the factor approaching infinity as speed of light. If it did, its momentum would become infinite, which is an unreasonable value. however, relativistic momentum behaves differently from classical momentum by (See Figure 10.7.) This is another indication that an object with mass cannot reach the approaches Figure 10.7 Relativistic momentum approaches infinity as the velocity of an object approaches the speed of light. Relativistic momentum is defined in such a way that the conservation of momentum will hold in all inertial frames. Whenever the net external force on a system is zero, relativistic momentum is conserved, just as is the case for classical momentum. This 316 Chapter 10 • Special Relativity has been verified in numerous experiments. Mass-Energy Equivalence Let us summarize the calculation of relativistic effects on objects moving at speeds near the speed of light. In each case we will need to calculate the relativistic factor, given by where v and care as defined earlier. We use u as the velocity of a particle or an object in one frame of reference, and v for the velocity of one frame of reference with respect to another. Time Dilation Elapsed time on a moving object, on the moving object when it is taken to be the frame or reference. as seen by a stationary observer is given by Length Contraction Length measured by a person at rest with respect to a moving object, L, is given by where is the time observed where L0 is the length measured on the moving object. Relativistic Momentum Momentum, p, of an object of mass, m, traveling at relativistic speeds is given by object as seen by a stationary observer. where u is velocity of a moving Relativistic Energy The original source of all the energy we use is the conversion of mass into energy. Most of this energy is generated by nuclear reactions in the sun and radiated to Earth in the form of electromagnetic radiation, where it is then transformed into all the forms with which we are familiar. The remaining energy from nuclear reactions is produced in nuclear power plants and in Earth’s interior. In each of these cases, the source of the energy is
the conversion of a small amount of mass into a large amount of energy. These sources are shown in Figure 10.8. Figure 10.8 The sun (a) and the Susquehanna Steam Electric Station (b) both convert mass into energy. ((a) NASA/Goddard Space Flight Center, Scientific Visualization Studio; (b) U.S. government) The first postulate of relativity states that the laws of physics are the same in all inertial frames. Einstein showed that the law of conservation of energy is valid relativistically, if we define energy to include a relativistic factor. The result of his analysis is that a particle or object of mass mmoving at velocity u has relativistic energy given by This is the expression for the total energy of an object of mass mat any speed u and includes both kinetic and potential energy. Look back at the equation for and you will see that it is equal to 1 when u is 0; that is, when an object is at rest. Then the rest Access for free at openstax.org. 10.2 • Consequences of Special Relativity 317 energy, E0, is simply This is the correct form of Einstein’s famous equation. This equation is very useful to nuclear physicists because it can be used to calculate the energy released by a nuclear reaction. This is done simply by subtracting the mass of the products of such a reaction from the mass of the reactants. The difference is the min Here is a simple example: A positron is a type of antimatter that is just like an electron, except that it has a positive charge. When a positron and an electron collide, their masses are completely annihilated and converted to energy in the form of gamma rays. Because both particles have a rest mass of 9.11 × 10–31 kg, we multiply the mc2 term by 2. So the energy of the gamma rays is 10.4 where we have the expression for the joule (J) in terms of its SI base units of kg, m, and s. In general, the nuclei of stable isotopes have less mass then their constituent subatomic particles. The energy equivalent of this difference is called the binding energy of the nucleus. This energy is released during the formation of the isotope from its constituent particles because the product is more stable than the reactants. Expressed as mass, it is called the mass defect. For example, a helium nucleus is made of two neutrons and
two protons and has a mass of 4.0003 atomic mass units (u). The sum of the masses of two protons and two neutrons is 4.0330 u. The mass defect then is 0.0327 u. Converted to kg, the mass defect is 5.0442 × 10–30 kg. Multiplying this mass times c2 gives a binding energy of 4.540 × 10–12 J. This does not sound like much because it is only one atom. If you were to make one gram of helium out of neutrons and protons, it would release 683,000,000,000 J. By comparison, burning one gram of coal releases about 24 J. BOUNDLESS PHYSICS The RHIC Collider Figure 10.9 shows the Brookhaven National Laboratory in Upton, NY. The circular structure houses a particle accelerator called the RHIC, which stands for Relativistic Heavy Ion Collider. The heavy ions in the name are gold nuclei that have been stripped of their electrons. Streams of ions are accelerated in several stages before entering the big ring seen in the figure. Here, they are accelerated to their final speed, which is about 99.7 percent the speed of light. Such high speeds are called relativistic. All the relativistic phenomena we have been discussing in this chapter are very pronounced in this case. At this speed = 12.9, so that relativistic time dilates by a factor of about 13, and relativistic length contracts by the same factor. Figure 10.9 Brookhaven National Laboratory. The circular structure houses the RHIC. (energy.gov, Wikimedia Commons) Two ion beams circle the 2.4-mile long track around the big ring in opposite directions. The paths can then be made to cross, thereby causing ions to collide. The collision event is very short-lived but amazingly intense. The temperatures and pressures produced are greater than those in the hottest suns. At 4 trillion degrees Celsius, this is the hottest material ever created in a 318 Chapter 10 • Special Relativity laboratory But what is the point of creating such an extreme event? Under these conditions, the neutrons and protons that make up the gold nuclei are smashed apart into their components, which are called quarks and gluons. The goal is to recreate the conditions that theorists believe existed at the very beginning of the universe. It is thought that, at that time, matter was a sort of soup of quarks and glu
ons. When things cooled down after the initial bang, these particles condensed to form protons and neutrons. Some of the results have been surprising and unexpected. It was thought the quark-gluon soup would resemble a gas or plasma. Instead, it behaves more like a liquid. It has been called a perfectliquid because it has virtually no viscosity, meaning that it has no resistance to flow. GRASP CHECK Calculate the relativistic factor γ, for a particle traveling at 99.7 percent of the speed of light. a. 0.08 b. 0.71 1.41 c. 12.9 d. WORKED EXAMPLE The Speed of Light One night you are out looking up at the stars and an extraterrestrial spaceship flashes across the sky. The ship is 50 meters long and is travelling at 95 percent of the speed of light. What would the ship’s length be when measured from your earthbound frame of reference? Strategy List the knowns and unknowns. Knowns: proper length of the ship, L0= 50 m; velocity, v, = 0.95c Unknowns: observed length of the ship accounting for relativistic length contraction, L. Choose the relevant equation. Solution Discussion Calculations of sure to also square the decimal representing the percentage before subtracting from 1. Note that the aliens will still see the length as L0 because they are moving with the frame of reference that is the ship. can usually be simplified in this way when vis expressed as a percentage of cbecause the c2 terms cancel. Be Practice Problems 7. Calculate the relativistic factor, γ, for an object traveling at 2.00×108 m/s. a. 0.74 b. 0.83 c. d. 1.2 1.34 8. The distance between two points, called the proper length, L0, is 1.00 km. An observer in motion with respect to the frame of Access for free at openstax.org. 10.2 • Consequences of Special Relativity 319 reference of the two points measures 0.800 km, which is L. What is the relative speed of the frame of reference with respect to the observer? 1.80×108 m/s a. b. 2.34×108 m/s 3.84×108 m/s c. 5.00×108 m/s d. 9. Consider the nuclear fission reaction. If a neutron
has a rest mass of 1.009u, has rest mass of 136.907u, and has a rest mass of 96.937u, what is the value of Ein has a rest mass of 235.044u, joules? a. b. c. d. J J J J Solution The correct answer is (b). The mass deficit in the reaction is Converting that mass to kg and applying to find the energy equivalent of the mass deficit gives or 0.191u. 10. Consider the nuclear fusion reaction. If has a rest mass of 2.014u, has a rest mass of 3.016u, and has a rest mass of 1.008u, what is the value of Ein joules? a. b. c. d. J J J J Solution The correct answer is (a). The mass deficit in the reaction is mass to kg and applying to find the energy equivalent of the mass deficit gives, or 0.004u. Converting that Check Your Understanding 11. Describe time dilation and state under what conditions it becomes significant. a. When the speed of one frame of reference past another reaches the speed of light, a time interval between two events at the same location in one frame appears longer when measured from the second frame. b. When the speed of one frame of reference past another becomes comparable to the speed of light, a time interval between two events at the same location in one frame appears longer when measured from the second frame. c. When the speed of one frame of reference past another reaches the speed of light, a time interval between two events at the same location in one frame appears shorter when measured from the second frame. d. When the speed of one frame of reference past another becomes comparable to the speed of light, a time interval between two events at the same location in one frame appears shorter when measured from the second frame. 12. The equation used to calculate relativistic momentum is p= γ · m · u. Define the terms to the right of the equal sign and state how mand uare measured. a. γis the relativistic factor, mis the rest mass measured when the object is at rest in the frame of reference, and uis the velocity of the frame. b. γis the relativistic factor, mis the rest mass measured when the object is at rest in the frame of reference, and uis the velocity relative to an observer. c. γis the
relativistic factor, mis the relativistic mass measured when the object is moving in the frame of reference, and uis the velocity of the frame. 320 Chapter 10 • Special Relativity d. γis the relativistic factor, mis the relativistic mass measured when the object is moving in the frame of reference, and uis the velocity relative to an observer. 13. Describe length contraction and state when it occurs. a. When the speed of an object becomes the speed of light, its length appears to shorten when viewed by a stationary observer. b. When the speed of an object approaches the speed of light, its length appears to shorten when viewed by a stationary observer. c. When the speed of an object becomes the speed of light, its length appears to increase when viewed by a stationary observer. d. When the speed of an object approaches the speed of light, its length appears to increase when viewed by a stationary observer. Access for free at openstax.org. Chapter 10 • Key Terms 321 KEY TERMS binding energy the energy equivalent of the difference between the mass of a nucleus and the masses of its nucleons effects that become significant only when an object is to be moving close enough to the speed of light for significantly greater than 1 ether scientists once believed there was a medium that carried light waves; eventually, experiments proved that ether does not exist relativistic energy the total energy of a moving object or which includes both its rest energy particle mc2 and its kinetic energy frame of reference the point or collection of points relativistic factor, where u is the velocity of a arbitrarily chosen, which motion is measured in relation to general relativity the theory proposed to explain gravity and acceleration inertial reference frame a frame of reference where all objects follow Newton’s first law of motion length contraction the shortening of an object as seen by an observer who is moving relative to the frame of reference of the object mass defect the difference between the mass of a nucleus and the masses of its nucleons postulate a statement that is assumed to be true for the purposes of reasoning in a scientific or mathematic argument proper length the length of an object within its own frame of reference, as opposed to the length observed by an observer moving relative to that frame of reference relativistic having to do with modern relativity, such as the SECTION SUMMARY 10.1 Postulates of Special Relativity • One postulate of special relativity theory is that the laws of physics are the same in all inertial frames of reference.
• The other postulate is that the speed of light in a vacuum is the same in all inertial frames. • Einstein showed that simultaneity, or lack of it, depends on the frame of reference of the observer. KEY EQUATIONS 10.1 Postulates of Special Relativity speed of light constant value for the speed of light moving object and cis the speed of light relativistic momentum p = γmu, where is the relativistic factor, mis rest mass of an object, and u is the velocity relative to an observer relativity the explanation of how objects move relative to one another rest mass the mass of an object that is motionless with respect to its frame of reference simultaneity the property of events that occur at the same time special relativity the theory proposed to explain the consequences of requiring the speed of light and the laws of physics to be the same in all inertial frames time dilation the contraction of time as seen by an observer in a frame of reference that is moving relative to the observer 10.2 Consequences of Special Relativity • Time dilates, length contracts, and momentum increases as an object approaches the speed of light. • Energy and mass are interchangeable, according to the relationship E = mc2. The laws of conservation of mass and energy are combined into the law of conservation of mass-energy. 10.2 Consequences of Special Relativity elapsed time relativistic factor length contraction relativistic momentum 322 Chapter 10 • Chapter Review relativistic energy rest energy CHAPTER REVIEW Concept Items 10.1 Postulates of Special Relativity 1. Why was it once believed that light must travel through a medium and could not propagate across empty space? a. The longitudinal nature of light waves implies this. b. Light shows the phenomenon of diffraction. c. The speed of light is the maximum possible speed. d. All other wave energy needs a medium to travel. 2. Describe the relative motion of Earth and the sun: 1. 2. if Earth is taken as the inertial frame of reference and if the sun is taken as the inertial frame of reference. 1. Earth is at rest and the sun orbits Earth. a. 2. The sun is at rest and Earth orbits the sun. b. c. d. 1. The sun is at rest and Earth orbits the sun. 2. Earth is at rest and the sun orbits Earth. 1. The sun is at rest and Earth orbits the sun. 2. The sun is at rest and Earth orbits the sun.
1. Earth is at rest and the sun orbits Earth. 2. Earth is at rest and the sun orbits Earth. 10.2 Consequences of Special Relativity 3. A particle (a free electron) is speeding around the track Critical Thinking Items 10.1 Postulates of Special Relativity 6. Explain how the two postulates of Einstein’s theory of special relativity, when taken together, could lead to a situation that seems to contradict the mechanics and laws of motion as described by Newton. a. In Newtonian mechanics, velocities are multiplicative but the speed of a moving light source cannot be multiplied to the speed of light because, according to special relativity, the speed of light is the maximum speed possible. In Newtonian mechanics, velocities are additive but the speed of a moving light source cannot be added to the speed of light because the speed of light is the maximum speed possible. b. c. An object that is at rest in one frame of reference may appear to be in motion in another frame of reference, while in Newtonian mechanics such a situation is not possible. Access for free at openstax.org. in a cyclotron, rapidly gaining speed. How will the particle’s momentum change as its speed approaches the speed of light? Explain. a. The particle’s momentum will rapidly decrease. b. The particle’s momentum will rapidly increase. c. The particle’s momentum will remain constant. d. The particle’s momentum will approach zero. 4. An astronaut goes on a long space voyage at near the speed of light. When she returns home, how will her age compare to the age of her twin who stayed on Earth? a. Both of them will be the same age. b. This is a paradox and hence the ages cannot be compared. c. The age of the twin who traveled will be less than the age of her twin. d. The age of the twin who traveled will be greater than the age of her twin. 5. A comet reaches its greatest speed as it travels near the sun. True or false— Relativistic effects make the comet’s tail look longer to an observer on Earth. a. True b. False d. The postulates of Einstein’s theory of special relativity do not contradict any situation that Newtonian mechanics explains. 7. It takes light to travel from the sun to the planet Venus. How far is Venus from the sun? a. b. c
. d. 8. In 2003, Earth and Mars were the closest they had been in 50,000 years. The two planets were aligned so that Earth was between Mars and the sun. At that time it took light from the sun 500 s to reach Earth and 687 s to get to Mars. What was the distance from Mars to Earth? 5.6×107 km a. 5.6×1010 km b. c. 6.2×106 km d. 6.2×1012 km 9. Describe two ways in which light differs from all other forms of wave energy. a. 1. Light travels as a longitudinal wave. 2. Light travels through a medium that fills up the empty space in the universe. b. 1. Light travels as a transverse wave. 2. Light travels through a medium that fills up the empty space in the universe. c. 1. Light travels at the maximum possible speed in the universe. 2. Light travels through a medium that fills up the empty space in the universe. d. 1. Light travels at the maximum possible speed in the universe. 2. Light does not require any material medium to travel. 10. Use the postulates of the special relativity theory to explain why the speed of light emitted from a fastmoving light source cannot exceed 3.00×108 m/s. a. The speed of light is maximum in the frame of reference of the moving object. b. The speed of light is minimum in the frame of reference of the moving object. c. The speed of light is the same in all frames of reference, including in the rest frame of its source. d. Light always travels in a vacuum with a speed less than 3.00×108 m/s, regardless of the speed of the Problems 10.2 Consequences of Special Relativity 13. Deuterium (2 H) is an isotope of hydrogen that has one proton and one neutron in its nucleus. The binding energy of deuterium is 3.56×10-13 J. What is the mass defect of deuterium? 3.20×10-4 kg a. 1.68×10-6 kg b. 1.19×10-21 kg c. 3.96×10-30 kg d. 14. The sun orbits the center of the galaxy at a speed of 2.3×105 m/s. The diameter of the sun is 1.391684×109 m. An observer is in a frame
of reference that is stationary with respect to the center of the galaxy. True or false—The sun is moving fast enough for the observer to notice length contraction of the sun’s diameter. a. True b. False 15. Consider the nuclear fission reaction Chapter 10 • Chapter Review 323 source. 10.2 Consequences of Special Relativity 11. Halley’s Comet comes near Earth every 75 years as it travels around its 22 billion km orbit at a speed of up to 700, 000 m/s. If it were possible to put a clock on the comet and read it each time the comet passed, which part of special relativity theory could be tested? What would be the expected result? Explain. a. It would test time dilation. The clock would appear to be slightly slower. It would test time dilation. The clock would appear to be slightly faster. It would test length contraction. The length of the orbit would appear to be shortened from Earth’s frame of reference. It would test length contraction. The length of the orbit would appear to be shortened from the comet’s frame of reference. b. c. d. 12. The nucleus of the isotope fluorine-18 (18 F) has mass defect of 2.44×10-28 kg. What is the binding energy of 18F? a. 2.2×10-11 J 7.3×10-20 J b. c. 2.2×10-20 J d. 2.4×10-28 J has a rest mass of 1.009u, has a rest mass of. If a neutron has rest mass of 143.923u, and 235.044u, has a rest mass of 88.918u, what is the value of Ein joules? a. b. c. d. J J J J 16. Consider the nuclear fusion reaction. If has a rest mass of has a rest has a rest mass of 3.016u, 2.014u, mass of 4.003u, and a neutron has a rest mass of 1.009u, what is the value of Ein joules? a. b. c. d. J J J J 324 Chapter 10 • Test Prep Performance Task 10.2 Consequences of Special Relativity 17. People are fascinated by the possibility of traveling across the universe to discover intelligent life on other planets. To do this, we would have to travel enormous distances.
Suppose we could somehow travel at up to 90 percent of the speed of light. The closest star is Alpha Centauri, which is 4.37 light years away. (A light year is the distance light travels in one year.) TEST PREP Multiple Choice 10.1 Postulates of Special Relativity 18. What was the purpose of the Michelson–Morley experiment? a. To determine the exact speed of light b. To analyze the electromagnetic spectrum c. To establish that Earth is the true frame of reference a. How long, from the point of view of people on Earth, would it take a space ship to travel to Alpha Centauri and back at 0.9c? b. How much would the astronauts on the spaceship have aged by the time they got back to Earth? c. Discuss the problems related to travel to stars that are 20 or 30 light years away. Assume travel speeds near the speed of light. been in 50,000 years. People looking up saw Mars as a very bright red light on the horizon. If Mars was 2.06×108 km from the sun, how long did the reflected light people saw take to travel from the sun to Earth? a. b. c. d. 14 min and 33 s 12 min and 15 s 11 min and 27 s 3 min and 7 s d. To learn how the ether affected the propagation of 10.2 Consequences of Special Relativity light 19. What is the speed of light in a vacuum to three 23. What does this expression represent: significant figures? a. b. c. d. 20. How far does light travel in? a. b. c. d. a. b. c. d. time dilation relativistic factor relativistic energy length contraction 24. What is the rest energy, E0, of an object with a mass of 1.00 g? 3.00×105 J a. 3.00×1011 J b. c. 9.00×1013 J d. 9.00×1016 J 21. Describe what is meant by the sentence, “Simultaneity is 25. The fuel rods in a nuclear reactor must be replaced from not absolute.” a. Events may appear simultaneous in all frames of reference. b. Events may not appear simultaneous in all frames of reference. c. The speed of light is not the same in all frames of reference. d. The laws of physics may be different in different inertial frames of reference. 22. In
2003, Earth and Mars were aligned so that Earth was between Mars and the sun. Earth and Mars were 5.6×107 km from each other, which was the closest they had time to time because so much of the radioactive material has reacted that they can no longer produce energy. How would the mass of the spent fuel rods compare to their mass when they were new? Explain your answer. a. The mass of the spent fuel rods would decrease. b. The mass of the spent fuel rods would increase. c. The mass of the spent fuel rods would remain the same. d. The mass of the spent fuel rods would become close to zero. Access for free at openstax.org. Chapter 10 • Test Prep 325 Short Answer 10.2 Consequences of Special Relativity 10.1 Postulates of Special Relativity 30. What is the relationship between the binding energy 26. What is the postulate having to do with the speed of light on which the theory of special relativity is based? a. The speed of light remains the same in all inertial frames of reference. b. The speed of light depends on the speed of the source emitting the light. c. The speed of light changes with change in medium through which it travels. d. The speed of light does not change with change in medium through which it travels. 27. What is the postulate having to do with reference frames on which the theory of special relativity is based? a. The frame of reference chosen is arbitrary as long as it is inertial. and the mass defect of an atomic nucleus? a. The binding energy is the energy equivalent of the mass defect, as given by E0 = mc. b. The binding energy is the energy equivalent of the mass defect, as given by E0 = mc2. c. The binding energy is the energy equivalent of the mass defect, as given by d. The binding energy is the energy equivalent of the mass defect, as given by 31. True or false—It is possible to just use the relationships F= maand E= Fdto show that both sides of the equation E0 = mc2 have the same units. a. True b. False b. The frame of reference is chosen to have constant 32. Explain why the special theory of relativity caused the nonzero acceleration. c. The frame of reference is chosen in such a way that the object under observation is at rest. d. The frame of reference is chosen in such a way that the object under observation
is moving with a constant speed. 28. If you look out the window of a moving car at houses going past, you sense that you are moving. What have you chosen as your frame of reference? the car a. the sun b. c. a house 29. Why did Michelson and Morley orient light beams at right angles to each other? a. To observe the particle nature of light b. To observe the effect of the passing ether on the speed of light c. To obtain a diffraction pattern by combination of light d. To obtain a constant path difference for interference of light Extended Response 10.1 Postulates of Special Relativity 34. Explain how Einstein’s conclusion that nothing can travel faster than the speed of light contradicts an older concept about the speed of an object propelled from another, already moving, object. a. The older concept is that speeds are subtractive. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the law of conservation of energy to be modified. a. The law of conservation of energy is not valid in relativistic mechanics. b. The law of conservation of energy has to be modified because of time dilation. c. The law of conservation of energy has to be modified because of length contraction. d. The law of conservation of energy has to be modified because of mass-energy equivalence. 33. The sun loses about 4 × 109 kg of mass every second. Explain in terms of special relativity why this is happening. a. The sun loses mass because of its high temperature. b. The sun loses mass because it is continuously releasing energy. c. The Sun loses mass because the diameter of the sun is contracted. d. The sun loses mass because the speed of the sun is very high and close to the speed of light. speed at which the person was running minus the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves faster than the speed of light emitted from a stationary source. b. The older concept is that speeds are additive. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the speed at which the person was running plus the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves no 326 Chapter 10 • Test Prep faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light.
c. The older concept is that speeds are multiplicative. For example, if a person throws a ball while running, the speed of the ball relative to the ground is the speed at which the person was running multiplied by the speed of the throw. A relativistic example is when light is emitted from car headlights, it moves no faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light. d. The older concept is that speeds are frame independent. For example, if a person throws a ball while running, the speed of the ball relative to the ground has nothing to do with the speed at which the person was running. A relativistic example is when light is emitted from car headlights, it moves no faster than the speed of light emitted from a stationary source. The car's speed does not affect the speed of light. 35. A rowboat is drifting downstream. One person swims 20 m toward the shore and back, and another, leaving at the same time, swims upstream 20 m and back to the boat. The swimmer who swam toward the shore gets back first. Explain how this outcome is similar to the outcome expected in the Michelson–Morley experiment. a. The rowboat represents Earth, the swimmers are beams of light, and the water is acting as the ether. Light going against the current of the ether would get back later because, by then, Earth would have moved on. b. The rowboat represents the beam of light, the swimmers are the ether, and water is acting as Earth. Light going against the current of the ether would get back later because, by then, Earth would have moved on. c. The rowboat represents the ether, the swimmers are ray of light, and the water is acting as the earth. Light going against the current of the ether would get back later because, by then, Earth would have moved on. d. The rowboat represents the Earth, the swimmers are the ether, and the water is acting as the rays of light. Light going against the current of the ether would get back later because, by then, Earth would have moved on. 10.2 Consequences of Special Relativity 36. A helium-4 nucleus is made up of two neutrons and two protons. The binding energy of helium-4 is 4.53×10-12 J. What is the difference in the mass of this helium nucleus and the sum of the masses of
two neutrons and two protons? Which weighs more, the nucleus or its constituents? a. b. c. d. 1.51×10-20 kg; the constituents weigh more 5.03×10-29 kg; the constituents weigh more 1.51×10-29 kg; the nucleus weighs more 5.03×10-29 kg; the nucleus weighs more 37. Use the equation for length contraction to explain the relationship between the length of an object perceived by a stationary observer who sees the object as moving, and the proper length of the object as measured in the frame of reference where it is at rest. a. As the speed vof an object moving with respect to a stationary observer approaches c, the length perceived by the observer approaches zero. For other speeds, the length perceived is always less than the proper length. b. As the speed vof an object moving with respect to a stationary observer approaches c, the length perceived by the observer approaches zero. For other speeds, the length perceived is always greater than the proper length. c. As the speed vof an object moving with respect to a stationary observer approaches c, the length perceived by the observer approaches infinity. For other speeds, the length perceived is always less than the proper length. d. As the speed vof an object moving with respect to a stationary observer approaches c, the length perceived by the observer approaches infinity. For other speeds, the length perceived is always greater than the proper length. Access for free at openstax.org. CHAPTER 11 Thermal Energy, Heat, and Work Figure 11.1 The welder’s gloves and helmet protect the welder from the electric arc, which transfers enough thermal energy to melt the rod, spray sparks, and emit high-energy electromagnetic radiation that can burn the retina of an unprotected eye. The thermal energy can be felt on exposed skin a few meters away, and its light can be seen for kilometers (Kevin S. O’Brien, U.S. Navy) Chapter Outline 11.1 Temperature and Thermal Energy 11.2 Heat, Specific Heat, and Heat Transfer 11.3 Phase Change and Latent Heat Heat is something familiar to all of us. We feel the warmth of the summer sun, the hot vapor rising up out of INTRODUCTION a cup of hot cocoa, and the cooling effect of our sweat. When we feel warmth, it means that heat is transferring energy toour bodies; when we feel cold, that means heat is transferring
energy away fromour bodies. Heat transfer is the movement of thermal energy from one place or material to another, and is caused by temperature differences. For example, much of our weather is caused by Earth evening out the temperature across the planet through wind and violent storms, which are driven by heat transferring energy away from the equator towards the cold poles. In this chapter, we’ll explore the precise meaning of heat, how it relates to temperature as well as to other forms of energy, and its connection to work. 11.1 Temperature and Thermal Energy Section Learning Objectives By the end of this section, you will be able to do the following: • Explain that temperature is a measure of internal kinetic energy • Interconvert temperatures between Celsius, Kelvin, and Fahrenheit scales 328 Chapter 11 • Thermal Energy, Heat, and Work Section Key Terms absolute zero Celsius scale degree Celsius thermal energy degree Fahrenheit Fahrenheit scale heat kelvin (K) Kelvin scale temperature Temperature What is temperature? It’s one of those concepts so ingrained in our everyday lives that, although we know what it means intuitively, it can be hard to define. It is tempting to say that temperature measures heat, but this is not strictly true. Heat is the transfer of energy due to a temperature difference. Temperature is defined in terms of the instrument we use to tell us how hot or cold an object is, based on a mechanism and scale invented by people. Temperature is literally defined as what we measure on a thermometer. Heat is often confused with temperature. For example, we may say that the heat was unbearable, when we actually mean that the temperature was high. This is because we are sensitive to the flow of energy by heat, rather than the temperature. Since heat, like work, transfers energy, it has the SI unit of joule (J). Atoms and molecules are constantly in motion, bouncing off one another in random directions. Recall that kinetic energy is the energy of motion, and that it increases in proportion to velocity squared. Without going into mathematical detail, we can say that thermal energy—the energy associated with heat—is the average kinetic energy of the particles (molecules or atoms) in a substance. Faster moving molecules have greater kinetic energies, and so the substance has greater thermal energy, and thus a higher temperature. The total internal energy of a system is the sum of the kinetic and potential energies of its atoms and molecules. Thermal energy is one of the subcategories of internal energy, as is chemical energy. To measure
temperature, some scale must be used as a standard of measurement. The three most commonly used temperature scales are the Fahrenheit, Celsius, and Kelvin scales. Both the Fahrenheit scale and Celsius scale are relative temperature scales, meaning that they are made around a reference point. For example, the Celsius scale uses the freezing point of water as its reference point; all measurements are either lower than the freezing point of water by a given number of degrees (and have a negative sign), or higher than the freezing point of water by a given number of degrees (and have a positive sign). The boiling point of water is 100 for the Celsius scale, and its unit is the degree Celsius ). On the Fahrenheit scale, the freezing point of water is at 32. The unit of temperature on ). Note that the difference in degrees between the freezing and boiling points is greater this scale is the degree Fahrenheit for the Fahrenheit scale than for the Celsius scale. Therefore, a temperature difference of one degree Celsius is greater than a temperature difference of one degree Fahrenheit. Since 100 Celsius degrees span the same range as 180 Fahrenheit degrees, one degree on the Celsius scale is 1.8 times larger than one degree on the Fahrenheit scale (because, and the boiling point is at 212 ). This relationship can be used to convert between temperatures in Fahrenheit and Celsius (see Figure 11.2). Access for free at openstax.org. 11.1 • Temperature and Thermal Energy 329 Figure 11.2 Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales, rounded to the nearest degree. The relative sizes of the scales are also shown. The Kelvin scale is the temperature scale that is commonly used in science because it is an absolute temperature scale. This means that the theoretically lowest-possible temperature is assigned the value of zero. Zero degrees on the Kelvin scale is known as absolute zero; it is theoretically the point at which there is no molecular motion to produce thermal energy. On the original Kelvin scale first created by Lord Kelvin, all temperatures have positive values, making it useful for scientific work. The official temperature unit on this scale is the kelvin, which is abbreviated as K. The freezing point of water is 273.15 K, and the boiling point of water is 373.15 K. Although absolute zero is possible in theory, it cannot be reached in practice. The lowest temperature ever created and measured K, at Helsinki University of Technology in Finland. In comparison, the coldest during a laboratory experiment was recorded temperature for a place on Earth’s surface was 183 K (
–89 °C ), at Vostok, Antarctica, and the coldest known place (outside the lab) in the universe is the Boomerang Nebula, with a temperature of 1 K. Luckily, most of us humans will never have to experience such extremes. The average normal body temperature is 98.6 ). to 111 ranging from 75 to 44 (24 (37.0 ), but people have been known to survive with body temperatures WATCH PHYSICS Comparing Celsius and Fahrenheit Temperature Scales This video shows how the Fahrenheit and Celsius temperature scales compare to one another. Click to view content (https://www.openstax.org/l/02celfahtemp) GRASP CHECK Even without the number labels on the thermometer, you could tell which side is marked Fahrenheit and which is Celsius by how the degree marks are spaced. Why? a. The separation between two consecutive divisions on the Fahrenheit scale is greater than a similar separation on the Celsius scale, because each degree Fahrenheit is equal to degrees Celsius. b. The separation between two consecutive divisions on the Fahrenheit scale is smaller than the similar separation on the Celsius scale, because each degree Celsius is equal to degrees Fahrenheit. c. The separation between two consecutive divisions on the Fahrenheit scale is greater than a similar separation on the Celsius scale, because each degree Fahrenheit is equal to degrees Celsius. d. The separation between two consecutive divisions on the Fahrenheit scale is smaller than a similar separation on the Celsius scale, because each degree Celsius is equal to degrees Fahrenheit. 330 Chapter 11 • Thermal Energy, Heat, and Work Converting Between Celsius, Kelvin, and Fahrenheit Scales While the Fahrenheit scale is still the most commonly used scale in the United States, the majority of the world uses Celsius, and scientists prefer Kelvin. It’s often necessary to convert between these scales. For instance, if the TV meteorologist gave the local weather report in kelvins, there would likely be some confused viewers! Table 11.1 gives the equations for conversion between the three temperature scales. To Convert From… Use This Equation Celsius to Fahrenheit Fahrenheit to Celsius Celsius to Kelvin Kelvin to Celsius Fahrenheit to Kelvin Kelvin to Fahrenheit Table 11.1 Temperature Conversions WORKED EXAMPLE Room temperatureis generally defined to be 25 (a) What is room temperature in (b) What is it in K? STRATEGY To answer these questions, all we need to do is choose the correct conversion equations and plug in the known values. Solution for (a) 1. Choose the right equation
. To convert from to, use the equation 2. Plug the known value into the equation and solve. Solution for (b) 1. Choose the right equation. To convert from to K, use the equation 2. Plug the known value into the equation and solve. 11.1 11.2 11.3 11.4 Discussion Living in the United States, you are likely to have more of a sense of what the temperature feels like if it’s described as 77 as 25 (or 298 K, for that matter). than Access for free at openstax.org. WORKED EXAMPLE 11.1 • Temperature and Thermal Energy 331 Converting Between Temperature Scales: The Reaumur Scale The Reaumur scale is a temperature scale that was used widely in Europe in the 18th and 19th centuries. On the Reaumur If “room temperature” is 25 temperature scale, the freezing point of water is 0 the Celsius scale, what is it on the Reaumur scale? STRATEGY To answer this question, we must compare the Reaumur scale to the Celsius scale. The difference between the freezing point and boiling point of water on the Reaumur scale is 80 scales start at 0 for freezing, so we can create a simple formula to convert between temperatures on the two scales. and the boiling temperature is 80. On the Celsius scale, it is 100. Therefore, 100. Both on Solution 1. Derive a formula to convert from one scale to the other. 2. Plug the known value into the equation and solve. 11.5 11.6 Discussion As this example shows, relative temperature scales are somewhat arbitrary. If you wanted, you could create your own temperature scale! Practice Problems 1. What is 12.0 °C in kelvins? a. 112.0 K b. 273.2 K c. 12.0 K d. 285.2 K 2. What is 32.0 °C in degrees Fahrenheit? a. 57.6 °F b. 25.6 °F c. 305.2 °F d. 89.6 °F TIPS FOR SUCCESS Sometimes it is not so easy to guess the temperature of the air accurately. Why is this? Factors such as humidity and wind speed affect how hot or cold we feel. Wind removes thermal energy from our bodies at a faster rate than usual, making us feel colder than we otherwise would; on a cold day, you may have heard the TV weather person refer to the
wind chill. On humid summer days, people tend to feel hotter because sweat doesn’t evaporate from the skin as efficiently as it does on dry days, when the evaporation of sweat cools us off. Check Your Understanding 3. What is thermal energy? a. The thermal energy is the average potential energy of the particles in a system. b. The thermal energy is the total sum of the potential energies of the particles in a system. c. The thermal energy is the average kinetic energy of the particles due to the interaction among the particles in a system. d. The thermal energy is the average kinetic energy of the particles in a system. 4. What is used to measure temperature? 332 Chapter 11 • Thermal Energy, Heat, and Work a. a galvanometer b. a manometer c. a thermometer d. a voltmeter 11.2 Heat, Specific Heat, and Heat Transfer Section Learning Objectives By the end of this section, you will be able to do the following: • Explain heat, heat capacity, and specific heat • Distinguish between conduction, convection, and radiation • Solve problems involving specific heat and heat transfer Section Key Terms conduction convection heat capacity radiation specific heat Heat Transfer, Specific Heat, and Heat Capacity We learned in the previous section that temperature is proportional to the average kinetic energy of atoms and molecules in a substance, and that the average internal kinetic energy of a substance is higher when the substance’s temperature is higher. If two objects at different temperatures are brought in contact with each other, energy is transferred from the hotter object (that is, the object with the greater temperature) to the colder (lower temperature) object, until both objects are at the same temperature. There is no net heat transfer once the temperatures are equal because the amount of heat transferred from one object to the other is the same as the amount of heat returned. One of the major effects of heat transfer is temperature change: Heating increases the temperature while cooling decreases it. Experiments show that the heat transferred to or from a substance depends on three factors—the change in the substance’s temperature, the mass of the substance, and certain physical properties related to the phase of the substance. The equation for heat transfer Qis 11.7 where mis the mass of the substance and ΔTis the change in its temperature, in units of Celsius or Kelvin. The symbol cstands for specific heat, and depends on the material and phase. The specific heat is the amount of
heat necessary to change the temperature of 1.00 kg of mass by 1.00 ºC. The specific heat cis a property of the substance; its SI unit is J/(kg K) or J/(kg The temperature change ( closely related to the concept of heat capacity. Heat capacity is the amount of heat necessary to change the temperature of a, where mis mass and cis specific heat. Note that heat substance by 1.00 capacity is the same as specific heat, but without any dependence on mass. Consequently, two objects made up of the same material but with different masses will have different heat capacities. This is because the heat capacity is a property of an object, but specific heat is a property of anyobject made of the same material. ) is the same in units of kelvins and degrees Celsius (but not degrees Fahrenheit). Specific heat is. In equation form, heat capacity Cis ). Values of specific heat must be looked up in tables, because there is no simple way to calculate them. Table 11.2 gives the values of specific heat for a few substances as a handy reference. We see from this table that the specific heat of water is five times that of glass, which means that it takes five times as much heat to raise the temperature of 1 kg of water than to raise the temperature of 1 kg of glass by the same number of degrees. Substances Specific Heat (c) Solids Aluminum J/(kg ) 900 Table 11.2 Specific Heats of Various Substances. Access for free at openstax.org. 11.2 • Heat, Specific Heat, and Heat Transfer 333 Substances Specific Heat (c) Asbestos Concrete, granite (average) Copper Glass Gold Human body (average) Ice (average) Iron, steel Lead Silver Wood Liquids Benzene Ethanol Glycerin Mercury Water Gases (at 1 atm constant pressure) Air (dry) Ammonia Carbon dioxide Nitrogen Oxygen Steam 800 840 387 840 129 3500 2090 452 128 235 1700 1740 2450 2410 139 4186 1015 2190 833 1040 913 2020 Table 11.2 Specific Heats of Various Substances. 334 Chapter 11 • Thermal Energy, Heat, and Work Snap Lab Temperature Change of Land and Water What heats faster, land or water? You will answer this question by taking measurements to study differences in specific heat capacity. • Open flame—Tie back all loose hair and clothing before igniting an open flame. Follow all of your teacher's instructions
on how to ignite the flame. Never leave an open flame unattended. Know the location of fire safety equipment in the laboratory. • Sand or soil • Water • Oven or heat lamp • Two small jars • Two thermometers Instructions Procedure 1. Place equal masses of dry sand (or soil) and water at the same temperature into two small jars. (The average density of soil or sand is about 1.6 times that of water, so you can get equal masses by using 50 percent more water by volume.) 2. Heat both substances (using an oven or a heat lamp) for the same amount of time. 3. Record the final temperatures of the two masses. 4. Now bring both jars to the same temperature by heating for a longer period of time. 5. Remove the jars from the heat source and measure their temperature every 5 minutes for about 30 minutes. GRASP CHECK Did it take longer to heat the water or the sand/soil to the same temperature? Which sample took longer to cool? What does this experiment tell us about how the specific heat of water compared to the specific heat of land? a. The sand/soil will take longer to heat as well as to cool. This tells us that the specific heat of land is greater than that of water. b. The sand/soil will take longer to heat as well as to cool. This tells us that the specific heat of water is greater than that of land. c. The water will take longer to heat as well as to cool. This tells us that the specific heat of land is greater than that of water. d. The water will take longer to heat as well as to cool. This tells us that the specific heat of water is greater than that of land. Conduction, Convection, and Radiation Whenever there is a temperature difference, heat transfer occurs. Heat transfer may happen rapidly, such as through a cooking pan, or slowly, such as through the walls of an insulated cooler. There are three different heat transfer methods: conduction, convection, and radiation. At times, all three may happen simultaneously. See Figure 11.3. Access for free at openstax.org. 11.2 • Heat, Specific Heat, and Heat Transfer 335 Figure 11.3 In a fireplace, heat transfer occurs by all three methods: conduction, convection, and radiation. Radiation is responsible for most of the heat transferred into the room. Heat transfer also occurs through conduction into the room, but at a
much slower rate. Heat transfer by convection also occurs through cold air entering the room around windows and hot air leaving the room by rising up the chimney. Conduction is heat transfer through direct physical contact. Heat transferred between the electric burner of a stove and the bottom of a pan is transferred by conduction. Sometimes, we try to control the conduction of heat to make ourselves more comfortable. Since the rate of heat transfer is different for different materials, we choose fabrics, such as a thick wool sweater, that slow down the transfer of heat away from our bodies in winter. As you walk barefoot across the living room carpet, your feet feel relatively comfortable…until you step onto the kitchen’s tile floor. Since the carpet and tile floor are both at the same temperature, why does one feel colder than the other? This is explained by different rates of heat transfer: The tile material removes heat from your skin at a greater rate than the carpeting, which makes it feelcolder. Some materials simply conduct thermal energy faster than others. In general, metals (like copper, aluminum, gold, and silver) are good heat conductors, whereas materials like wood, plastic, and rubber are poor heat conductors. Figure 11.4 shows particles (either atoms or molecules) in two bodies at different temperatures. The (average) kinetic energy of a particle in the hot body is higher than in the colder body. If two particles collide, energy transfers from the particle with greater kinetic energy to the particle with less kinetic energy. When two bodies are in contact, many particle collisions occur, resulting in a net flux of heat from the higher-temperature body to the lower-temperature body. The heat flux depends on the temperature difference water.. Therefore, you will get a more severe burn from boiling water than from hot tap Figure 11.4 The particles in two bodies at different temperatures have different average kinetic energies. Collisions occurring at the contact surface tend to transfer energy from high-temperature regions to low-temperature regions. In this illustration, a particle in the lower- temperature region (right side) has low kinetic energy before collision, but its kinetic energy increases after colliding with the contact 336 Chapter 11 • Thermal Energy, Heat, and Work surface. In contrast, a particle in the higher-temperature region (left side) has more kinetic energy before collision, but its energy decreases after colliding with the contact surface. Convection is heat transfer by the movement of a fluid. This
type of heat transfer happens, for example, in a pot boiling on the stove, or in thunderstorms, where hot air rises up to the base of the clouds. TIPS FOR SUCCESS In everyday language, the term fluidis usually taken to mean liquid. For example, when you are sick and the doctor tells you to “push fluids,” that only means to drink more beverages—not to breath more air. However, in physics, fluid means a liquid or a gas. Fluids move differently than solid material, and even have their own branch of physics, known as fluid dynamics, that studies how they move. As the temperature of fluids increase, they expand and become less dense. For example, Figure 11.4 could represent the wall of a balloon with different temperature gases inside the balloon than outside in the environment. The hotter and thus faster moving gas particles inside the balloon strike the surface with more force than the cooler air outside, causing the balloon to expand. This decrease in density relative to its environment creates buoyancy (the tendency to rise). Convection is driven by buoyancy—hot air rises because it is less dense than the surrounding air. Sometimes, we control the temperature of our homes or ourselves by controlling air movement. Sealing leaks around doors with weather stripping keeps out the cold wind in winter. The house in Figure 11.5 and the pot of water on the stove in Figure 11.6 are both examples of convection and buoyancy by human design. Ocean currents and large-scale atmospheric circulation transfer energy from one part of the globe to another, and are examples of natural convection. Figure 11.5 Air heated by the so-called gravity furnace expands and rises, forming a convective loop that transfers energy to other parts of the room. As the air is cooled at the ceiling and outside walls, it contracts, eventually becoming denser than room air and sinking to the floor. A properly designed heating system like this one, which uses natural convection, can be quite efficient in uniformly heating a home. Figure 11.6 Convection plays an important role in heat transfer inside this pot of water. Once conducted to the inside fluid, heat transfer to other parts of the pot is mostly by convection. The hotter water expands, decreases in density, and rises to transfer heat to other regions of the water, while colder water sinks to the bottom. This process repeats as long as there is water in the pot. Radiation is a form of heat transfer that occurs when electromagnetic radiation is
emitted or absorbed. Electromagnetic Access for free at openstax.org. 11.2 • Heat, Specific Heat, and Heat Transfer 337 radiation includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays, all of which have different wavelengths and amounts of energy (shorter wavelengths have higher frequency and more energy). You can feel the heat transfer from a fire and from the sun. Similarly, you can sometimes tell that the oven is hot without touching its door or looking inside—it may just warm you as you walk by. Another example is thermal radiation from the human body; people are constantly emitting infrared radiation, which is not visible to the human eye, but is felt as heat. Radiation is the only method of heat transfer where no medium is required, meaning that the heat doesn’t need to come into direct contact with or be transported by any matter. The space between Earth and the sun is largely empty, without any possibility of heat transfer by convection or conduction. Instead, heat is transferred by radiation, and Earth is warmed as it absorbs electromagnetic radiation emitted by the sun. Figure 11.7 Most of the heat transfer from this fire to the observers is through infrared radiation. The visible light transfers relatively little thermal energy. Since skin is very sensitive to infrared radiation, you can sense the presence of a fire without looking at it directly. (Daniel X. O’Neil) All objects absorb and emit electromagnetic radiation (see Figure 11.7). The rate of heat transfer by radiation depends mainly on the color of the object. Black is the most effective absorber and radiator, and white is the least effective. People living in hot climates generally avoid wearing black clothing, for instance. Similarly, black asphalt in a parking lot will be hotter than adjacent patches of grass on a summer day, because black absorbs better than green. The reverse is also true—black radiates better than green. On a clear summer night, the black asphalt will be colder than the green patch of grass, because black radiates energy faster than green. In contrast, white is a poor absorber and also a poor radiator. A white object reflects nearly all radiation, like a mirror. Virtual Physics Energy Forms and Changes Click to view content (http://www.openstax.org/l/28energyForms) In this animation, you will explore heat transfer with different materials. Experiment with heating and cooling the iron, brick, and water. This is done by dragging and
dropping the object onto the pedestal and then holding the lever either to Heat or Cool. Drag a thermometer beside each object to measure its temperature—you can watch how quickly it heats or cools in real time. Now let’s try transferring heat between objects. Heat the brick and then place it in the cool water. Now heat the brick again, but then place it on top of the iron. What do you notice? Selecting the fast forward option lets you speed up the heat transfers, to save time. GRASP CHECK Compare how quickly the different materials are heated or cooled. Based on these results, what material do you think has the greatest specific heat? Why? Which has the smallest specific heat? Can you think of a real-world situation where you would want to use an object with large specific heat? a. Water will take the longest, and iron will take the shortest time to heat, as well as to cool. Objects with greater specific heat would be desirable for insulation. For instance, woolen clothes with large specific heat would prevent heat loss from the body. 338 Chapter 11 • Thermal Energy, Heat, and Work b. Water will take the shortest, and iron will take the longest time to heat, as well as to cool. Objects with greater specific heat would be desirable for insulation. For instance, woolen clothes with large specific heat would prevent heat loss from the body. c. Brick will take shortest and iron will take longest time to heat up as well as to cool down. Objects with greater specific heat would be desirable for insulation. For instance, woolen clothes with large specific heat would prevent heat loss from the body. d. Water will take shortest and brick will take longest time to heat up as well as to cool down. Objects with greater specific heat would be desirable for insulation. For instance, woolen clothes with large specific heat would prevent heat loss from the body. Solving Heat Transfer Problems WORKED EXAMPLE Calculating the Required Heat: Heating Water in an Aluminum Pan A 0.500 kg aluminum pan on a stove is used to heat 0.250 L of water from 20.0 What percentage of the heat is used to raise the temperature of (b) the pan and (c) the water? STRATEGY The pan and the water are always at the same temperature. When you put the pan on the stove, the temperature of the water and the pan is increased by the same amount. We use the equation for heat transfer for the given temperature change and
masses of water and aluminum. The specific heat values for water and aluminum are given in the previous table.. (a) How much heat is required? to 80.0 Solution to (a) Because the water is in thermal contact with the aluminum, the pan and the water are at the same temperature. 1. Calculate the temperature difference. 11.8 2. Calculate the mass of water using the relationship between density, mass, and volume. Density is mass per unit volume, or. Rearranging this equation, solve for the mass of water. 3. Calculate the heat transferred to the water. Use the specific heat of water in the previous table. 4. Calculate the heat transferred to the aluminum. Use the specific heat for aluminum in the previous table. 5. Find the total transferred heat. Solution to (b) The percentage of heat going into heating the pan is Solution to (c) The percentage of heat going into heating the water is 11.9 11.10 11.11 11.12 11.13 11.14 Discussion In this example, most of the total heat transferred is used to heat the water, even though the pan has twice as much mass. This is Access for free at openstax.org. 11.2 • Heat, Specific Heat, and Heat Transfer 339 because the specific heat of water is over four times greater than the specific heat of aluminum. Therefore, it takes a bit more than twice as much heat to achieve the given temperature change for the water than for the aluminum pan. Water can absorb a tremendous amount of energy with very little resulting temperature change. This property of water allows for life on Earth because it stabilizes temperatures. Other planets are less habitable because wild temperature swings make for a harsh environment. You may have noticed that climates closer to large bodies of water, such as oceans, are milder than climates landlocked in the middle of a large continent. This is due to the climate-moderating effect of water’s large heat capacity—water stores large amounts of heat during hot weather and releases heat gradually when it’s cold outside. WORKED EXAMPLE Calculating Temperature Increase: Truck Brakes Overheat on Downhill Runs When a truck headed downhill brakes, the brakes must do work to convert the gravitational potential energy of the truck to internal energy of the brakes. This conversion prevents the gravitational potential energy from being converted into kinetic energy of the truck, and keeps the truck from speeding up and losing control. The increased internal energy of
the brakes raises their temperature. When the hill is especially steep, the temperature increase may happen too quickly and cause the brakes to overheat. Calculate the temperature increase of 100 kg of brake material with an average specific heat of 800 J/kg truck descending 75.0 m (in vertical displacement) at a constant speed. from a 10,000 kg STRATEGY We first calculate the gravitational potential energy (Mgh) of the truck, and then find the temperature increase produced in the brakes. Solution 1. Calculate the change in gravitational potential energy as the truck goes downhill. 2. Calculate the temperature change from the heat transferred by rearranging the equation to solve for 11.15 11.16 where mis the mass of the brake material (not the entire truck). Insert the values Q= 7.35×106 J (since the heat transfer is equal to the change in gravitational potential energy), m 100 kg, and c 800 J/kg to find 11.17 Discussion This temperature is close to the boiling point of water. If the truck had been traveling for some time, then just before the descent, the brake temperature would likely be higher than the ambient temperature. The temperature increase in the descent would likely raise the temperature of the brake material above the boiling point of water, which would be hard on the brakes. This is why truck drivers sometimes use a different technique for called “engine braking” to avoid burning their brakes during steep descents. Engine braking is using the slowing forces of an engine in low gear rather than brakes to slow down. 340 Chapter 11 • Thermal Energy, Heat, and Work Practice Problems 5. How much heat does it take to raise the temperature of 10.0 kg of water by 1.0 °C? a. 84 J b. 42 J c. 84 kJ d. 42 kJ 6. Calculate the change in temperature of 1.0 kg of water that is initially at room temperature if 3.0 kJ of heat is added. 358 °C a. 716 °C b. c. 0.36 °C d. 0.72 °C Check Your Understanding 7. What causes heat transfer? a. The mass difference between two objects causes heat transfer. b. The density difference between two objects causes heat transfer. c. The temperature difference between two systems causes heat transfer. d. The pressure difference between two objects causes heat transfer. 8. When two bodies of different temperatures are in contact, what is the overall direction of heat transfer? a. The
overall direction of heat transfer is from the higher-temperature object to the lower-temperature object. b. The overall direction of heat transfer is from the lower-temperature object to the higher-temperature object. c. The direction of heat transfer is first from the lower-temperature object to the higher-temperature object, then back again to the lower-temperature object, and so-forth, until the objects are in thermal equilibrium. d. The direction of heat transfer is first from the higher-temperature object to the lower-temperature object, then back again to the higher-temperature object, and so-forth, until the objects are in thermal equilibrium. 9. What are the different methods of heat transfer? conduction, radiation, and reflection conduction, reflection, and convection convection, radiation, and reflection conduction, radiation, and convection a. b. c. d. 10. True or false—Conduction and convection cannot happen simultaneously a. True b. False 11.3 Phase Change and Latent Heat Section Learning Objectives By the end of this section, you will be able to do the following: • Explain changes in heat during changes of state, and describe latent heats of fusion and vaporization • Solve problems involving thermal energy changes when heating and cooling substances with phase changes Section Key Terms condensation freezing latent heat sublimation latent heat of fusion latent heat of vaporization melting vaporization phase change phase diagram plasma Access for free at openstax.org. 11.3 • Phase Change and Latent Heat 341 Phase Changes So far, we have learned that adding thermal energy by heat increases the temperature of a substance. But surprisingly, there are situations where adding energy does not change the temperature of a substance at all! Instead, the additional thermal energy acts to loosen bonds between molecules or atoms and causes a phase change. Because this energy enters or leaves a system during a phase change without causing a temperature change in the system, it is known as latent heat (latent means hidden). The three phases of matter that you frequently encounter are solid, liquid and gas (see Figure 11.8). Solid has the least energetic state; atoms in solids are in close contact, with forces between them that allow the particles to vibrate but not change position with neighboring particles. (These forces can be thought of as springs that can be stretched or compressed, but not easily broken.) Liquid has a more energetic state, in which particles can slide smoothly past one another
and change neighbors, although they are still held together by their mutual attraction. Gas has a more energetic state than liquid, in which particles are broken free of their bonds. Particles in gases are separated by distances that are large compared with the size of the particles. The most energetic state of all is plasma. Although you may not have heard much about plasma, it is actually the most common state of matter in the universe—stars are made up of plasma, as is lightning. The plasma state is reached by heating a gas to the point where particles are pulled apart, separating the electrons from the rest of the particle. This produces an ionized gas that is a combination of the negatively charged free electrons and positively charged ions, known as plasma. Figure 11.8 (a) Particles in a solid always have the same neighbors, held close by forces represented here by springs. These particles are essentially in contact with one another. A rock is an example of a solid. This rock retains its shape because of the forces holding its atoms or molecules together. (b) Particles in a liquid are also in close contact but can slide over one another. Forces between them strongly resist attempts to push them closer together and also hold them in close contact. Water is an example of a liquid. Water can flow, but it also remains in an open container because of the forces between its molecules. (c) Particles in a gas are separated by distances that are considerably larger than the size of the particles themselves, and they move about freely. A gas must be held in a closed container to prevent it from moving out into its surroundings. (d) The atmosphere is ionized in the extreme heat of a lightning strike. During a phase change, matter changes from one phase to another, either through the addition of energy by heat and the transition to a more energetic state, or from the removal of energy by heat and the transition to a less energetic state. Phase changes to a more energetic state include the following: • Melting—Solid to liquid • Vaporization—Liquid to gas (included boiling and evaporation) • Sublimation—Solid to gas Phase changes to a less energetic state are as follows: • Condensation—Gas to liquid • Freezing—Liquid to solid Energy is required to melt a solid because the bonds between the particles in the solid must be broken. Since the energy involved in a phase changes is used to break bonds, there is no increase in the kinetic energies of the particles, and therefore no rise in temperature.
Similarly, energy is needed to vaporize a liquid to overcome the attractive forces between particles in the liquid. There is no temperature change until a phase change is completed. The temperature of a cup of soda and ice that is initially at 0 stays at 0 until all of the ice has melted. In the reverse of these processes—freezing and condensation—energy is released 342 Chapter 11 • Thermal Energy, Heat, and Work from the latent heat (see Figure 11.9). Figure 11.9 (a) Energy is required to partially overcome the attractive forces between particles in a solid to form a liquid. That same energy must be removed for freezing to take place. (b) Particles are separated by large distances when changing from liquid to vapor, requiring significant energy to overcome molecular attraction. The same energy must be removed for condensation to take place. There is no temperature change until a phase change is completed. (c) Enough energy is added that the liquid state is skipped over completely as a substance undergoes sublimation. The heat, Q, required to change the phase of a sample of mass mis (for melting/freezing), (for vaporization/condensation), is the latent heat of fusion, and where needed to cause a phase change between solid and liquid. The latent heat of vaporization is the amount of heat needed to cause a is the latent heat of vaporization. The latent heat of fusion is the amount of heat Access for free at openstax.org. 11.3 • Phase Change and Latent Heat 343 phase change between liquid and gas. strength of intermolecular forces, and both have standard units of J/kg. See Table 11.3 for values of substances. are coefficients that vary from substance to substance, depending on the of different and and Substance Melting Point ( ) Lf (kJ/kg) Boiling Point ( ) Lv (kJ/kg) Helium ‒269.7 Hydrogen ‒259.3 Nitrogen ‒210.0 Oxygen ‒218.8 Ethanol ‒114 Ammonia ‒78 Mercury ‒38.9 Water 0.00 Sulfur Lead 119 327 Antimony 631 Aluminum 660 Silver Gold Copper 961 1063 1083 Uranium 1133 Tungsten 3410 5.23 58.6 25.5 13.8 104 332 11.8 334 38.1 24.5 165 380 88.3 64.5 134 84 184 ‒268.9 �
�252.9 ‒195.8 ‒183.0 78.3 ‒33.4 357 100.0 444.6 1750 1440 2520 2193 2660 2595 3900 5900 20.9 452 201 213 854 1370 272 2256 326 871 561 11400 2336 1578 5069 1900 4810 Table 11.3 Latent Heats of Fusion and Vaporization, along with Melting and Boiling Points Let’s consider the example of adding heat to ice to examine its transitions through all three phases—solid to liquid to gas. A phase diagram indicating the temperature changes of water as energy is added is shown in Figure 11.10. The ice starts out at −20, and its temperature rises linearly, absorbing heat at a constant rate until it reaches 0 Once at this temperature, the ice gradually melts, absorbing 334 kJ/kg. The temperature remains constant at 0 melted, the temperature of the liquid water rises, absorbing heat at a new constant rate. At 100 the temperature again remains constant while the water absorbs 2256 kJ/kg during this phase change. When all the liquid has become steam, the temperature rises again at a constant rate. during this phase change. Once all the ice has, the water begins to boil and 344 Chapter 11 • Thermal Energy, Heat, and Work Figure 11.10 A graph of temperature versus added energy. The system is constructed so that no vapor forms while ice warms to become liquid water, and so when vaporization occurs, the vapor remains in the system. The long stretches of constant temperature values at 0 and 100 reflect the large latent heats of melting and vaporization, respectively. We have seen that vaporization requires heat transfer to a substance from its surroundings. Condensation is the reverse process, where heat in transferred away froma substance toits surroundings. This release of latent heat increases the temperature of the surroundings. Energy must be removed from the condensing particles to make a vapor condense. This is why condensation occurs on cold surfaces: the heat transfers energy away from the warm vapor to the cold surface. The energy is exactly the same as that required to cause the phase change in the other direction, from liquid to vapor, and so it can be calculated from. Latent heat is also released into the environment when a liquid freezes, and can be calculated from. FUN IN PHYSICS Making Ice Cream Figure 11.11 With the proper ingredients, some ice and a couple of plastic bags, you
could make your own ice cream in five minutes. (ElinorD, Wikimedia Commons) Ice cream is certainly easy enough to buy at the supermarket, but for the hardcore ice cream enthusiast, that may not be satisfying enough. Going through the process of making your own ice cream lets you invent your own flavors and marvel at the physics firsthand (Figure 11.11). The first step to making homemade ice cream is to mix heavy cream, whole milk, sugar, and your flavor of choice; it could be as Access for free at openstax.org. 11.3 • Phase Change and Latent Heat 345 simple as cocoa powder or vanilla extract, or as fancy as pomegranates or pistachios. The next step is to pour the mixture into a container that is deep enough that you will be able to churn the mixture without it spilling over, and that is also freezer-safe. After placing it in the freezer, the ice cream has to be stirred vigorously every 45 minutes for four to five hours. This slows the freezing process and prevents the ice cream from turning into a solid block of ice. Most people prefer a soft creamy texture instead of one giant popsicle. As it freezes, the cream undergoes a phase change from liquid to solid. By now, we’re experienced enough to know that this means that the cream must experience a loss of heat. Where does that heat go? Due to the temperature difference between the freezer and the ice cream mixture, heat transfers thermal energy from the ice cream to the air in the freezer. Once the temperature in the freezer rises enough, the freezer is cooled by pumping excess heat outside into the kitchen. A faster way to make ice cream is to chill it by placing the mixture in a plastic bag, surrounded by another plastic bag half full of ice. (You can also add a teaspoon of salt to the outer bag to lower the temperature of the ice/salt mixture.) Shaking the bag for five minutes churns the ice cream while cooling it evenly. In this case, the heat transfers energy out of the ice cream mixture and into the ice during the phase change. This video (http://www.openstax.org/l/28icecream) gives a demonstration of how to make home-made ice cream using ice and plastic bags. GRASP CHECK Why does the ice bag method work so much faster than the freezer method for making ice cream? a. Ice has a smaller specific heat than the surrounding air in a freezer. Hence
, it absorbs more energy from the ice-cream mixture. Ice has a smaller specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture. Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs more energy from the ice-cream mixture. Ice has a greater specific heat than the surrounding air in a freezer. Hence, it absorbs less energy from the ice-cream mixture. b. c. d. Solving Thermal Energy Problems with Phase Changes WORKED EXAMPLE Calculating Heat Required for a Phase Change Calculate a) how much energy is needed to melt 1.000 kg of ice at 0 vaporize 1.000 kg of water at 100 STRATEGY FOR (A) Using the equation for the heat required for melting, and the value of the latent heat of fusion of water from the previous table, we can solve for part (a). (freezing point), and b) how much energy is required to (boiling point). Solution to (a) The energy to melt 1.000 kg of ice is STRATEGY FOR (B) To solve part (b), we use the equation for heat required for vaporization, along with the latent heat of vaporization of water from the previous table. 11.18 Solution to (b) The energy to vaporize 1.000 kg of liquid water is 11.19 346 Chapter 11 • Thermal Energy, Heat, and Work Discussion The amount of energy need to melt a kilogram of ice (334 kJ) is the same amount of energy needed to raise the temperature of 1.000 kg of liquid water from 0 energy associated with temperature changes. It also demonstrates that the amount of energy needed for vaporization is even greater.. This example shows that the energy for a phase change is enormous compared to to 79.8 WORKED EXAMPLE and with a mass of Calculating Final Temperature from Phase Change: Cooling Soda with Ice Cubes Ice cubes are used to chill a soda at 20 cubes is 0.018 kg. Assume that the soda is kept in a foam container so that heat loss can be ignored, and that the soda has the same specific heat as water. Find the final temperature when all of the ice has melted. STRATEGY The ice cubes are at the melting temperature of 0 occurs in two steps: first, the phase change occurs and solid (ice) transforms into liquid water at the melting temperature; then,, so more heat is transferred from
the soda to this water until the temperature of this water rises. Melting yields water at 0 they are the same temperature. Since the amount of heat leaving the soda is the same as the amount of heat transferred to the ice.. Heat is transferred from the soda to the ice for melting. Melting of ice and the total mass of the ice. The ice is at 0 11.20 The heat transferred to the ice goes partly toward the phase change (melting), and partly toward raising the temperature after melting. Recall from the last section that the relationship between heat and temperature change is temperature change is. The total heat transferred to the ice is therefore. For the ice, the Since the soda doesn’t change phase, but only temperature, the heat given off by the soda is Since, 11.21 11.22 11.23 Bringing all terms involving to the left-hand-side of the equation, and all other terms to the right-hand-side, we can solve for. Substituting the known quantities 11.24 11.25 Discussion This example shows the enormous energies involved during a phase change. The mass of the ice is about 7 percent the mass of the soda, yet it causes a noticeable change in the soda’s temperature. TIPS FOR SUCCESS If the ice were not already at the freezing point, we would also have to factor in how much energy would go into raising its temperature up to 0 often below 0, before the phase change occurs. This would be a realistic scenario, because the temperature of ice is. Access for free at openstax.org. Practice Problems 11. How much energy is needed to melt 2.00 kg of ice at 0 °C? 11.3 • Phase Change and Latent Heat 347 334 kJ a. 336 kJ b. c. 167 kJ d. 668 kJ 12. If a. b. c. d. of energy is just enough to melt of a substance, what is the substance’s latent heat of fusion? Check Your Understanding 13. What is latent heat? a. b. c. d. It is the heat that must transfer energy to or from a system in order to cause a mass change with a slight change in the temperature of the system. It is the heat that must transfer energy to or from a system in order to cause a mass change without a temperature change in the system. It is the heat that must transfer energy to or from a system in order to cause a phase change
with a slight change in the temperature of the system. It is the heat that must transfer energy to or from a system in order to cause a phase change without a temperature change in the system. 14. In which phases of matter are molecules capable of changing their positions? a. gas, liquid, solid liquid, plasma, solid b. c. liquid, gas, plasma d. plasma, gas, solid 348 Chapter 11 • Key Terms KEY TERMS absolute zero lowest possible temperature; the temperature at which all molecular motion ceases Kelvin scale temperature scale in which 0 K is the lowest possible temperature, representing absolute zero Celsius scale temperature scale in which the freezing point latent heat heat related to the phase change of a substance of water is 0 at 1 atm of pressure and the boiling point of water is 100 condensation phase change from gas to liquid conduction heat transfer through stationary matter by physical contact convection heat transfer by the movement of fluid degree Celsius unit on the Celsius temperature scale degree Fahrenheit unit on the Fahrenheit temperature scale Fahrenheit scale temperature scale in which the freezing and the boiling point of water is point of water is 32 212 freezing phase change from liquid to solid heat transfer of thermal (or internal) energy due to a temperature difference heat capacity amount of heat necessary to change the rather than a change of temperature latent heat of fusion amount of heat needed to cause a phase change between solid and liquid latent heat of vaporization amount of heat needed to cause a phase change between liquid and gas melting phase change from solid to liquid phase change transition between solid, liquid, or gas states of a substance plasma ionized gas that is a combination of the negatively charged free electrons and positively charged ions radiation energy transferred by electromagnetic waves specific heat amount of heat necessary to change the temperature of 1.00 kg of a substance by 1.00 sublimation phase change from solid to gas temperature quantity measured by a thermometer thermal energy average random kinetic energy of a temperature of a substance by 1.00 molecule or an atom Kelvin unit on the Kelvin temperature scale; note that it is vaporization phase change from liquid to gas never referred to in terms of “degrees” Kelvin SECTION SUMMARY 11.1 Temperature and Thermal Energy • Temperature is the quantity measured by a thermometer. • Temperature is related to the average kinetic energy of atoms and molecules in a system. • Absolute zero is the temperature at which there is no molecular motion. • There are three main temperature scales: Celsius, Fahrenheit, and Kelvin. • Temperatures on one scale can be converted into temperatures on
another scale. 11.2 Heat, Specific Heat, and Heat Transfer • Heat is thermal (internal) energy transferred due to a temperature difference. • The transfer of heat Qthat leads to a change temperature of a body with mass m is where cis the specific heat of the material. • Heat is transferred by three different methods: in the, conduction, convection, and radiation. • Heat conduction is the transfer of heat between two objects in direct contact with each other. • Convection is heat transfer by the movement of mass. • Radiation is heat transfer by electromagnetic waves. 11.3 Phase Change and Latent Heat • Most substances have four distinct phases: solid, liquid, gas, and plasma. • Gas is the most energetic state and solid is the least. • During a phase change, a substance undergoes transition to a higher energy state when heat is added, or to a lower energy state when heat is removed. • Heat is added to a substance during melting and vaporization. • Latent heat is released by a substance during condensation and freezing. • Phase changes occur at fixed temperatures called boiling and freezing (or melting) points for a given substance. Access for free at openstax.org. KEY EQUATIONS 11.1 Temperature and Thermal Energy 11.2 Heat, Specific Heat, and Heat Transfer Chapter 11 • Key Equations 349 Celsius to Fahrenheit conversion Fahrenheit to Celsius conversion Celsius to Kelvin conversion Kelvin to Celsius conversion Fahrenheit to Kelvin conversion Kelvin to Fahrenheit conversion heat transfer density 11.3 Phase Change and Latent Heat heat transfer for melting/freezing phase change heat transfer for vaporization/ condensation phase change CHAPTER REVIEW Concept Items 11.1 Temperature and Thermal Energy 1. A glass of water has a temperature of 31 degrees Celsius. solid liquid What state of matter is it in? a. b. c. gas d. plasma 2. What is the difference between thermal energy and internal energy? a. The thermal energy of the system is the average kinetic energy of the system’s constituent particles due to their motion. The total internal energy of the system is the sum of the kinetic energies and the potential energies of its constituent particles. b. The thermal energy of the system is the average potential energy of the system’s constituent particles due to their motion. The total internal energy of the system is the sum of the kinetic energies and the potential energies of its constituent particles. c. The thermal energy of the system is the average kinetic energy of the system’s constituent particles
due to their motion. The total internal energy of the system is the sum of the kinetic energies of its constituent particles. d. The thermal energy of the system is the average potential energy of the systems’ constituent particles due to their motion. The total internal energy of the system is the sum of the kinetic energies of its constituent particles. 3. What does the Celsius scale use as a reference point? a. The boiling point of mercury b. The boiling point of wax c. The freezing point of water d. The freezing point of wax 11.2 Heat, Specific Heat, and Heat Transfer 4. What are the SI units of specific heat? a. b. c. d. 5. What is radiation? a. The transfer of energy through emission and absorption of the electromagnetic waves is known as radiation. b. The transfer of energy without any direct physical 350 Chapter 11 • Chapter Review contact between any two substances. c. The transfer of energy through direct physical contact between any two substances. d. The transfer of energy by means of the motion of fluids at different temperatures and with different densities. 11.3 Phase Change and Latent Heat 6. Why is there no change in temperature during a phase change, even if energy is absorbed by the system? a. The energy is used to break bonds between particles, and so does not increase the potential energy of the system’s particles. b. The energy is used to break bonds between particles, Critical Thinking Items 11.1 Temperature and Thermal Energy 8. The temperature of two equal quantities of water needs to be raised - the first container by degrees Celsius and the second by degrees Fahrenheit. Which one would require more heat? a. The heat required by the first container is more than the second because each degree Celsius is equal to degrees Fahrenheit. b. The heat required by the first container is less than the second because each degree Fahrenheit is equal to degrees Celsius. c. The heat required by the first container is more than the second because each degree Celsius is equal to degrees Fahrenheit. d. The heat required by the first container is less than the second because each degree Fahrenheit is equal to degrees Celsius. 9. What is 100.00 °C in kelvins? a. 212.00 K b. 100.00 K c. 473.15 K 373.15 K d. 11.2 Heat, Specific Heat, and Heat Transfer 10. The value of specific heat is the same whether the units are J/kg⋅K or J/kg
⋅ºC. How? a. Temperature difference is dependent on the chosen temperature scale. b. Temperature change is different in units of kelvins and degrees Celsius. c. Reading of temperatures in kelvins and degree Celsius are the same. Access for free at openstax.org. and so increases the potential energy of the system’s particles. c. The energy is used to break bonds between particles, and so does not increase the kinetic energy of the system’s particles. d. The energy is used to break bonds between particles, and so increases the kinetic energy of the system’s particles. 7. In which two phases of matter do atoms and molecules have the most distance between them? a. gas and solid b. gas and liquid c. gas and plasma d. liquid and plasma d. The temperature change is the same in units of kelvins and degrees Celsius. 11. If the thermal energy of a perfectly black object is increased by conduction, will the object remain black in appearance? Why or why not? a. No, the energy of the radiation increases as the temperature increases, and the radiation becomes visible at certain temperatures. b. Yes, the energy of the radiation decreases as the temperature increases, and the radiation remains invisible at those energies. c. No, the energy of the radiation decreases as the temperature increases, until the frequencies of the radiation are the same as those of visible light. d. Yes, as the temperature increases, and the energy is transferred from the object by other mechanisms besides radiation, so that the energy of the radiation does not increase. 12. What is the specific heat of a substance that requires 5.00 kJ of heat to raise the temperature of 3.00 kg by 5.00 °F? 3.33×103 J/kg ⋅° C a. b. 6.00×103 J/kg ⋅° C 3.33×102 J/kg ⋅ ° C c. d. 6.00×102 J/kg ⋅ ° C 11.3 Phase Change and Latent Heat 13. Assume 1.0 kg of ice at 0 °C starts to melt. It absorbs 300 kJ of energy by heat. What is the temperature of the water afterwards? a. 10 °C b. 20 °C c. 5 °C d. 0 °C Problems 11.1 Temperature and Thermal Energy 14. What is 35.0 °F in kelvins
? 1.67 K a. 35.0 K b. c. -271.5 K d. 274.8 K 15. Design a temperature scale where the freezing point of water is 0 degrees and its boiling point is 70 degrees. What would be the room temperature on this scale? a. If room temperature is 25.0 °C, the temperature on the new scale will be 17.5 °. If room temperature is 25.0 °C, the temperature on the new scale will be 25.0°. If the room temperature is 25.0 °C, the temperature on the new scale will be 35.7°. If the room temperature is 25.0 °C, the temperature on the new scale will be 50.0°. b. c. d. 11.2 Heat, Specific Heat, and Heat Transfer 16. A certain quantity of water is given 4.0 kJ of heat. This raises its temperature by 30.0 °F. What is the mass of the water in grams? 5.7 g a. 570 g b. Performance Task 11.3 Phase Change and Latent Heat 20. You have been tasked with designing a baking pan that will bake batter the fastest. There are four materials available for you to test. • Four pans of similar design, consisting of aluminum, iron (steel), copper, and glass • Oven or similar heating source • Device for measuring high temperatures • Balance for measuring mass Instructions Procedure 1. Design a safe experiment to test the specific heat of each material (i.e., no extreme temperatures TEST PREP Multiple Choice 11.1 Temperature and Thermal Energy 21. The temperature difference of is the same as Chapter 11 • Test Prep 351 c. d. 5700 g 57 g 17. 5290 J of heat is given to 0.500 kg water at 15.00 °C. What will its final temperature be? a. 15.25° C 12.47 ° C b. c. 40.3° C 17.53° C d. 11.3 Phase Change and Latent Heat 18. How much energy would it take to heat 1.00 kg of ice at 0 °C to water at 15.0 °C? a. 271 kJ b. 334 kJ c. 62.8 kJ 397 kJ d. 19. Ice cubes are used to chill a soda with a mass msoda = 0.300 kg at 15.0 °C. The ice is at 0 °C
, and the total mass of the ice cubes is 0.020 kg. Assume that the soda is kept in a foam container so that heat loss can be ignored, and that the soda has the same specific heat as water. Find the final temperature when all ice has melted. a. 19.02 °C b. 90.3 °C c. 0.11 °C d. 9.03 °C should be used) 2. Write down the materials needed for your experiment and the procedure you will follow. Make sure that you include every detail, so that the experiment can be repeated by others. 3. Carry out the experiment and record any data collected. 4. Review your results and make a recommendation as to which metal should be used for the pan. a. What physical quantities do you need to measure to determine the specific heats for the different materials? b. How does the glass differ from the metals in terms of thermal properties? c. What are your sources of error? a. b. c. d. degree Celsius degree Fahrenheit degrees Celsius degrees Fahrenheit 352 Chapter 11 • Test Prep 22. What is the preferred temperature scale used in celsius fahrenheit scientific laboratories? a. b. c. kelvin d. rankine 11.2 Heat, Specific Heat, and Heat Transfer 23. Which phase of water has the largest specific heat? solid liquid a. b. c. gas 24. What kind of heat transfer requires no medium? a. b. c. d. conduction convection reflection radiation 25. Which of these substances has the greatest specific heat? a. copper b. mercury c. aluminum d. wood 26. Give an example of heat transfer through convection. a. The energy emitted from the filament of an electric bulb b. The energy coming from the sun c. A pan on a hot burner d. Water boiling in a pot 11.3 Phase Change and Latent Heat 27. What are the SI units of latent heat? Short Answer 11.1 Temperature and Thermal Energy 31. What is absolute zeroon the Fahrenheit scale? a. 0 °F 32 °F b. -273.15 °F c. -459.67 °F d. 32. What is absolute zeroon the Celsius scale? a. 0 °C b. 273.15 °C c. d. -459.67 °C -273.15 °C 33. A planet’s atmospheric pressure is such that water there boils at a lower temperature than it does at
sea level on Access for free at openstax.org. a. b. c. d. 28. Which substance has the largest latent heat of fusion? a. gold b. water c. mercury tungsten d. 29. In which phase changes does matter undergo a transition to a more energetic state? a. freezing and vaporization b. melting and sublimation c. melting and vaporization d. melting and freezing 30. A room has a window made from thin glass. The room is colder than the air outside. There is some condensation on the glass window. On which side of the glass would the condensation most likely be found? a. Condensation is on the outside of the glass when the cool, dry air outside the room comes in contact with the cold pane of glass. b. Condensation is on the outside of the glass when the warm, moist air outside the room comes in contact with the cold pane of glass. c. Condensation is on the inside of the glass when the cool, dry air inside the room comes in contact with the cold pane of glass. d. Condensation is on the inside of the glass when the warm, moist air inside the room comes in contact with the cold pane of glass. Earth. If a Celsius scale is derived on this planet, will it be the same as that on Earth? a. The Celsius scale derived on the planet will be the same as that on Earth, because the Celsius scale is independent of the freezing and boiling points of water. b. The Celsius scale derived on that planet will not be the same as that on Earth, because the Celsius scale is dependent and derived by using the freezing and boiling points of water. c. The Celsius scale derived on the planet will be the same as that on Earth, because the Celsius scale is an absolute temperature scale based on molecular motion, which is independent of pressure. d. The Celsius scale derived on the planet will not be the same as that on Earth, but the Fahrenheit scale Chapter 11 • Test Prep 353 will be the same, because its reference temperatures are not based on the freezing and boiling points of water. b. 63 °C c. d. 6.3 °C 1.8×10-2 °C 34. What is the difference between the freezing point and 40. Aluminum has a specific heat of 900 J/kg·ºC. How much boiling point of water on the Reaumur scale? a. The boiling point of water is 80° on the Reaum
ur scale. b. Reaumur scale is less than 120°. c. 100° d. 80° energy would it take to change the temperature of 2 kg aluminum by 3 ºC? a. 1.3 kJ b. 0.60 kJ 54 kJ c. 5.4 kJ d. 11.2 Heat, Specific Heat, and Heat Transfer 35. In the specific heat equation what does cstand for? a. Total heat b. Specific heat c. Specific temperature d. Specific mass 36. Specific heat may be measured in J/kg · K, J/kg · °C. What other units can it be measured in? a. kg/kcal · °C b. kcal · °C/kg c. kg · °C/kcal d. kcal/kg · °C 37. What is buoyancy? a. Buoyancy is a downward force exerted by a solid that opposes the weight of an object. b. Buoyancy is a downward force exerted by a fluid that opposes the weight of an immersed object. c. Buoyancy is an upward force exerted by a solid that opposes the weight an object. d. Buoyancy is an upward force exerted by a fluid that opposes the weight of an immersed object. 38. Give an example of convection found in nature. a. heat transfer through metallic rod b. heat transfer from the sun to Earth c. heat transfer through ocean currents d. heat emitted by a light bulb into its environment 39. Calculate the temperature change in a substance with specific heat 735 J/kg · °C when 14 kJ of heat is given to a 3.0-kg sample of that substance. a. 57 °C 11.3 Phase Change and Latent Heat 41. Upon what does the required amount of heat removed to freeze a sample of a substance depend? a. The mass of the substance and its latent heat of vaporization b. The mass of the substance and its latent heat of fusion c. The mass of the substance and its latent heat of sublimation d. The mass of the substance only 42. What do latent heats, Lf and Lv, depend on? a. Lf and Lv depend on the forces between the particles in the substance. b. Lf and Lv depend on the mass of the substance. c. Lf and Lv depend on the volume of the substance. d. Lf and Lv depend on the temperature of the substance. 43. How
much energy is required to melt 7.00 kg a block of aluminum that is at its melting point? (Latent heat of fusion of aluminum is 380 kJ/kg.) 54.3 kJ a. b. 2.66 kJ c. 0.0184 kJ d. 2.66×103 kJ 44. A 3.00 kg sample of a substance is at its boiling point. If 5,360 kJ of energy are enough to boil away the entire substance, what is its latent heat of vaporization? a. 2,685 kJ/kg b. 3,580 kJ/kg c. 895 kJ/kg d. 1,790 kJ/kg Extended Response 11.1 Temperature and Thermal Energy 45. What is the meaning of absolute zero? a. It is the temperature at which the internal energy of the system is maximum, because the speed of its b. constituent particles increases to maximum at this point. It is the temperature at which the internal energy of the system is maximum, because the speed of its constituent particles decreases to zero at this point. 354 Chapter 11 • Test Prep c. d. It is the temperature at which the internal energy of the system approaches zero, because the speed of its constituent particles increases to a maximum at this point. It is that temperature at which the internal energy of the system approaches zero, because the speed of its constituent particles decreases to zero at this point. 46. Why does it feel hotter on more humid days, even though there is no difference in temperature? a. On hot, dry days, the evaporation of the sweat from the skin cools the body, whereas on humid days the concentration of water in the atmosphere is lower, which reduces the evaporation rate from the skin’s surface. b. On hot, dry days, the evaporation of the sweat from the skin cools the body, whereas on humid days the concentration of water in the atmosphere is higher, which reduces the evaporation rate from the skin’s surface. c. On hot, dry days, the evaporation of the sweat from the skin cools the body, whereas on humid days the concentration of water in the atmosphere is lower, which increases the evaporation rate from the skin’s surface. d. On hot, dry days, the evaporation of the sweat from the skin cools the body, whereas on humid days the concentration of water in the atmosphere is higher, which increases
the evaporation rate from the skin’s surface. 11.2 Heat, Specific Heat, and Heat Transfer 47. A hot piece of metal needs to be cooled. If you were to put the metal in ice or in cold water, such that the ice did not melt and the temperature of either changed by the same amount, which would reduce the metal’s temperature more? Why? a. Water would reduce the metal’s temperature more, because water has a greater specific heat than ice. b. Water would reduce the metal’s temperature more, because water has a smaller specific heat than ice. Ice would reduce the metal’s temperature more, because ice has a smaller specific heat than water. c. d. Ice would reduce the metal’s temperature more, because ice has a greater specific heat than water. 48. On a summer night, why does a black object seem colder than a white one? a. The black object radiates energy faster than the white one, and hence reaches a lower temperature in less time. b. The black object radiates energy slower than the white one, and hence reaches a lower temperature in less time. c. The black object absorbs energy faster than the white one, and hence reaches a lower temperature in less time. d. The black object absorbs energy slower than the white one, and hence reaches a lower temperature in less time. 49. Calculate the difference in heat required to raise the temperatures of 1.00 kg of gold and 1.00 kg of aluminum by 1.00 °C. (The specific heat of aluminum equals 900 J/kg · °C; the specific heat of gold equals 129 J/ kg · °C.) 771 J a. b. 129 J c. 90 J d. 900 J 11.3 Phase Change and Latent Heat 50. True or false—You have an ice cube floating in a glass of water with a thin thread resting across the cube. If you cover the ice cube and thread with a layer of salt, they will stick together, so that you are able to lift the icecube when you pick up the thread. a. True b. False 51. Suppose the energy required to freeze 0.250 kg of water were added to the same mass of water at an initial temperature of 1.0 °C. What would be the final temperature of the water? -69.8 °C a. 79.8 °C b. c. -78.8 °C d
. 80.8 °C Access for free at openstax.org. CHAPTER 12 Thermodynamics Figure 12.1 A steam engine uses energy transfer by heat to do work. (Modification of work by Gerald Friedrich, Pixabay) Chapter Outline 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 12.2 First law of Thermodynamics: Thermal Energy and Work 12.3 Second Law of Thermodynamics: Entropy 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators Energy can be transferred to or from a system, either through a temperature difference between it and INTRODUCTION another system (i.e., by heat) or by exerting a force through a distance (work). In these ways, energy can be converted into other forms of energy in other systems. For example, a car engine burns fuel for heat transfer into a gas. Work is done by the gas as it exerts a force through a distance by pushing a piston outward. This work converts the energy into a variety of other forms—into an increase in the car’s kinetic or gravitational potential energy; into electrical energy to run the spark plugs, radio, and lights; and back into stored energy in the car’s battery. But most of the thermal energy transferred by heat from the fuel burning in the engine does not do work on the gas. Instead, much of this energy is released into the surroundings at lower temperature (i.e., lost through heat), which is quite inefficient. Car engines are only about 25 to 30 percent efficient. This inefficiency leads to increased fuel costs, so there is great interest in improving fuel efficiency. However, it is common knowledge that modern gasoline engines cannot be made much more efficient. The same is true about the conversion to electrical energy in large power stations, whether they are coal, oil, natural gas, or nuclear powered. Why is this the case? The answer lies in the nature of heat. Basic physical laws govern how heat transfer for doing work takes place and limit the 356 Chapter 12 • Thermodynamics maximum possible efficiency of the process. This chapter will explore these laws as well their applications to everyday machines. These topics are part of thermodynamics—the study of heat and its relationship to doing work. 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium Section Learning Objectives By the end of this section, you will be able to do the following: • Explain the zeroth
law of thermodynamics Section Key Terms thermal equilibrium zeroth law of thermodynamics We learned in the previous chapter that when two objects (or systems) are in contact with one another, heat will transfer thermal energy from the object at higher temperature to the one at lower temperature until they both reach the same temperature. The objects are then in thermal equilibrium, and no further temperature changes will occur if they are isolated from other systems. The systems interact and change because their temperatures are different, and the changes stop once their temperatures are the same. Thermal equilibrium is established when two bodies are in thermal contactwith each other—meaning heat transfer (i.e., the transfer of energy by heat) can occur between them. If two systems cannot freely exchange energy, they will not reach thermal equilibrium. (It is fortunate that empty space stands between Earth and the sun, because a state of thermal equilibrium with the sun would be too toasty for life on this planet!) If two systems, A and B, are in thermal equilibrium with each another, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C. This statement may seem obvious, because all three have the same temperature, but it is basic to thermodynamics. It is called the zeroth law of thermodynamics. TIPS FOR SUCCESS The zeroth law of thermodynamics is very similar to the transitive property of equality in mathematics: If a = b and b = c, then a = c. You may be wondering at this point, why the wacky name? Shouldn’t this be called the firstlaw of thermodynamics rather than the zeroth? The explanation is that this law was discovered after the first and second laws of thermodynamics but is so fundamental that scientists decided it should logically come first. As an example of the zeroth law in action, consider newborn babies in neonatal intensive-care units in hospitals. Prematurely born or sick newborns are placed in special incubators. These babies have very little covering while in the incubators, so to an observer, they look as though they may not be warm enough. However, inside the incubator, the temperature of the air, the cot, and the baby are all the same—that is, they are in thermal equilibrium. The ambient temperature is just high enough to keep the baby safe and comfortable. WORK IN PHYSICS Thermodynamics Engineer Thermodynamics engineers apply the principles of thermodynamics to mechanical systems so as
to create or test products that rely on the interactions between heat, work, pressure, temperature, and volume. This type of work typically takes place in the aerospace industry, chemical manufacturing companies, industrial manufacturing plants, power plants (Figure 12.2), engine manufacturers, or electronics companies. Access for free at openstax.org. 12.1 • Zeroth Law of Thermodynamics: Thermal Equilibrium 357 Figure 12.2 An engineer makes a site visit to the Baghdad South power plant. The need for energy creates quite a bit of demand for thermodynamics engineers, because both traditional energy companies and alternative (green) energy startups rely on interactions between heat and work and so require the expertise of thermodynamics engineers. Traditional energy companies use mainly nuclear energy and energy from burning fossil fuels, such as coal. Alternative energy is finding new ways to harness renewable and, often, more readily available energy sources, such as solar, water, wind, and bio-energy. A thermodynamics engineer in the energy industry can find the most efficient way to turn the burning of a biofuel or fossil fuel into energy, store that energy for times when it’s needed most, or figure out how to best deliver that energy from where it’s produced to where it’s used: in homes, factories, and businesses. Additionally, he or she might also design pollution-control equipment to remove harmful pollutants from the smoke produced as a by-product of burning fuel. For example, a thermodynamics engineer may develop a way to remove mercury from burning coal in a coal-fired power plant. Thermodynamics engineering is an expanding field, where employment opportunities are expected to grow by as much as 27 percent between 2012 and 2022, according to the U.S. Bureau of Labor Statistics. To become a thermodynamics engineer, you must have a college degree in chemical engineering, mechanical engineering, environmental engineering, aerospace engineering, civil engineering, or biological engineering (depending on which type of career you wish to pursue), with coursework in physics and physical chemistry that focuses on thermodynamics. GRASP CHECK What would be an example of something a thermodynamics engineer would do in the aeronautics industry? a. Test the fuel efficiency of a jet engine b. Test the functioning of landing gear c. Test the functioning of a lift control device d. Test the autopilot functions Check Your Understanding 1. What is thermal equilibrium? a. When two objects in contact with each other are at the same pressure, they are said to be in
thermal equilibrium. b. When two objects in contact with each other are at different temperatures, they are said to be in thermal equilibrium. c. When two objects in contact with each other are at the same temperature, they are said to be in thermal equilibrium. d. When two objects not in contact with each other are at the same pressure, they are said to be in thermal equilibrium. 2. What is the zeroth law of thermodynamics? 358 Chapter 12 • Thermodynamics a. Energy can neither be created nor destroyed in a chemical reaction. b. If two systems, A and B, are in thermal equilibrium with each another, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C. c. Entropy of any isolated system not in thermal equilibrium always increases. d. Entropy of a system approaches a constant value as temperature approaches absolute zero. 12.2 First law of Thermodynamics: Thermal Energy and Work Section Learning Objectives By the end of this section, you will be able to do the following: • Describe how pressure, volume, and temperature relate to one another and to work, based on the ideal gas law • Describe pressure–volume work • Describe the first law of thermodynamics verbally and mathematically • Solve problems involving the first law of thermodynamics Section Key Terms Boltzmann constant first law of thermodynamics ideal gas law internal energy pressure Pressure, Volume, Temperature, and the Ideal Gas Law Before covering the first law of thermodynamics, it is first important to understand the relationship between pressure, volume, and temperature. Pressure, P, is defined as where Fis a force applied to an area, A, that is perpendicular to the force. Depending on the area over which it is exerted, a given force can have a significantly different effect, as shown in Figure 12.3. 12.1 Figure 12.3 (a) Although the person being poked with the finger might be irritated, the force has little lasting effect. (b) In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin. The SI unit for pressure is the pascal, where Pressure is defined for all states of matter but is particularly important when discussing fluids (such as air). You have probably heard the word pressurebeing used in relation to blood (high or low blood pressure) and in relation to the weather (high- and low-pressure weather systems). These are only
two of many examples of pressures in fluids. The relationship between the pressure, volume, and temperature for an ideal gas is given by the ideal gas law. A gas is considered ideal at low pressure and fairly high temperature, and forces between its component particles can be ignored. The ideal gas law states that 12.2 where Pis the pressure of a gas, Vis the volume it occupies, Nis the number of particles (atoms or molecules) in the gas, and Tis Access for free at openstax.org. 12.2 • First law of Thermodynamics: Thermal Energy and Work 359 its absolute temperature. The constant kis called the Boltzmann constant and has the value purposes of this chapter, we will not go into calculations using the ideal gas law. Instead, it is important for us to notice from the equation that the following are true for a given mass of gas: For the • When volume is constant, pressure is directly proportional to temperature. • When temperature is constant, pressure is inversely proportional to volume. • When pressure is constant, volume is directly proportional to temperature. This last point describes thermal expansion—the change in size or volume of a given mass with temperature. What is the underlying cause of thermal expansion? An increase in temperature means that there’s an increase in the kinetic energy of the individual atoms. Gases are especially affected by thermal expansion, although liquids expand to a lesser extent with similar increases in temperature, and even solids have minor expansions at higher temperatures. This is why railroad tracks and bridges have expansion joints that allow them to freely expand and contract with temperature changes. To get some idea of how pressure, temperature, and volume of a gas are related to one another, consider what happens when you pump air into a deflated tire. The tire’s volume first increases in direct proportion to the amount of air injected, without much increase in the tire pressure. Once the tire has expanded to nearly its full size, the walls limit volume expansion. If you continue to pump air into tire (which now has a nearly constant volume), the pressure increases with increasing temperature (see Figure 12.4). Figure 12.4 (a) When air is pumped into a deflated tire, its volume first increases without much increase in pressure. (b) When the tire is filled to a certain point, the tire walls resist further expansion, and the pressure increases as more air is added. (c) Once the tire is inflated fully, its pressure increases with temperature. Pressure–Volume
Work Pressure–volume workis the work that is done by the compression or expansion of a fluid. Whenever there is a change in volume and external pressure remains constant, pressure–volume work is taking place. During a compression, a decrease in volume increases the internal pressure of a system as work is done onthe system. During an expansion (Figure 12.5), an increase in volume decreases the internal pressure of a system as the system doeswork. 360 Chapter 12 • Thermodynamics Figure 12.5 An expansion of a gas requires energy transfer to keep the pressure constant. Because pressure is constant, the work done is. Recall that the formula for work is in terms of pressure. We can rearrange the definition of pressure, to get an expression for force Substituting this expression for force into the definition of work, we get Because area multiplied by displacement is the change in volume, pressure–volume work is, the mathematical expression for 12.3 12.4 12.5 Just as we say that work is force acting over a distance, for fluids, we can say that work is the pressure acting through the change in volume. For pressure–volume work, pressure is analogous to force, and volume is analogous to distance in the traditional definition of work. WATCH PHYSICS Work from Expansion This video describes work from expansion (or pressure–volume work). Sal combines the equations and to get. Click to view content (https://www.openstax.org/l/28expansionWork) GRASP CHECK If the volume of a system increases while pressure remains constant, is the value of work done by the system Wpositive or negative? Will this increase or decrease the internal energy of the system? a. Positive; internal energy will decrease b. Positive; internal energy will increase c. Negative; internal energy will decrease d. Negative; internal energy will increase The First Law of Thermodynamics Heat (Q) and work (W) are the two ways to add or remove energy from a system. The processes are very different. Heat is driven Access for free at openstax.org. 12.2 • First law of Thermodynamics: Thermal Energy and Work 361 by temperature differences, while work involves a force exerted through a distance. Nevertheless, heat and work can produce identical results. For example, both can cause a temperature increase. Heat transfers energy into a system, such as when the sun warms the air in a bicycle tire and increases the air’s temperature. Similarly, work can be done
on the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by heat or work. Heat and work are both energy in transit—neither is stored as such in a system. However, both can change the internal energy, U, of a system. Internal energy is the sum of the kinetic and potential energies of a system’s atoms and molecules. It can be divided into many subcategories, such as thermal and chemical energy, and depends only on the state of a system (that is, P, V, and T), not on how the energy enters or leaves the system. In order to understand the relationship between heat, work, and internal energy, we use the first law of thermodynamics. The first law of thermodynamics applies the conservation of energyprinciple to systems where heat and work are the methods of transferring energy into and out of the systems. It can also be used to describe how energy transferred by heat is converted and transferred again by work. TIPS FOR SUCCESS Recall that the principle of conservation of energy states that energy cannot be created or destroyed, but it can be altered from one form to another. The first law of thermodynamics states that the change in internal energy of a closed system equals the net heat transfer intothe system minus the net work done bythe system. In equation form, the first law of thermodynamics is 12.6 is the change in internal energy, U, of the system. As shown in Figure 12.6, Qis the net heat transferred into the Here, system—that is, Qis the sum of all heat transfers into and out of the system. Wis the net work done by the system—that is, Wis the sum of all work done on or by the system. By convention, if Qis positive, then there is a net heat transfer into the system; if Wis positive, then there is net work done by the system. So positive Qadds energy to the system by heat, and positive Wtakes energy from the system by work. Note that if heat transfers more energy into the system than that which is done by work, the difference is stored as internal energy. Figure 12.6 The first law of thermodynamics is the conservation of energyprinciple stated for a system, where heat and work are the methods of transferring energy to and from a system. Qrepresents the net heat transfer—it is the sum of all transfers
of energy by heat into and out of the system. Qis positive for net heat transfer intothe system. is the work done bythe system, and is the work done on the system. Wis the total work done on or bythe system. Wis positive when more work is done bythe system than onit. The change in the internal energy of the system,, is related to heat and work by the first law of thermodynamics: It follows also that negative Qindicates that energy is transferred awayfrom the system by heat and so decreases the system’s internal energy, whereas negative Wis work done onthe system, which increases the internal energy. WATCH PHYSICS First Law of Thermodynamics/Internal Energy This video explains the first law of thermodynamics, conservation of energy, and internal energy. It goes over an example of energy transforming between kinetic energy, potential energy, and heat transfer due to air resistance. Click to view content (https://www.openstax.org/l/28FirstThermo) 362 Chapter 12 • Thermodynamics GRASP CHECK Consider the example of tossing a ball when there’s air resistance. As air resistance increases, what would you expect to happen to the final velocity and final kinetic energy of the ball? Why? a. Both will decrease. Energy is transferred to the air by heat due to air resistance. b. Both will increase. Energy is transferred from the air to the ball due to air resistance. c. Final velocity will increase, but final kinetic energy will decrease. Energy is transferred by heat to the air from the ball through air resistance. d. Final velocity will decrease, but final kinetic energy will increase. Energy is transferred by heat from the air to the ball through air resistance. WATCH PHYSICS More on Internal Energy This video goes into further detail, explaining internal energy and how to use the equation the equation system., where Wis the work done onthe system, whereas we use Wto represent work done bythe Note that Sal uses Click to view content (https://www.openstax.org/l/28IntrnEnergy) GRASP CHECK are taken away by heat from the system, and the system does If system? a. b. c. d. of work, what is the change in internal energy of the LINKS TO PHYSICS Biology: Biological Thermodynamics We often think about thermodynamics as being useful for inventing or testing machinery, such as engines or steam turbines. However,
thermodynamics also applies to living systems, such as our own bodies. This forms the basis of the biological thermodynamics (Figure 12.7). Figure 12.7 (a) The first law of thermodynamics applies to metabolism. Heat transferred out of the body (Q) and work done by the body (W) remove internal energy, whereas food intake replaces it. (Food intake may be considered work done on the body.) (b) Plants convert part of Access for free at openstax.org. 12.2 • First law of Thermodynamics: Thermal Energy and Work 363 the radiant energy in sunlight into stored chemical energy, a process called photosynthesis. Life itself depends on the biological transfer of energy. Through photosynthesis, plants absorb solar energy from the sun and use this energy to convert carbon dioxide and water into glucose and oxygen. Photosynthesis takes in one form of energy—light—and converts it into another form—chemical potential energy (glucose and other carbohydrates). Human metabolismis the conversion of food into energy given off by heat, work done by the body’s cells, and stored fat. Metabolism is an interesting example of the first law of thermodynamics in action. Eating increases the internal energy of the body by adding chemical potential energy; this is an unromantic view of a good burrito. The body metabolizes all the food we consume. Basically, metabolism is an oxidation process in which the chemical potential energy of food is released. This implies that food input is in the form of work. Exercise helps you lose weight, because it provides energy transfer from your body by both heat and work and raises your metabolic rate even when you are at rest. Biological thermodynamics also involves the study of transductions between cells and living organisms. Transductionis a process where genetic material—DNA—is transferred from one cell to another. This often occurs during a viral infection (e.g., influenza) and is how the virus spreads, namely, by transferring its genetic material to an increasing number of previously healthy cells. Once enough cells become infected, you begin to feel the effects of the virus (flu symptoms—muscle weakness, coughing, and congestion). Energy is transferred along with the genetic material and so obeys the first law of thermodynamics. Energy is transferred—not created or destroyed—in the process. When work is done on a cell or heat transfers energy to a cell, the cell’s internal energy increases. When a cell does work or loses heat, its
internal energy decreases. If the amount of work done by a cell is the same as the amount of energy transferred in by heat, or the amount of work performed on a cell matches the amount of energy transferred out by heat, there will be no net change in internal energy. GRASP CHECK Based on what you know about heat transfer and the first law of thermodynamics, do you need to eat more or less to maintain a constant weight in colder weather? Explain why. a. more; as more energy is lost by the body in colder weather, the need to eat increases so as to maintain a constant weight b. more; eating more food means accumulating more fat, which will insulate the body from colder weather and will reduce c. d. the energy loss less; as less energy is lost by the body in colder weather, the need to eat decreases so as to maintain a constant weight less; eating less food means accumulating less fat, so less energy will be required to burn the fat, and, as a result, weight will remain constant Solving Problems Involving the First Law of Thermodynamics WORKED EXAMPLE Calculating Change in Internal Energy Suppose 40.00 J of energy is transferred by heat to a system, while the system does 10.00 J of work. Later, heat transfers 25.00 J out of the system, while 4.00 J is done by work on the system. What is the net change in the system’s internal energy? STRATEGY You must first calculate the net heat and net work. Then, using the first law of thermodynamics, change in internal energy. find the Solution The net heat is the transfer into the system by heat minus the transfer out of the system by heat, or The total work is the work done by the system minus the work done on the system, or 12.7 12.8 364 Chapter 12 • Thermodynamics The change in internal energy is given by the first law of thermodynamics. Discussion A different way to solve this problem is to find the change in internal energy for each of the two steps separately and then add the two changes to get the total change in internal energy. This approach would look as follows: For 40.00 J of heat in and 10.00 J of work out, the change in internal energy is 12.9 For 25.00 J of heat out and 4.00 J of work in, the change in internal energy is The total change is 12.10 12.11 12.12 No matter
whether you look at the overall process or break it into steps, the change in internal energy is the same. WORKED EXAMPLE Calculating Change in Internal Energy: The Same Change in Uis Produced by Two Different Processes What is the change in the internal energy of a system when a total of 150.00 J is transferred by heat from the system and 159.00 J is done by work on the system? STRATEGY The net heat and work are already given, so simply use these values in the equation Solution Here, the net heat and total work are given directly as so that 12.13 Access for free at openstax.org. Discussion 12.2 • First law of Thermodynamics: Thermal Energy and Work 365 Figure 12.8 Two different processes produce the same change in a system. (a) A total of 15.00 J of heat transfer occurs into the system, while work takes out a total of 6.00 J. The change in internal energy is ΔU = Q – W = 9.00 J. (b) Heat transfer removes 150.00 J from the system while work puts 159.00 J into it, producing an increase of 9.00 J in internal energy. If the system starts out in the same state in (a) and (b), it will end up in the same final state in either case—its final state is related to internal energy, not how that energy was acquired. A very different process in this second worked example produces the same 9.00 J change in internal energy as in the first worked example. Note that the change in the system in both parts is related to system ends up in the samestate in both problems. Note that, as usual, in Figure 12.8 above, and and not to the individual Q’s or W’s involved. The is work done onthe system. is work done bythe system, Practice Problems 3. What is the pressure-volume work done by a system if a pressure of causes a change in volume of? a. b. c. d. 4. What is the net heat out of the system when is transferred by heat into the system and is transferred out of it? a. b. c. d. 366 Chapter 12 • Thermodynamics Check Your Understanding 5. What is pressure? a. Pressure is force divided by length. b. Pressure is force divided by area. c. Pressure is force divided by volume. d. Pressure is force divided by mass.
6. What is the SI unit for pressure? a. pascal, or N/m3 coulomb b. c. newton d. pascal, or N/m2 7. What is pressure-volume work? a. b. c. d. It is the work that is done by the compression or expansion of a fluid. It is the work that is done by a force on an object to produce a certain displacement. It is the work that is done by the surface molecules of a fluid. It is the work that is done by the high-energy molecules of a fluid. 8. When is pressure-volume work said to be done ON a system? a. When there is an increase in both volume and internal pressure. b. When there is a decrease in both volume and internal pressure. c. When there is a decrease in volume and an increase in internal pressure. d. When there is an increase in volume and a decrease in internal pressure. 9. What are the ways to add energy to or remove energy from a system? a. Transferring energy by heat is the only way to add energy to or remove energy from a system. b. Doing compression work is the only way to add energy to or remove energy from a system. c. Doing expansion work is the only way to add energy to or remove energy from a system. d. Transferring energy by heat or by doing work are the ways to add energy to or remove energy from a system. 10. What is internal energy? a. b. c. d. It is the sum of the kinetic energies of a system’s atoms and molecules. It is the sum of the potential energies of a system’s atoms and molecules. It is the sum of the kinetic and potential energies of a system’s atoms and molecules. It is the difference between the magnitudes of the kinetic and potential energies of a system’s atoms and molecules. 12.3 Second Law of Thermodynamics: Entropy Section Learning Objectives By the end of this section, you will be able to do the following: • Describe entropy • Describe the second law of thermodynamics • Solve problems involving the second law of thermodynamics Section Key Terms entropy second law of thermodynamics Entropy Recall from the chapter introduction that it is not even theoretically possible for engines to be 100 percent efficient. This phenomenon is explained by the second law of thermodynamics, which relies on a concept known as entropy. Entropy is a
measure of the disorder of a system. Entropy also describes how much energy is notavailable to do work. The more disordered a system and higher the entropy, the less of a system's energy is available to do work. Access for free at openstax.org. 12.3 • Second Law of Thermodynamics: Entropy 367 Although all forms of energy can be used to do work, it is not possible to use the entire available energy for work. Consequently, not all energy transferred by heat can be converted into work, and some of it is lost in the form of waste heat—that is, heat that does not go toward doing work. The unavailability of energy is important in thermodynamics; in fact, the field originated from efforts to convert heat to work, as is done by engines. The equation for the change in entropy,, is where Qis the heat that transfers energy during a process, and Tis the absolute temperature at which the process takes place. Qis positive for energy transferred intothe system by heat and negative for energy transferred out ofthe system by heat. In SI, entropy is expressed in units of joules per kelvin (J/K). If temperature changes during the process, then it is usually a good approximation (for small changes in temperature) to take Tto be the average temperature in order to avoid trickier math (calculus). TIPS FOR SUCCESS Absolute temperature is the temperature measured in Kelvins. The Kelvin scale is an absolute temperature scale that is measured in terms of the number of degrees above absolute zero. All temperatures are therefore positive. Using temperatures from another, nonabsolute scale, such as Fahrenheit or Celsius, will give the wrong answer. Second Law of Thermodynamics Have you ever played the card game 52 pickup? If so, you have been on the receiving end of a practical joke and, in the process, learned a valuable lesson about the nature of the universe as described by the second law of thermodynamics. In the game of 52 pickup, the prankster tosses an entire deck of playing cards onto the floor, and you get to pick them up. In the process of picking up the cards, you may have noticed that the amount of work required to restore the cards to an orderly state in the deck is much greater than the amount of work required to toss the cards and create the disorder. The second law of thermodynamics states that the total entropy of a system either increases or remains constant in any spontaneous process; it never decreases
.An important implication of this law is that heat transfers energy spontaneously from higher- to lower-temperature objects, but never spontaneously in the reverse direction. This is because entropy increases for heat transfer of energy from hot to cold (Figure 12.9). Because the change in entropy is Q/T, there is a larger change in at lower temperatures (smaller T). The decrease in entropy of the hot (larger T) object is therefore less than the increase in entropy of the cold (smaller T) object, producing an overall increase in entropy for the system. Figure 12.9 The ice in this drink is slowly melting. Eventually, the components of the liquid will reach thermal equilibrium, as predicted by the second law of thermodynamics—that is, after heat transfers energy from the warmer liquid to the colder ice. (Jon Sullivan, PDPhoto.org) Another way of thinking about this is that it is impossible for any process to have, as its sole result, heat transferring energy from a cooler to a hotter object. Heat cannot transfer energy spontaneously from colder to hotter, because the entropy of the 368 Chapter 12 • Thermodynamics overall system would decrease. Suppose we mix equal masses of water that are originally at two different temperatures, say will be water at an intermediate temperature of has become unavailable to do work, and the system has become less orderly. Let us think about each of these results.. The result. Three outcomes have resulted: entropy has increased, some energy and First, why has entropy increased? Mixing the two bodies of water has the same effect as the heat transfer of energy from the higher-temperature substance to the lower-temperature substance. The mixing decreases the entropy of the hotter water but increases the entropy of the colder water by a greater amount, producing an overall increase in entropy. Second, once the two masses of water are mixed, there is no more temperature difference left to drive energy transfer by heat and therefore to do work. The energy is still in the water, but it is now unavailableto do work. Third, the mixture is less orderly, or to use another term, less structured. Rather than having two masses at different temperatures and with different distributions of molecular speeds, we now have a single mass with a broad distribution of molecular speeds, the average of which yields an intermediate temperature. These three results—entropy, unavailability of energy, and disorder—not only are related but are, in fact, essentially equivalent. Heat transfer of energy from hot to cold is related to the
tendency in nature for systems to become disordered and for less energy to be available for use as work. Based on this law, what cannot happen? A cold object in contact with a hot one never spontaneously transfers energy by heat to the hot object, getting colder while the hot object gets hotter. Nor does a hot, stationary automobile ever spontaneously cool off and start moving. Another example is the expansion of a puff of gas introduced into one corner of a vacuum chamber. The gas expands to fill the chamber, but it never regroups on its own in the corner. The random motion of the gas molecules could take them all back to the corner, but this is never observed to happen (Figure 12.10). Access for free at openstax.org. 12.3 • Second Law of Thermodynamics: Entropy 369 Figure 12.10 Examples of one-way processes in nature. (a) Heat transfer occurs spontaneously from hot to cold, but not from cold to hot. (b) The brakes of this car convert its kinetic energy to increase their internal energy (temperature), and heat transfers this energy to the environment. The reverse process is impossible. (c) The burst of gas released into this vacuum chamber quickly expands to uniformly fill every part of the chamber. The random motions of the gas molecules will prevent them from returning altogether to the corner. We've explained that heat never transfers energy spontaneously from a colder to a hotter object. The key word here is spontaneously. If we do workon a system, it ispossible to transfer energy by heat from a colder to hotter object. We'll learn more about this in the next section, covering refrigerators as one of the applications of the laws of thermodynamics. Sometimes people misunderstand the second law of thermodynamics, thinking that based on this law, it is impossible for entropy to decrease at any particular location. But, it actually ispossible for the entropy of one partof the universe to decrease, as long as the total change in entropy of the universe increases. In equation form, we can write this as Based on this equation, we see that can be negative as long as is positive and greater in magnitude. How is it possible for the entropy of a system to decrease? Energy transfer is necessary. If you pick up marbles that are scattered about the room and put them into a cup, your work has decreased the entropy of that system. If you gather iron ore from the ground and convert it into steel and build a bridge, your work has decreased the entropy of
that system. Energy coming from the sun can decrease the entropy of local systems on Earth—that is, universe increases by a greater amount—that is, although you made the system of the bridge and steel more structured, you did so at the expense of the universe. Altogether, the entropy of the universe is increased by the disorder created by digging up the ore and converting it to steel. Therefore, is positive and greater in magnitude. In the case of the iron ore, is negative. But the overall entropy of the rest of the 12.14 370 Chapter 12 • Thermodynamics and the second law of thermodynamics is notviolated. Every time a plant stores some solar energy in the form of chemical potential energy, or an updraft of warm air lifts a soaring bird, Earth experiences local decreases in entropy as it uses part of the energy transfer from the sun into deep space to do work. There is a large total increase in entropy resulting from this massive energy transfer. A small part of this energy transfer by heat is stored in structured systems on Earth, resulting in much smaller, local decreases in entropy. Solving Problems Involving the Second Law of Thermodynamics Entropy is related not only to the unavailability of energy to do work; it is also a measure of disorder. For example, in the case of a melting block of ice, a highly structured and orderly system of water molecules changes into a disorderly liquid, in which molecules have no fixed positions (Figure 12.11). There is a large increase in entropy for this process, as we'll see in the following worked example. Figure 12.11 These ice floes melt during the Arctic summer. Some of them refreeze in the winter, but the second law of thermodynamics predicts that it would be extremely unlikely for the water molecules contained in these particular floes to reform in the distinctive alligator- like shape they possessed when this picture was taken in the summer of 2009. (Patrick Kelley, U.S. Coast Guard, U.S. Geological Survey) WORKED EXAMPLE Entropy Associated with Disorder Find the increase in entropy of 1.00 kg of ice that is originally at STRATEGY The change in entropy can be calculated from the definition of and melts to form water at. once we find the energy, Q, needed to melt the ice. Solution The change in entropy is defined as Here, Qis the heat necessary to melt 1.00 kg of ice and is given by where mis the mass and is the latent heat of fusion
. for water, so Because Qis the amount of energy heat adds to the ice, its value is positive, and Tis the melting temperature of ice, So the change in entropy is 12.15 12.16 12.17 12.18 Access for free at openstax.org. Discussion 12.3 • Second Law of Thermodynamics: Entropy 371 Figure 12.12 When ice melts, it becomes more disordered and less structured. The systematic arrangement of molecules in a crystal structure is replaced by a more random and less orderly movement of molecules without fixed locations or orientations. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder. The change in entropy is positive, because heat transfers energy intothe ice to cause the phase change. This is a significant increase in entropy, because it takes place at a relatively low temperature. It is accompanied by an increase in the disorder of the water molecules. Practice Problems are added by heat to water at, what is the change in entropy? 11. If a. b. c. d. 12. What is the increase in entropy when of ice at melt to form water at? a. b. c. d. Check Your Understanding 13. What is entropy? a. Entropy is a measure of the potential energy of a system. b. Entropy is a measure of the net work done by a system. c. Entropy is a measure of the disorder of a system. d. Entropy is a measure of the heat transfer of energy into a system. 14. Which forms of energy can be used to do work? a. Only work is able to do work. b. Only heat is able to do work. c. Only internal energy is able to do work. d. Heat, work, and internal energy are all able to do work. 15. What is the statement for the second law of thermodynamics? a. All the spontaneous processes result in decreased total entropy of a system. b. All the spontaneous processes result in increased total entropy of a system. c. All the spontaneous processes result in decreased or constant total entropy of a system. d. All the spontaneous processes result in increased or constant total entropy of a system. 16. For heat transferring energy from a high to a low temperature, what usually happens to the entropy of the whole system? It decreases. It must remain constant. a. b. c. The entropy of the system cannot be predicted without specific values for the temperatures. 372 Chapter 12 •
Thermodynamics d. It increases. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators Section Learning Objectives By the end of this section, you will be able to do the following: • Explain how heat engines, heat pumps, and refrigerators work in terms of the laws of thermodynamics • Describe thermal efficiency • Solve problems involving thermal efficiency Section Key Terms cyclical process heat engine heat pump thermal efficiency Heat Engines, Heat Pumps, and Refrigerators In this section, we’ll explore how heat engines, heat pumps, and refrigerators operate in terms of the laws of thermodynamics. One of the most important things we can do with heat is to use it to do work for us. A heat engine does exactly this—it makes use of the properties of thermodynamics to transform heat into work. Gasoline and diesel engines, jet engines, and steam turbines that generate electricity are all examples of heat engines. Figure 12.13 illustrates one of the ways in which heat transfers energy to do work. Fuel combustion releases chemical energy that heat transfers throughout the gas in a cylinder. This increases the gas temperature, which in turn increases the pressure of the gas and, therefore, the force it exerts on a movable piston. The gas does work on the outside world, as this force moves the piston through some distance. Thus, heat transfer of energy to the gas in the cylinder results in work being done. Access for free at openstax.org. 12.4 • Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 373 Figure 12.13 (a) Heat transfer to the gas in a cylinder increases the internal energy of the gas, creating higher pressure and temperature. (b) The force exerted on the movable cylinder does work as the gas expands. Gas pressure and temperature decrease during expansion, indicating that the gas’s internal energy has decreased as it does work. (c) Heat transfer of energy to the environment further reduces pressure in the gas, so that the piston can more easily return to its starting position. To repeat this process, the piston needs to be returned to its starting point. Heat now transfers energy from the gas to the surroundings, so that the gas’s pressure decreases, and a force is exerted by the surroundings to push the piston back through some distance. A cyclical process brings a system, such as the gas in a cylinder, back to its original state at the
end of every cycle. All heat engines use cyclical processes., from the high-temperature object (or hot reservoir), whereas heat transfers unused energy, Heat engines do work by using part of the energy transferred by heat from some source. As shown in Figure 12.14, heat transfers energy, temperature object (or cold reservoir), and the work done by the engine is W. In physics, a reservoiris defined as an infinitely large mass that can take in or put out an unlimited amount of heat, depending upon the needs of the system. The temperature of the hot reservoir is and the temperature of the cold reservoir is, into the low-. 374 Chapter 12 • Thermodynamics Figure 12.14 (a) Heat transfers energy spontaneously from a hot object to a cold one, as is consistent with the second law of thermodynamics. (b) A heat engine, represented here by a circle, uses part of the energy transferred by heat to do work. The hot and cold objects are called the hot and cold reservoirs. Qh is the heat out of the hot reservoir, Wis the work output, and Qc is the unused heat into the cold reservoir. As noted, a cyclical process brings the system back to its original condition at the end of every cycle. Such a system’s internal energy, U, is the same at the beginning and end of every cycle—that is,. The first law of thermodynamics states that where Qis the netheat transfer during the cycle, and Wis the network done by the system. The net heat transfer is the energy transferred in by heat from the hot reservoir minus the amount that is transferred out to the cold reservoir ( ). Because there is no change in internal energy for a complete cycle ( ), we have so that Therefore, the net work done by the system equals the net heat into the system, or for a cyclical process. 12.19 12.20 12.21 Because the hot reservoir is heated externally, which is an energy-intensive process, it is important that the work be done as efficiently as possible. In fact, we want Wto equal Unfortunately, this is impossible. According to the second law of thermodynamics, heat engines cannot have perfect conversion of heat into work. Recall that entropy is a measure of the disorder of a system, which is also how much energy is unavailable to do work. The second law of thermodynamics requires that the total entropy of a system either increases or remains constant in that cannot be used for work. The amount of heat
rejected to the cold any process. Therefore, there is a minimum amount of reservoir,, the smaller the value of depends upon the efficiency of the heat engine. The smaller the increase in entropy,, and for there to be no heat to the environment (that is, )., and the more heat energy is available to do work. Heat pumps, air conditioners, and refrigerators utilize heat transfer of energy from low to high temperatures, which is the opposite of what heat engines do. Heat transfers energy into a hot one. This requires work input, W, which produces a transfer of energy by heat. Therefore, the total heat transfer to the hot reservoir is from a cold reservoir and delivers energy 12.22 The purpose of a heat pump is to transfer energy by heat to a warm environment, such as a home in the winter. The great advantage of using a heat pump to keep your home warm rather than just burning fuel in a fireplace or furnace is that a heat pump supplies You only pay for W, and you get an additional heat transfer of much energy is transferred to the heated space as is used to run the heat pump. When you burn fuel to keep warm, you pay for all of it. The disadvantage to a heat pump is that the work input (required by the second law of thermodynamics) is sometimes comes from the outside air, even at a temperature below freezing, to the indoor space. from the outside at no cost. In many cases, at least twice as. Heat Access for free at openstax.org. 12.4 • Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 375 more expensive than simply burning fuel, especially if the work is provided by electrical energy. The basic components of a heat pump are shown in Figure 12.15. A working fluid, such as a refrigerant, is used. In the outdoor coils (the evaporator), heat enters the working fluid from the cold outdoor air, turning it into a gas. Figure 12.15 A simple heat pump has four basic components: (1) an evaporator, (2) a compressor, (3) a condenser, and (4) an expansion valve. In the heating mode, heat transfers to the working fluid in the evaporator (1) from the colder, outdoor air, turning it into a gas. The electrically driven compressor (2) increases the temperature and pressure of the gas and forces it into the condenser coils (3) inside the heated space. Because the
temperature of the gas is higher than the temperature in the room, heat transfers energy from the gas to the room as the gas condenses into a liquid. The working fluid is then cooled as it flows back through an expansion valve (4) to the outdoor evaporator coils. The electrically driven compressor (work input W) raises the temperature and pressure of the gas and forces it into the condenser coils that are inside the heated space. Because the temperature of the gas is higher than the temperature inside the room, heat transfers energy to the room, and the gas condenses into a liquid. The liquid then flows back through an expansion (pressure-reducing) valve. The liquid, having been cooled through expansion, returns to the outdoor evaporator coils to resume the cycle. The quality of a heat pump is judged by how much energy is transferred by heat into the warm space ( much input work (W) is required. ) compared with how Figure 12.16 Heat pumps, air conditioners, and refrigerators are heat engines operated backward. Almost every home contains a refrigerator. Most people don’t realize that they are also sharing their homes with a heat pump. Air conditioners and refrigerators are designed to cool substances by transferring energy by heat to a warmer one, where heat is given up. In the case of a refrigerator, heat is moved out of the inside of the fridge into the out of a cool environment 376 Chapter 12 • Thermodynamics surrounding room. For an air conditioner, heat is transferred outdoors from inside a home. Heat pumps are also often used in a reverse setting to cool rooms in the summer. As with heat pumps, work input is required for heat transfer of energy from cold to hot. The quality of air conditioners and refrigerators is judged by how much energy is removed by heat W, is required. So, what is considered the energy benefit in a heat pump, is considered waste heat in a refrigerator. from a cold environment, compared with how much work, Thermal Efficiency In the conversion of energy into work, we are always faced with the problem of getting less out than we put in. The problem is that, in all processes, there is some heat that. A way to quantify how efficiently a machine runs is through a quantity called thermal efficiency. that transfers energy to the environment—and usually a very significant amount at We define thermal efficiency, Eff, to be the ratio of useful energy output to the energy input (or, in other words, the ratio of what we get to what
we spend). The efficiency of a heat engine is the output of net work, W, divided by heat-transferred energy, into the engine; that is, An efficiency of 1, or 100 percent, would be possible only if there were no heat to the environment ( ). TIPS FOR SUCCESS All values of heat ( plus or minus sign. For example, and ) are positive; there is no such thing as negative heat. The directionof heat is indicated by a is out of the system, so it is preceded by a minus sign in the equation for net heat. 12.23 Solving Thermal Efficiency Problems WORKED EXAMPLE Daily Work Done by a Coal-Fired Power Station and Its Efficiency A coal-fired power station is a huge heat engine. It uses heat to transfer energy from burning coal to do work to turn turbines, which are used then to generate electricity. In a single day, a large coal power station transfers burning coal and transfers What is the efficiency of the power station? STRATEGY We can use water is boiled under pressure to form high-temperature steam, which is used to run steam turbine-generators and then condensed back to water to start the cycle again. by heat from by heat into the environment. (a) What is the work done by the power station? (b) to find the work output, W, assuming a cyclical process is used in the power station. In this process, 12.24 12.25, because is given, and work, W, was calculated in the first part of this Solution Work output is given by Substituting the given values, STRATEGY The efficiency can be calculated with example. Solution Efficiency is given by Access for free at openstax.org. 12.4 • Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 377 The work, W, is found to be, and is given ( ), so the efficiency is 12.26 12.27 Discussion The efficiency found is close to the usual value of 42 percent for coal-burning power stations. It means that fully 59.2 percent of the energy is transferred by heat to the environment, which usually results in warming lakes, rivers, or the ocean near the power station and is implicated in a warming planet generally. While the laws of thermodynamics limit the efficiency of such plants—including plants fired by nuclear fuel, oil, and natural gas—the energy transferred by heat to the environment could be, and sometimes is,
used for heating homes or for industrial processes. Practice Problems 17. A heat engine is given by heat and releases by heat to the environment. What is the amount of work done by the system? a. b. c. d. 18. A heat engine takes in 6.0 kJ from heat and produces waste heat of 4.8 kJ. What is its efficiency? a. 25 percent b. 2.50 percent c. 2.00 percent d. 20 percent Check Your Understanding 19. What is a heat engine? a. A heat engine converts mechanical energy into thermal energy. b. A heat engine converts thermal energy into mechanical energy. c. A heat engine converts thermal energy into electrical energy. d. A heat engine converts electrical energy into thermal energy. 20. Give an example of a heat engine. a. A generator b. A battery c. A water pump d. A car engine 21. What is thermal efficiency? a. Thermal efficiency is the ratio of work input to the energy input. b. Thermal efficiency is the ratio of work output to the energy input. c. Thermal efficiency is the ratio of work input to the energy output. d. Thermal efficiency is the ratio of work output to the energy output. 22. What is the mathematical expression for thermal efficiency? a. b. c. d. 378 Chapter 12 • Key Terms KEY TERMS Boltzmann constant constant with the value k= 1.38×10−23 of the gas J/K, which is used in the ideal gas law cyclical process process in which a system is brought back internal energy sum of the kinetic and potential energies of a system’s constituent particles (atoms or molecules) to its original state at the end of every cycle pressure force per unit area perpendicular to the force, entropy measurement of a system's disorder and how much energy is not available to do work in a system states that the change in first law of thermodynamics internal energy of a system equals the net energy transfer by heat intothe system minus the net work done bythe system over which the force acts second law of thermodynamics states that the total entropy of a system either increases or remains constant in any spontaneous process; it never decreases thermal efficiency ratio of useful energy output to the energy input heat engine machine that uses energy transfer by heat to thermal equilibrium condition in which heat no longer do work heat pump machine that generates the heat transfer of energy from cold to hot transfers energy between two objects that are in contact; the two objects have the same temperature
zeroth law of thermodynamics states that if two objects ideal gas law physical law that relates the pressure and volume of a gas to the number of gas molecules or atoms, or number of moles of gas, and the absolute temperature are in thermal equilibrium, and a third object is in thermal equilibrium with one of those objects, it is also in thermal equilibrium with the other object SECTION SUMMARY 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium • Systems are in thermal equilibrium when they have the same temperature. • Thermal equilibrium occurs when two bodies are in contact with each other and can freely exchange energy. • The zeroth law of thermodynamics states that when two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, then A is also in thermal equilibrium with C. 12.2 First law of Thermodynamics: Thermal Energy and Work • Pressure is the force per unit area over which the force is applied perpendicular to the area. • Thermal expansion is the increase, or decrease, of the size (length, area, or volume) of a body due to a change in temperature. • The ideal gas law relates the pressure and volume of a gas to the number of gas particles (atoms or molecules) and the absolute temperature of the gas. • Heat and work are the two distinct methods of energy transfer. • Heat is energy transferred solely due to a temperature difference. • The first law of thermodynamics is given as, where is the change in internal energy of a system, Qis the net energy transfer into the system by heat (the sum of all transfers by heat into and out of the system), and Wis the net work done by the Access for free at openstax.org. system (the sum of all energy transfers by work out of or into the system). • Both Qand Wrepresent energy in transit; only represents an independent quantity of energy capable of being stored. • The internal energy Uof a system depends only on the state of the system, and not how it reached that state. 12.3 Second Law of Thermodynamics: Entropy • Entropy is a measure of a system's disorder: the greater the disorder, the larger the entropy. • Entropy is also the reduced availability of energy to do work. • The second law of thermodynamics states that, for any spontaneous process, the total entropy of a system either increases or remains constant; it never decreases. • Heat transfers energy
spontaneously from higher- to lower-temperature bodies, but never spontaneously in the reverse direction. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators • Heat engines use the heat transfer of energy to do work. • Cyclical processes are processes that return to their original state at the end of every cycle. • The thermal efficiency of a heat engine is the ratio of work output divided by the amount of energy input. • The amount of work a heat engine can do is determined by the net heat transfer of energy during a cycle; more waste heat leads to less work output. • Heat pumps draw energy by heat from cold outside air and use it to heat an interior room. • A refrigerator is a type of heat pump; it takes energy KEY EQUATIONS 12.2 First law of Thermodynamics: Thermal Energy and Work Chapter 12 • Key Equations 379 from the warm air from the inside compartment and transfers it to warmer exterior air. 12.3 Second Law of Thermodynamics: Entropy ideal gas law change in entropy first law of thermodynamics pressure pressure–volume work CHAPTER REVIEW Concept Items 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 1. When are two bodies in thermal equilibrium? a. When they are in thermal contact and are at different pressures b. When they are not in thermal contact but are at the same pressure c. When they are not in thermal contact but are at different temperatures d. When they are in thermal contact and are at the same temperature 2. What is thermal contact? a. Two objects are said to be in thermal contact when they are in contact with each other in such a way that the transfer of energy by heat can occur between them. b. Two objects are said to be in thermal contact when they are in contact with each other in such a way that the transfer of energy by mass can occur between them. c. Two objects are said to be in thermal contact when they neither lose nor gain energy by heat. There is no transfer of energy between them. d. Two objects are said to be in thermal contact when they only gain energy by heat. There is transfer of energy between them. 3. To which mathematical property is the zeroth law of 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators thermal efficiency of a heat engine work output for a cyclical process thermodynamics similar? a. Associative property b. Commutative property
c. Distributive property d. Transitive property 12.2 First law of Thermodynamics: Thermal Energy and Work 4. Why does thermal expansion occur? a. An increase in temperature causes intermolecular distances to increase. b. An increase in temperature causes intermolecular distances to decrease. c. An increase in temperature causes an increase in the work done on the system. d. An increase in temperature causes an increase in the work done by the system. 5. How does pressure-volume work relate to heat and internal energy of a system? a. The energy added to a system by heat minus the change in the internal energy of that system is equal to the pressure-volume work done by the system. b. The sum of the energy released by a system by heat and the change in the internal energy of that system is equal to the pressure-volume work done by the system. c. The product of the energy added to a system by heat and the change in the internal energy of that system 380 Chapter 12 • Chapter Review d. is equal to the pressure-volume work done by the system. If the energy added to a system by heat is divided by the change in the internal energy of that system, the quotient is equal to the pressure-volume work done by the system. 6. On what does internal energy depend? a. The path of energy changes in the system b. The state of the system c. The size of the system d. The shape of the system 7. The first law of thermodynamics helps us understand the relationships among which three quantities? a. Heat, work, and internal energy b. Heat, work, and external energy c. Heat, work, and enthalpy d. Heat, work, and entropy 12.3 Second Law of Thermodynamics: Entropy 8. Air freshener is sprayed from a bottle. The molecules spread throughout the room and cannot make their way back into the bottle. Why is this the case? a. The entropy of the molecules increases. b. The entropy of the molecules decreases. c. The heat content (enthalpy, or total energy available 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 10. What is the quality by which air conditioners are judged? a. The amount of energy generated by heat from a hot environment, compared with the required work input b. The amount of energy transferred by heat from a cold environment, compared with the required work input
c. The amount of energy transferred by heat from a hot environment, compared with the required work output d. The amount of energy transferred by heat from a cold environment, compared with the required work output 11. Why is the efficiency of a heat engine never 100 percent? a. Some energy is always gained by heat from the environment. b. Some energy is always lost by heat to the environment. c. Work output is always greater than energy input. d. Work output is infinite for any energy input. 12. What is a cyclic process? a. A process in which the system returns to its original for heat) of the molecules increases. state at the end of the cycle d. The heat content (enthalpy, or total energy available b. A process in which the system does not return to its for heat) of the molecules decreases. 9. Give an example of entropy as experienced in everyday rotation of Earth formation of a solar eclipse life. a. b. c. filling a car tire with air d. motion of a pendulum bob original state at the end of the cycle c. A process in which the system follows the same path for every cycle d. A process in which the system follows a different path for every cycle Critical Thinking Items 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 13. What are the necessary conditions for energy transfer by heat to occur between two bodies through the process of conduction? a. They should be at the same temperature, and they should be in thermal contact. b. They should be at the same temperature, and they should not be in thermal contact. c. They should be at different temperatures, and they should be in thermal contact. should not be in thermal contact. 14. Oil is heated in a pan on a hot plate. The pan is in thermal equilibrium with the hot plate and also with the oil. The temperature of the hot plate is 150 °C. What is the temperature of the oil? a. b. c. d. 160 °C 150 °C 140 °C 130 °C 12.2 First law of Thermodynamics: Thermal Energy and Work d. They should be at different temperatures, and they 15. When an inflated balloon experiences a decrease in size, Access for free at openstax.org. the air pressure inside the balloon remains nearly constant. If there is no transfer of energy by heat to or from the balloon, what physical change takes place in the balloon? a. The average kinetic energy of the gas
particles decreases, so the balloon becomes colder. b. The average kinetic energy of the gas particles increases, so the balloon becomes hotter. c. The average potential energy of the gas particles decreases, so the balloon becomes colder. d. The average potential energy of the gas particles increases, so the balloon becomes hotter. 16. When heat adds energy to a system, what is likely to happen to the pressure and volume of the system? a. Pressure and volume may both decrease with added energy. b. Pressure and volume may both increase with added energy. c. Pressure must increase with added energy, while volume must remain constant. d. Volume must decrease with added energy, while pressure must remain constant. 17. If more energy is transferred into the system by net heat as compared to the net work done by the system, what happens to the difference in energy? a. b. c. d. It is transferred back to its surroundings. It is stored in the system as internal energy. It is stored in the system as potential energy. It is stored in the system as entropy. 18. Air is pumped into a car tire, causing its temperature to increase. In another tire, the temperature increase is due to exposure to the sun. Is it possible to tell what caused the temperature increase in each tire? Explain your answer. a. No, because it is a chemical change, and the cause of that change does not matter; the final state of both systems are the same. b. Although the final state of each system is identical, the source is different in each case. c. No, because the changes in energy for both systems are the same, and the cause of that change does not matter; the state of each system is identical. d. Yes, the changes in the energy for both systems are the same, but the causes of that change are different, so the states of each system are not identical. 19. How does the transfer of energy from the sun help plants? a. Plants absorb solar energy from the sun and utilize it during the fertilization process. b. Plants absorb solar energy from the sun and utilize Chapter 12 • Chapter Review 381 it during the process of photosynthesis to turn it into plant matter. c. Plants absorb solar energy from the sun and utilize it to increase the temperature inside them. d. Plants absorb solar energy from the sun and utilize it during the shedding of their leaves and fruits. 12.3 Second Law of Thermodynamics: Entropy 20. If an engine were constructed to
perform such that there would be no losses due to friction, what would be its efficiency? a. b. c. d. It would be 0 percent. It would be less than 100 percent. It would be 100 percent. It would be greater than 100 percent. 21. Entropy never decreases in a spontaneous process. Give an example to support this statement. a. The transfer of energy by heat from colder bodies to hotter bodies is a spontaneous process in which the entropy of the system of bodies increases. b. The melting of an ice cube placed in a room causes an increase in the entropy of the room. c. The dissolution of salt in water is a spontaneous process in which the entropy of the system increases. d. A plant uses energy from the sun and converts it into sugar molecules by the process of photosynthesis. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 22. What is the advantage of a heat pump as opposed to burning fuel (as in a fireplace) for keeping warm? a. A heat pump supplies energy by heat from the cold, outside air. b. A heat pump supplies energy generated by the work done. c. A heat pump supplies energy by heat from the cold, outside air and also from the energy generated by the work done. d. A heat pump supplies energy not by heat from the cold, outside air, nor from the energy generated by the work done, but from more accessible sources. 23. What is thermal efficiency of an engine? Can it ever be 100 percent? Why or why not? a. Thermal efficiency is the ratio of the output (work) to the input (heat). It is always 100 percent. b. Thermal efficiency is the ratio of the output (heat) 382 Chapter 12 • Chapter Review to the input (work). It is always 100 percent. c. Thermal efficiency is the ratio of the output (heat) to the input (work). It is never 100 percent. environment b. When mass transferred to the environment is zero c. When mass transferred to the environment is at a d. Thermal efficiency is the ratio of the output (work) maximum to the input (heat). It is never 100 percent. d. When no energy is transferred by heat to the 24. When would 100 percent thermal efficiency be possible? a. When all energy is transferred by heat to the environment Problems 12.2 First law of Thermodynamics: Thermal Energy and Work 25. Some amount of energy is transferred
by heat into a, while. What is the system. The net work done by the system is the increase in its internal energy is amount of net heat? a. b. c. d. 26. Eighty joules are added by heat to a system, while it are added by heat to the of work. What is the change in of work. Later, does system, and it does the system’s internal energy? a. b. c. d. Performance Task 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 29. You have been tasked to design and construct a thermometer that works on the principle of thermal expansion. There are four materials available for you to test, each of which will find use under different sets of conditions and temperature ranges: Materials • Four sample materials with similar mass or volume: copper, steel, water, and alcohol (ethanol or isopropanol) • Oven or similar heating source • Instrument (e.g., meter ruler, Vernier calipers, or micrometer) for measuring changes in dimension • Balance for measuring mass Procedure 1. Design a safe experiment to analyze the thermal Access for free at openstax.org. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 27. A coal power station functions at 40.0 percent efficiency. What is the amount of work it does if it takes in 1.20×1012 J by heat? 3×1010 J a. b. 4.8×1011 J 3×1012 J c. d. 4.8×1013 J 28. A heat engine functions with 70.7 percent thermal efficiency and consumes 12.0 kJ from heat daily. If its efficiency were raised to 75.0 percent, how much energy from heat would be saved daily, while providing the same output? a. −10.8 kJ b. −1.08 kJ c. 0.7 kJ 7 kJ d. expansion properties of each material. 2. Write down the materials needed for your experiment and the procedure you will follow. Make sure that you include every detail so that the experiment can be repeated by others. 3. Select an appropriate material to measure temperature over a predecided temperature range, and give reasons for your choice. 4. Calibrate your instrument to measure temperature changes accurately. a. Which physical quantities are affected by temperature change and
thermal expansion? b. How do such properties as specific heat and thermal conductivity affect the use of each material as a thermometer? c. Does a change of phase take place for any of the tested materials over the temperature range to be examined? d. What are your independent and dependent variables for this series of tests? Which variables need to be controlled in the experiment? e. What are your sources of error? f. Can all the tested materials be used effectively in the same ranges of temperature? Which applications might be suitable for one or more of the tested substances but not the others? Chapter 12 • Test Prep 383 TEST PREP Multiple Choice 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 30. Which law of thermodynamics describes thermal equilibrium? a. zeroth b. first c. d. second third 31. Name any two industries in which the principles of thermodynamics are used. a. aerospace and information technology (IT) industries industrial manufacturing and aerospace b. c. mining and textile industries d. mining and agriculture industries 12.2 First law of Thermodynamics: Thermal Energy and Work 32. What is the value of the Boltzmann constant? a. b. c. d. 33. Which of the following involves work done BY a system? increasing internal energy compression a. b. c. expansion cooling d. 34. Which principle does the first law of thermodynamics state? a. b. c. d. the ideal gas law the transitive property of equality the law of conservation of energy the principle of thermal equilibrium a. A real gas behaves like an ideal gas at high temperature and low pressure. b. A real gas behaves like an ideal gas at high temperature and high pressure. c. A real gas behaves like an ideal gas at low temperature and low pressure. d. A real gas behaves like an ideal gas at low temperature and high pressure. 12.3 Second Law of Thermodynamics: Entropy 37. In an engine, what is the unused energy converted into? internal energy a. b. pressure c. work d. heat 38. It is natural for systems in the universe to _____ spontaneously. a. become disordered b. become ordered c. produce heat d. do work 39. If is and is, what is the change in entropy? a. b. c. d. 40. Why does entropy increase during a spontaneous process? a. Entropy increases because energy always transfers spontaneously from a dispersed state to a concentrated state. b. Ent
ropy increases because energy always transfers spontaneously from a concentrated state to a dispersed state. c. Entropy increases because pressure always 35. What is the change in internal energy of a system when increases spontaneously. and? a. b. c. d. 36. When does a real gas behave like an ideal gas? d. Entropy increases because temperature of any system always increases spontaneously. 41. A system consists of ice melting in a glass of water. What happens to the entropy of this system? a. The entropy of the ice decreases, while the entropy of the water cannot be predicted without more 384 Chapter 12 • Test Prep specific information. b. The entropy of the system remains constant. c. The entropy of the system decreases. d. The entropy of the system increases. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 42. Which equation represents the net work done by a system in a cyclic process? a. b. c. d. 43. Which of these quantities needs to be zero for efficiency to be 100 percent? a. ΔU b. W c. Qh d. Qc 44. Which of the following always has the greatest value in a system having 80 percent thermal efficiency? a. ΔU Short Answer 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 47. What does greenenergy development entail? a. Green energy involves finding new ways to harness clean and renewable alternative energy sources. b. Green energy involves finding new ways to conserve alternative energy sources. b. W c. Qh d. Qc 45. In the equation Q= Qh − Qc, what does the negative sign indicate? a. Heat transfer of energy is always negative. b. Heat transfer can only occur in one direction. c. Heat is directed into the system from the surroundings outside the system. d. Heat is directed out of the system. 46. What is the purpose of a heat pump? a. A heat pump uses work to transfer energy by heat from a colder environment to a warmer environment. b. A heat pump uses work to transfer energy by heat from a warmer environment to a colder environment. c. A heat pump does work by using heat to convey energy from a colder environment to a warmer environment. d. A heat pump does work by using heat to convey energy from a warmer environment to a colder environment. volume, which variable relates to pressure, and what is that relation? a. Temperature; inverse proportionality
b. Temperature, direct proportionality to square root c. Temperature; direct proportionality d. Temperature; direct proportionality to square c. Green energy involves decreasing the efficiency of 50. When is volume directly proportional to temperature? nonrenewable energy resources. d. Green energy involves finding new ways to harness nonrenewable energy resources. 48. Why are the sun and Earth not in thermal equilibrium? a. The mass of the sun is much greater than the mass of Earth. b. There is a vast amount of empty space between the sun and Earth. c. The diameter of the sun is much greater than the diameter of Earth. d. The sun is in thermal contact with Earth. 12.2 First law of Thermodynamics: Thermal Energy and Work 49. If a fixed quantity of an ideal gas is held at a constant a. when the pressure of the gas is variable b. when the pressure of the gas is constant c. when the mass of the gas is variable d. when the mass of the gas is constant 51. For fluids, what can work be defined as? a. pressure acting over the change in depth b. pressure acting over the change in temperature c. d. pressure acting over the change in volume temperature acting over the change in volume, what does 52. In the equation indicate? a. b. c. d. the work done on the system the work done by the system the heat into the system the heat out of the system Access for free at openstax.org. Chapter 12 • Test Prep 385 53. By convention, if Qis positive, what is the direction in which heat transfers energy with regard to the system? a. The direction of the heat transfer of energy depends on the changes in W, regardless of the sign of Q. a. Entropy depends on the change of phase of a system, but not on any other state conditions. b. Entropy does not depend on how the final state is reached from the initial state. c. Entropy is least when the path between the initial b. The direction of Qcannot be determined from just state and the final state is the shortest. the sign of Q. d. Entropy is least when the path between the initial c. The direction of net heat transfer of energy will be state and the final state is the longest. the work was done 61. What is the change in entropy caused by melting 5.00 kg out of the system. d. The direction of net heat transfer of energy
will be into the system. 54. What is net transfer of energy by heat? a. b. c. d. It is the sum of all energy transfers by heat into the system. It is the product of all energy transfers by heat into the system. It is the sum of all energy transfers by heat into and out of the system. It is the product of all energy transfers by heat into and out of the system. 55. Three hundred ten joules of heat enter a system, after which the system does of work. What is the change in its internal energy? Would this amount change if the energy transferred by heat were added after the work was done instead of before? a. ; this would change if heat added energy after the work was done ; this would change if heat added energy after ; this would not change even if heat added energy after the work was done ; this would not change even if heat added energy after the work was done 56. Ten joules are transferred by heat into a system,. What is the change in the followed by another system’s internal energy? What would be the difference in this change if the system at once? a. ; the change in internal energy would be same of energy were added by heat to even if the heat added the energy at once ; the change in internal energy would be same even if the heat added the energy at once ; the change in internal energy would be more if the heat added the energy at once ; the change in internal energy would be more b. c. d. if the heat added the energy at once 12.3 Second Law of Thermodynamics: Entropy 57. How does the entropy of a system depend on how the system reaches a given state? b. c. d. 58. Which sort of thermal energy do molecules in a solid possess? a. electric potential energy b. gravitational potential energy c. translational kinetic energy d. vibrational kinetic energy 59. A cold object in contact with a hot one never spontaneously transfers energy by heat to the hot object. Which law describes this phenomenon? the first law of thermodynamics a. the second law of thermodynamics b. the third law of thermodynamics c. the zeroth law of thermodynamics d. 60. How is it possible for us to transfer energy by heat from cold objects to hot ones? a. by doing work on the system b. by having work done by the system c. by increasing the specific heat of the cold body d. by increasing the
specific heat of the hot body of ice at 0 °C? a. 0 J/K b. 6.11×103 J/K c. 6.11×104 J/K d. ∞J/K 62. What is the amount of heat required to cause a change in the entropy of a system at? of a. b. c. d. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 63. In a refrigerator, what is the function of an evaporator? a. The evaporator converts gaseous refrigerant into liquid. b. The evaporator converts solid refrigerant into liquid. c. The evaporator converts solid refrigerant into gas. 386 Chapter 12 • Test Prep d. The evaporator converts liquid refrigerant into gas. 64. Which component of an air conditioner converts gas into liquid? a. b. c. d. the condenser the compressor the evaporator the thermostat 65. What is one example for which calculating thermal efficiency is of interest? a. A wind turbine b. An electric pump c. A bicycle d. A car engine 66. How is the efficiency of a refrigerator or heat pump expressed? a. Extended Response 12.1 Zeroth Law of Thermodynamics: Thermal Equilibrium 69. What is the meaning of efficiency in terms of a car engine? a. An engine’s efficiency equals the sum of useful energy (work) and the input energy. b. An engine’s efficiency equals the proportion of useful energy (work) to the input energy. c. An engine’s efficiency equals the product of useful energy (work) and the input energy. d. An engine’s efficiency equals the difference between the useful energy (work) and the input energy. 12.2 First law of Thermodynamics: Thermal Energy and Work 70. Why does a bridge have expansion joints? a. because the bridge expands and contracts with the change in temperature b. because the bridge expands and contracts with the change in motion of objects moving on the bridge c. because the bridge expands and contracts with the change in total load on the bridge d. because the bridge expands and contracts with the change in magnitude of wind blowing 71. Under which conditions will the work done by the gas in a system increase? a. It will increase when a large amount of energy is added to the system, and that energy causes an increase in the gas’s volume, its pressure
, or both. Access for free at openstax.org. b. c. d. 67. How can you mathematically express thermal efficiency in terms of and? a. b. c. d. 68. How can you calculate percentage efficiency? a. percentage efficiency b. percentage efficiency c. percentage efficiency d. percentage efficiency b. c. d. It will increase when a large amount of energy is extracted from the system, and that energy causes an increase in the gas’s volume, its pressure, or both. It will increase when a large amount of energy is added to the system, and that energy causes a decrease in the gas’s volume, its pressure, or both. It will increase when a large amount of energy is extracted from the system, and that energy causes a decrease in the gas’s volume, its pressure, or both. 72. How does energy transfer by heat aid in body metabolism? a. The energy is given to the body through the work done by the body (W) and through the intake of food, which may also be considered as the work done on the body. The transfer of energy out of the body is by heat (−Q). b. The energy given to the body is by the intake of food, which may also be considered as the work done on the body. The transfer of energy out of the body is by heat (−Q) and the work done by the body (W). c. The energy given to the body is by the transfer of energy by heat (Q) into the body, which may also be considered as the work done on the body. The transfer of energy out of the body is the work done by the body (W). d. The energy given to the body is by the transfer of energy by heat (Q) inside the body. The transfer of energy out of the body is by the intake of food and the work done by the body (W). 73. Two distinct systems have the same amount of stored internal energy. Five hundred joules are added by heat to the first system, and 300 J are added by heat to the second system. What will be the change in internal energy of the first system if it does 200 J of work? How much work will the second system have to do in order to have the same internal energy? a. b. c. d. 700 J; 0 J 300 J; 300 J 700 J; 300 J 300 J; 0 J 12.
3 Second Law of Thermodynamics: Entropy 74. Why is it not possible to convert all available energy into work? a. Due to the entropy of a system, some energy is always unavailable for work. b. Due to the entropy of a system, some energy is always available for work. c. Due to the decrease in internal energy of a system, some energy is always made unavailable for work. d. Due to the increase in internal energy of a system, some energy is always made unavailable for work. 75. Why does entropy increase when ice melts into water? a. Melting converts the highly ordered solid structure into a disorderly liquid, thereby increasing entropy. b. Melting converts the highly ordered liquid into a disorderly solid structure, thereby increasing entropy. c. Melting converts the highly ordered solid structure into a disorderly solid structure, thereby increasing entropy. d. Melting converts the highly ordered liquid into a disorderly liquid, thereby increasing entropy. 76. Why is change in entropy lower for higher temperatures? a. Increase in the disorder in the substance is low for high temperature. Chapter 12 • Test Prep 387 b. Increase in the disorder in the substance is high for high temperature. c. Decrease in the disorder in the substance is low for high temperature. d. Decrease in the disorder in the substance is high for high temperature. 12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators 77. In the equation W= Qh − Qc, if the value of Qc were equal to zero, what would it signify? a. The efficiency of the engine is 75 percent. b. The efficiency of the engine is 25 percent. c. The efficiency of the engine is 0 percent. d. The efficiency of the engine is 100 percent. 78. Can the value of thermal efficiency be greater than 1? Why or why not? a. No, according to the first law of thermodynamics, energy output can never be more than the energy input. b. No, according to the second law of thermodynamics, energy output can never be more than the energy input. c. Yes, according to the first law of thermodynamics, energy output can be more than the energy input. d. Yes, according to the second law of thermodynamics, energy output can be more than the energy input. 79. A coal power station transfers 3.0×1012 J by heat from burning coal and transfers 1.5×1012 J by heat into the
environment. What is the efficiency of the power station? a. 0.33 b. 0.5 c. 0.66 1 d. 388 Chapter 12 • Test Prep Access for free at openstax.org. CHAPTER 13 Waves and Their Properties Figure 13.1 Waves in the ocean behave similarly to all other types of waves. (Steve Jurveston, Flickr) Chapter Outline 13.1 Types of Waves 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period 13.3 Wave Interaction: Superposition and Interference Recall from the chapter on Motion in Two Dimensions that oscillations—the back-and-forth movement INTRODUCTION between two points—involve force and energy. Some oscillations create waves, such as the sound waves created by plucking a guitar string. Other examples of waves include earthquakes and visible light. Even subatomic particles, such as electrons, can behave like waves. You can make water waves in a swimming pool by slapping the water with your hand. Some of these waves, such as water waves, are visible; others, such as sound waves, are not. But every wave is a disturbance that moves from its source and carries energy. In this chapter, we will learn about the different types of waves, their properties, and how they interact with one another. 390 Chapter 13 • Waves and Their Properties 13.1 Types of Waves Section Learning Objectives By the end of this section, you will be able to do the following: • Define mechanical waves and medium, and relate the two • Distinguish a pulse wave from a periodic wave • Distinguish a longitudinal wave from a transverse wave and give examples of such waves Section Key Terms Mechanical Waves longitudinal wave mechanical wave medium wave periodic wave pulse wave transverse wave What do we mean when we say something is a wave? A wave is a disturbance that travels or propagatesfrom the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves; meaning, they require a medium to travel through. The medium may be a solid, a liquid, or a gas, and the speed of the wave depends on the material properties of the medium through which it is traveling. However, light is not a mechanical wave; it can travel through a vacuum such as the empty parts of outer space. A familiar wave that you can easily imagine is
the water wave. For water waves, the disturbance is in the surface of the water, an example of which is the disturbance created by a rock thrown into a pond or by a swimmer splashing the water surface repeatedly. For sound waves, the disturbance is caused by a change in air pressure, an example of which is when the oscillating cone inside a speaker creates a disturbance. For earthquakes, there are several types of disturbances, which include the disturbance of Earth’s surface itself and the pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Because water waves are common and visible, visualizing water waves may help you in studying other types of waves, especially those that are not visible. Water waves have characteristics common to all waves, such as amplitude, period, frequency, and energy, which we will discuss in the next section. Pulse Waves and Periodic Waves If you drop a pebble into the water, only a few waves may be generated before the disturbance dies down, whereas in a wave pool, the waves are continuous. A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions. Consider the simplified water wave in Figure 13.2. This wave is an up-and-down disturbance of the water surface, characterized by a sine wave pattern. The uppermost position is called the crestand the lowest is the trough. It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs pass under the bird. Figure 13.2 An idealized ocean wave passes under a seagull that bobs up and down in simple harmonic motion. Access for free at openstax.org. 13.1 • Types of Waves 391 Longitudinal Waves and Transverse Waves Mechanical waves are categorized by their type of motion and fall into any of two categories: transverse or longitudinal. Note that both transverse and longitudinal waves can be periodic. A transverse wave propagates so that the disturbance is perpendicular to the direction of propagation. An example of a transverse wave is shown in Figure 13.3, where a woman moves a
toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction. Figure 13.3 In this example of a transverse wave, the wave propagates horizontally and the disturbance in the toy spring is in the vertical direction. In contrast, in a longitudinal wave, the disturbance is parallel to the direction of propagation. Figure 13.4 shows an example of a longitudinal wave, where the woman now creates a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring. Figure 13.4 In this example of a longitudinal wave, the wave propagates horizontally and the disturbance in the toy spring is also in the horizontal direction. TIPS FOR SUCCESS Longitudinal waves are sometimes called compression wavesor compressional waves, and transverse waves are sometimes called shear waves. Waves may be transverse, longitudinal, or a combination of the two. The waves on the strings of musical instruments are transverse (as shown in Figure 13.5), and so are electromagnetic waves, such as visible light. Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids. 392 Chapter 13 • Waves and Their Properties Figure 13.5 The wave on a guitar string is transverse. However, the sound wave coming out of a speaker rattles a sheet of paper in a direction that shows that such sound wave is longitudinal. Sound in solids can be both longitudinal and transverse. Essentially, water waves are also a combination of transverse and longitudinal components, although the simplified water wave illustrated in Figure 13.2 does not show the longitudinal motion of the bird. Earthquake waves under Earth’s surface have both longitudinal and transverse components as well. The longitudinal waves in an earthquake are called pressure or P-waves, and the transverse waves are called shear or S-waves. These components have important individual characteristics; for example, they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water. WATCH PHYSICS Introduction to Waves This video explains wave propagation in terms of momentum using an example of a wave moving along a rope. It also covers the differences between transverse and longitudinal waves, and between pulse and periodic waves. Click to view content (https://openstax.org/l/02introtowaves) GRASP CHECK In a longitudinal sound wave, after a compression wave moves through a region,
the density of molecules briefly decreases. Why is this? a. After a compression wave, some molecules move forward temporarily. b. After a compression wave, some molecules move backward temporarily. c. After a compression wave, some molecules move upward temporarily. d. After a compression wave, some molecules move downward temporarily. FUN IN PHYSICS The Physics of Surfing Many people enjoy surfing in the ocean. For some surfers, the bigger the wave, the better. In one area off the coast of central California, waves can reach heights of up to 50 feet in certain times of the year (Figure 13.6). Access for free at openstax.org. 13.1 • Types of Waves 393 Figure 13.6 A surfer negotiates a steep take-off on a winter day in California while his friend watches. (Ljsurf, Wikimedia Commons) How do waves reach such extreme heights? Other than unusual causes, such as when earthquakes produce tsunami waves, most huge waves are caused simply by interactions between the wind and the surface of the water. The wind pushes up against the surface of the water and transfers energy to the water in the process. The stronger the wind, the more energy transferred. As waves start to form, a larger surface area becomes in contact with the wind, and even more energy is transferred from the wind to the water, thus creating higher waves. Intense storms create the fastest winds, kicking up massive waves that travel out from the origin of the storm. Longer-lasting storms and those storms that affect a larger area of the ocean create the biggest waves since they transfer more energy. The cycle of the tides from the Moon’s gravitational pull also plays a small role in creating waves. Actual ocean waves are more complicated than the idealized model of the simple transverse wave with a perfect sinusoidal shape. Ocean waves are examples of orbital progressive waves, where water particles at the surface follow a circular path from the crest to the trough of the passing wave, then cycle back again to their original position. This cycle repeats with each passing wave. As waves reach shore, the water depth decreases and the energy of the wave is compressed into a smaller volume. This creates higher waves—an effect known as shoaling. Since the water particles along the surface move from the crest to the trough, surfers hitch a ride on the cascading water, gliding along the surface. If ocean waves work exactly like the idealized transverse waves, surfing would be much less exciting as it
would simply involve standing on a board that bobs up and down in place, just like the seagull in the previous figure. Additional information and illustrations about the scientific principles behind surfing can be found in the “Using Science to Surf Better!” (http://www.openstax.org/l/28Surf) video. GRASP CHECK If we lived in a parallel universe where ocean waves were longitudinal, what would a surfer’s motion look like? a. The surfer would move side-to-side/back-and-forth vertically with no horizontal motion. b. The surfer would forward and backward horizontally with no vertical motion. Check Your Understanding 1. What is a wave? a. A wave is a force that propagates from the place where it was created. b. A wave is a disturbance that propagates from the place where it was created. c. A wave is matter that provides volume to an object. d. A wave is matter that provides mass to an object. 2. Do all waves require a medium to travel? Explain. a. No, electromagnetic waves do not require any medium to propagate. b. No, mechanical waves do not require any medium to propagate. c. Yes, both mechanical and electromagnetic waves require a medium to propagate. d. Yes, all transverse waves require a medium to travel. 3. What is a pulse wave? a. A pulse wave is a sudden disturbance with only one wave generated. b. A pulse wave is a sudden disturbance with only one or a few waves generated. 394 Chapter 13 • Waves and Their Properties c. A pulse wave is a gradual disturbance with only one or a few waves generated. d. A pulse wave is a gradual disturbance with only one wave generated. 4. Is the following statement true or false? A pebble dropped in water is an example of a pulse wave. a. False b. True 5. What are the categories of mechanical waves based on the type of motion? a. Both transverse and longitudinal waves b. Only longitudinal waves c. Only transverse waves d. Only surface waves 6. In which direction do the particles of the medium oscillate in a transverse wave? a. Perpendicular to the direction of propagation of the transverse wave b. Parallel to the direction of propagation of the transverse wave 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period Section Learning Objectives By the end of this section,
you will be able to do the following: • Define amplitude, frequency, period, wavelength, and velocity of a wave • Relate wave frequency, period, wavelength, and velocity • Solve problems involving wave properties Section Key Terms wavelength wave velocity Wave Variables In the chapter on motion in two dimensions, we defined the following variables to describe harmonic motion: • Amplitude—maximum displacement from the equilibrium position of an object oscillating around such equilibrium position • Frequency—number of events per unit of time • Period—time it takes to complete one oscillation For waves, these variables have the same basic meaning. However, it is helpful to word the definitions in a more specific way that applies directly to waves: • Amplitude—distance between the resting position and the maximum displacement of the wave • Frequency—number of waves passing by a specific point per second • Period—time it takes for one wave cycle to complete In addition to amplitude, frequency, and period, their wavelength and wave velocity also characterize waves. The wavelength is the distance between adjacent identical parts of a wave, parallel to the direction of propagation. The wave velocity is the speed at which the disturbance moves. TIPS FOR SUCCESS Wave velocity is sometimes also called the propagation velocityor propagation speedbecause the disturbance propagates from one location to another. Consider the periodic water wave in Figure 13.7. Its wavelength is the distance from crest to crest or from trough to trough. The wavelength can also be thought of as the distance a wave has traveled after one complete cycle—or one period. The time for one complete up-and-down motion is the simple water wave’s period T. In the figure, the wave itself moves to the right with a wave Access for free at openstax.org. 13.2 • Wave Properties: Speed, Amplitude, Frequency, and Period 395 velocity vw. Its amplitude Xis the distance between the resting position and the maximum displacement—either the crest or the trough—of the wave. It is important to note that this movement of the wave is actually the disturbancemoving to the right, not the water itself; otherwise, the bird would move to the right. Instead, the seagull bobs up and down in place as waves pass underneath, traveling a total distance of 2Xin one cycle. However, as mentioned in the text feature on surfing, actual ocean waves are more complex than this simplified example. Figure 13.7 The wave has a wavelength λ, which is the distance between adjacent identical
parts of the wave. The up-and-down disturbance of the surface propagates parallel to the surface at a speed vw. WATCH PHYSICS Amplitude, Period, Frequency, and Wavelength of Periodic Waves This video is a continuation of the video “Introduction to Waves” from the "Types of Waves" section. It discusses the properties of a periodic wave: amplitude, period, frequency, wavelength, and wave velocity. Click to view content (https://www.openstax.org/l/28wavepro) TIPS FOR SUCCESS The crest of a wave is sometimes also called the peak. GRASP CHECK If you are on a boat in the trough of a wave on the ocean, and the wave amplitude is position? a. b. c. d., what is the wave height from your The Relationship between Wave Frequency, Period, Wavelength, and Velocity Since wave frequency is the number of waves per second, and the period is essentially the number of seconds per wave, the relationship between frequency and period is or 13.1 13.2 just as in the case of harmonic motion of an object. We can see from this relationship that a higher frequency means a shorter period. Recall that the unit for frequency is hertz (Hz), and that 1 Hz is one cycle—or one wave—per second. The speed of propagation vw is the distance the wave travels in a given time, which is one wavelength in a time of one period. In 396 Chapter 13 • Waves and Their Properties equation form, it is written as or 13.3 13.4 From this relationship, we see that in a medium where vw is constant, the higher the frequency, the smaller the wavelength. See Figure 13.8. Figure 13.8 Because they travel at the same speed in a given medium, low-frequency sounds must have a greater wavelength than high- frequency sounds. Here, the lower-frequency sounds are emitted by the large speaker, called a woofer, while the higher-frequency sounds are emitted by the small speaker, called a tweeter. These fundamental relationships hold true for all types of waves. As an example, for water waves, vw is the speed of a surface wave; for sound, vw is the speed of sound; and for visible light, vw is the speed of light. The amplitude Xis completely independent of the speed of propagation vw and depends only on the amount of energy in the wave. Snap Lab Waves in a
Bowl In this lab, you will take measurements to determine how the amplitude and the period of waves are affected by the transfer of energy from a cork dropped into the water. The cork initially has some potential energy when it is held above the water—the greater the height, the higher the potential energy. When it is dropped, such potential energy is converted to kinetic energy as the cork falls. When the cork hits the water, that energy travels through the water in waves. • Large bowl or basin • Water • Cork (or ping pong ball) • Stopwatch • Measuring tape Instructions Procedure 1. Fill a large bowl or basin with water and wait for the water to settle so there are no ripples. 2. Gently drop a cork into the middle of the bowl. 3. Estimate the wavelength and the period of oscillation of the water wave that propagates away from the cork. You can estimate the period by counting the number of ripples from the center to the edge of the bowl while your partner times it. This information, combined with the bowl measurement, will give you the wavelength when the correct formula is used. 4. Remove the cork from the bowl and wait for the water to settle again. 5. Gently drop the cork at a height that is different from the first drop. 6. Repeat Steps 3 to 5 to collect a second and third set of data, dropping the cork from different heights and recording the resulting wavelengths and periods. Access for free at openstax.org. 13.2 • Wave Properties: Speed, Amplitude, Frequency, and Period 397 7. Interpret your results. GRASP CHECK A cork is dropped into a pool of water creating waves. Does the wavelength depend upon the height above the water from which the cork is dropped? a. No, only the amplitude is affected. b. Yes, the wavelength is affected. LINKS TO PHYSICS Geology: Physics of Seismic Waves Figure 13.9 The destructive effect of an earthquake is a palpable evidence of the energy carried in the earthquake waves. The Richter scale rating of earthquakes is related to both their amplitude and the energy they carry. (Petty Officer 2nd Class Candice Villarreal, U.S. Navy) Geologists rely heavily on physics to study earthquakes since earthquakes involve several types of wave disturbances, including disturbance of Earth’s surface and pressure disturbances under the surface. Surface earthquake waves are similar to surface waves on
water. The waves under Earth’s surface have both longitudinal and transverse components. The longitudinal waves in an earthquake are called pressure waves (P-waves) and the transverse waves are called shear waves (S-waves). These two types of waves propagate at different speeds, and the speed at which they travel depends on the rigidity of the medium through which they are traveling. During earthquakes, the speed of P-waves in granite is significantly higher than the speed of S-waves. Both components of earthquakes travel more slowly in less rigid materials, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves have speeds of 2 to 5 km/s, but both are faster in more rigid materials. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. For that reason, the time difference between the P- and S-waves is used to determine the distance to their source, the epicenter of the earthquake. We know from seismic waves produced by earthquakes that parts of the interior of Earth are liquid. Shear or transverse waves cannot travel through a liquid and are not transmitted through Earth’s core. In contrast, compression or longitudinal waves can pass through a liquid and they do go through the core. All waves carry energy, and the energy of earthquake waves is easy to observe based on the amount of damage left behind after the ground has stopped moving. Earthquakes can shake whole cities to the ground, performing the work of thousands of wrecking balls. The amount of energy in a wave is related to its amplitude. Large-amplitude earthquakes produce large ground displacements and greater damage. As earthquake waves spread out, their amplitude decreases, so there is less damage the farther they get from the source. GRASP CHECK What is the relationship between the propagation speed, frequency, and wavelength of the S-waves in an earthquake? a. The relationship between the propagation speed, frequency, and wavelength is b. The relationship between the propagation speed, frequency, and wavelength is c. The relationship between the propagation speed, frequency, and wavelength is 398 Chapter 13 • Waves and Their Properties d. The relationship between the propagation speed, frequency, and wavelength is Virtual Physics Wave on a String Click to view content (http://www.openstax.org/l/28wavestring) In this animation, watch how a string vibrates in slow motion by choosing the Slow Motion setting. Select
the No End and Manual options, and wiggle the end of the string to make waves yourself. Then switch to the Oscillate setting to generate waves automatically. Adjust the frequency and the amplitude of the oscillations to see what happens. Then experiment with adjusting the damping and the tension. GRASP CHECK Which of the settings—amplitude, frequency, damping, or tension—changes the amplitude of the wave as it propagates? What does it do to the amplitude? a. Frequency; it decreases the amplitude of the wave as it propagates. b. Frequency; it increases the amplitude of the wave as it propagates. c. Damping; it decreases the amplitude of the wave as it propagates. d. Damping; it increases the amplitude of the wave as it propagates. Solving Wave Problems WORKED EXAMPLE Calculate the Velocity of Wave Propagation: Gull in the Ocean Calculate the wave velocity of the ocean wave in the previous figure if the distance between wave crests is 10.0 m and the time for a seagull to bob up and down is 5.00 s. STRATEGY The values for the wavelength can use are given and we are asked to find Therefore, we to find the wave velocity. and the period Solution Enter the known values into Discussion This slow speed seems reasonable for an ocean wave. Note that in the figure, the wave moves to the right at this speed, which is different from the varying speed at which the seagull bobs up and down. 13.5 WORKED EXAMPLE Calculate the Period and the Wave Velocity of a Toy Spring The woman in creates two waves every second by shaking the toy spring up and down. (a)What is the period of each wave? (b) If each wave travels 0.9 meters after one complete wave cycle, what is the velocity of wave propagation? STRATEGY FOR (A) To find the period, we solve for, given the value of the frequency Access for free at openstax.org. 13.2 • Wave Properties: Speed, Amplitude, Frequency, and Period 399 Solution for (a) Enter the known value into 13.6 STRATEGY FOR (B) Since one definition of wavelength is the distance a wave has traveled after one complete cycle—or one period—the values for the wavelength as well as the frequency are given. Therefore, we can use to find the wave velocity. Solution for (b) Enter the known
values into Discussion We could have also used the equation to solve for the wave velocity since we already know the value of the period from our calculation in part (a), and we would come up with the same answer. Practice Problems 7. The frequency of a wave is 10 Hz. What is its period? a. The period of the wave is 100 s. b. The period of the wave is 10 s. c. The period of the wave is 0.01 s. d. The period of the wave is 0.1 s. 8. What is the velocity of a wave whose wavelength is 2 m and whose frequency is 5 Hz? a. 20 m/s b. 2.5 m/s c. 0.4 m/s 10 m/s d. Check Your Understanding 9. What is the amplitude of a wave? a. A quarter of the total height of the wave b. Half of the total height of the wave c. Two times the total height of the wave d. Four times the total height of the wave 10. What is meant by the wavelength of a wave? a. The wavelength is the distance between adjacent identical parts of a wave, parallel to the direction of propagation. b. The wavelength is the distance between adjacent identical parts of a wave, perpendicular to the direction of propagation. c. The wavelength is the distance between a crest and the adjacent trough of a wave, parallel to the direction of propagation. d. The wavelength is the distance between a crest and the adjacent trough of a wave, perpendicular to the direction of propagation. 11. How can you mathematically express wave frequency in terms of wave period? a. b. c. d. 12. When is the wavelength directly proportional to the period of a wave? 400 Chapter 13 • Waves and Their Properties a. When the velocity of the wave is halved b. When the velocity of the wave is constant c. When the velocity of the wave is doubled d. When the velocity of the wave is tripled 13.3 Wave Interaction: Superposition and Interference Section Learning Objectives By the end of this section, you will be able to do the following: • Describe superposition of waves • Describe interference of waves and distinguish between constructive and destructive interference of waves • Describe the characteristics of standing waves • Distinguish reflection from refraction of waves Section Key Terms antinode constructive interference destructive interference inversion nodes reflection refraction standing wave superposition Superposition of Waves Most waves do not look very simple. They
look more like the waves in Figure 13.10, rather than the simple water wave considered in the previous sections, which has a perfect sinusoidal shape. Figure 13.10 These waves result from the superposition of several waves from different sources, producing a complex pattern. (Waterborough, Wikimedia Commons) Most waves appear complex because they result from two or more simple waves that combine as they come together at the same place at the same time—a phenomenon called superposition. Waves superimpose by adding their disturbances; each disturbance corresponds to a force, and all the forces add. If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves, that is, their amplitudes add. Wave Interference The two special cases of superposition that produce the simplest results are pure constructive interference and pure destructive interference. Pure constructive interference occurs when two identical waves arrive at the same point exactly in phase. When waves are exactly in phase, the crests of the two waves are precisely aligned, as are the troughs. Refer to Figure 13.11. Because the disturbances add, the pure constructive interference of two waves with the same amplitude produces a wave that has twice the amplitude of the two individual waves, but has the same wavelength. Access for free at openstax.org. 13.3 • Wave Interaction: Superposition and Interference 401 Figure 13.11 The pure constructive interference of two identical waves produces a wave with twice the amplitude but the same wavelength. Figure 13.12 shows two identical waves that arrive exactly outof phase—that is, precisely aligned crest to trough—producing pure destructive interference. Because the disturbances are in opposite directions for this superposition, the resulting amplitude is zero for pure destructive interference; that is, the waves completely cancel out each other. Figure 13.12 The pure destructive interference of two identical waves produces zero amplitude, or complete cancellation. While pure constructive interference and pure destructive interference can occur, they are not very common because they require precisely aligned identical waves. The superposition of most waves that we see in nature produces a combination of constructive and destructive interferences. Waves that are not results of pure constructive or destructive interference can vary from place to place and time to time. The sound from a stereo, for example, can be loud in one spot and soft in another. The varying loudness means that the sound waves add partially constructively and partially destructively at different locations. A stereo has at least two speakers that create sound waves, and waves
can reflect from walls. All these waves superimpose. An example of sounds that vary over time from constructive to destructive is found in the combined whine of jet engines heard by a stationary passenger. The volume of the combined sound can fluctuate up and down as the sound from the two engines varies in time from constructive to destructive. The two previous examples considered waves that are similar—both stereo speakers generate sound waves with the same amplitude and wavelength, as do the jet engines. But what happens when two waves that are not similar, that is, having different amplitudes and wavelengths, are superimposed? An example of the superposition of two dissimilar waves is shown in Figure 13.13. Here again, the disturbances add and subtract, but they produce an even more complicated-looking wave. The resultant wave from the combined disturbances of two dissimilar waves looks much different than the idealized sinusoidal shape of a periodic wave. 402 Chapter 13 • Waves and Their Properties Figure 13.13 The superposition of nonidentical waves exhibits both constructive and destructive interferences. Virtual Physics Wave Interference Click to view content (http://www.openstax.org/l/28interference) In this simulation, make waves with a dripping faucet, an audio speaker, or a laser by switching between the water, sound, and light tabs. Contrast and compare how the different types of waves behave. Try rotating the view from top to side to make observations. Then experiment with adding a second source or a pair of slits to create an interference pattern. GRASP CHECK In the water tab, compare the waves generated by one drip versus two drips. What happens to the amplitude of the waves when there are two drips? Is this constructive or destructive interference? Why would this be the case? a. The amplitude of the water waves remains same because of the destructive interference as the drips of water hit the surface at the same time. b. The amplitude of the water waves is canceled because of the destructive interference as the drips of water hit the surface at the same time. c. The amplitude of water waves remains same because of the constructive interference as the drips of water hit the surface at the same time. d. The amplitude of water waves doubles because of the constructive interference as the drips of water hit the surface at the same time. Standing Waves Sometimes waves do not seem to move and they appear to just stand in place, vibrating. Such waves are called standing waves and are formed by the

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