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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious .
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if the history of man has changed over the hundreds of thousands of years , why do we still act like animals ( instinct wise ) ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us .
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why are humans just the ones who can build planes ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa .
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what happened to the other species of humans , such as the homo erectus and other species , that did n't happen to us ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us .
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why do things then that no longer live sill have a effect ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e .
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where the makers of these images considered to be nomadic peoples ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken .
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how old is the chauvet-pont-d'arc ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction .
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were the caves used as actual living spaces or were they more temple-like , visited only occasionally ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become .
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would you be able to tell the difference in time if one drawing was done 100 years ago , and then 50 years ago someone used the same peice of charcoal to draw a replica of the first drawing ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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what is the significance of the bear bones , and did they date the child 's foot print from the same period ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame .
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could the style in which these drawings are created be considered an artistic style the same way things like cubism and fauvism ( etc ) are ?
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the oldest art : ornamentation humans make art . we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre . wear patterns suggest that they may have been strung beads . nassarius shell beads found in israel may be more than 100,000 years old and in the blombos cave in south africa , pierced shells and small pieces of ochre ( red haematite ) etched with simple geometric patterns have been found in a 75,000-year-old layer of sediment . the oldest representational art the oldest known representational imagery comes from the aurignacian culture of the upper paleolithic period ( paleolithic means old stone age ) . archeological discoveries across a broad swath of europe ( especially southern france , northern spain , and swabia , in germany ) include over two hundred caves with spectacular aurignacian paintings , drawings and sculpture that are among the earliest undisputed examples of representational image-making . the oldest of these is a 2.4-inch tall female figure carved out of mammoth ivory that was found in six fragments in the hohle fels cave near schelklingen in southern germany . it dates to 35,000 b.c.e . the caves the caves at chauvet-pont-d'arc , lascaux , pech merle , and altamira contain the best known examples of pre-historic painting and drawing . here are remarkably evocative renderings of animals and some humans that employ a complex mix of naturalism and abstraction . archeologists that study paleolithic era humans , believe that the paintings discovered in 1994 , in the cave at chauvet-pont-d'arc in the ardéche valley in france , are more than 30,000 years old . the images found at lascaux and altamira are more recent , dating to approximately 15,000 b.c.e . the paintings at pech merle date to both 25,000 and 15,000 b.c.e . questions what can we really know about the creators of these paintings and what the images originally meant ? these are questions that are difficult enough when we study art made only 500 years ago . it is much more perilous to assert meaning for the art of people who shared our anatomy but had not yet developed the cultures or linguistic structures that shaped who we have become . do the tools of art history even apply ? here is evidence of a visual language that collapses the more than 1,000 generations that separate us , but we must be cautious . this is especially so if we want to understand the people that made this art as a way to understand ourselves . the desire to speculate based on what we see and the physical evidence of the caves is wildly seductive . chauvet-pont-d'arc the cave at chauvet-pont-d'arc is over 1,000 feet in length with two large chambers . carbon samples date the charcoal used to depict the two head-to-head rhinoceroses ( see the image above , bottom right ) to between 30,340 and 32,410 years before 1995 when the samples were taken . the cave 's drawings depict other large animals including horses , mammoths , musk ox , ibex , reindeer , aurochs , megaloceros deer , panther , and owl ( scholars note that these animals were not then a normal part of people 's diet ) . photographs show that the drawing shown above is very carefully rendered but may be misleading . we see a group of horses , rhinos and bison and we see them as a group , overlapping and skewed in scale . but the photograph distorts the way these animal figures would have been originally seen . the bright electric lights used by the photographer create a broad flat scope of vision ; how different to see each animal emerge from the dark under the flickering light cast by a flame . a word of caution in a 2009 presentation at uc san diego , dr. randell white , professor of anthropology at nyu , suggested that the overlapping horses pictured above might represent the same horse over time , running , eating , sleeping , etc . perhaps these are far more sophisticated representations than we have imagined . there is another drawing at chauvet-pont-d'arc that cautions us against ready assumptions . it has been interpreted as depicting the thighs and genitals of a woman but there is also a drawing of a bison and a lion and the images are nearly intertwined . in addition to the drawings , the cave is littered with the skulls and bones of cave bear and the track of a wolf . there is also a foot print thought to have been made by an eight-year-old boy . essay by dr. beth harris and dr. steven zucker additional resources : the cave of chauvet-pont-d'arc a carved female figurine dating to at least 35,000 years ago recovered from caves in the hohle fels region of germany ( video ) lascaux : a visit to the cave lascaux on the metropolitan museum of art 's heilbrunn timeline of art history `` ur-mothers '' in the new yorker
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we do this for many reasons and with whatever technologies are available to us . extremely old , non-representational ornamentation has been found across africa . the oldest firmly-dated example is a collection of 82,000 year old nassarius snail shells found in morocco that are pierced and covered with red ochre .
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if i took a really old painting and put fresh paint over it would it still be a really old painting ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex .
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does anyone really believe that the building of the pyramids `` had extra-terrestrial impetus '' ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court .
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what does it mean by `` rock cut tombs '' ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure .
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i wonder how many years it toke to make a piramaid ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain .
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why do queen , s pyramids have to be built differently ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers .
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if it took about 10 years to build a pyramid would n't that be kind of morbid , for the pharaoh ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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how many blocks are in the pyramid ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain .
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when were the pyramids of giza built , approximately ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed .
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what kind of stone was used ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used .
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how come there is n't a single smooth part of the pyramid left ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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did all the triangular blocks fall out or erode ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain .
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were menkaure , khafre and khufu such special pharaohs that the egyptians built pyramids for them ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain .
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why pyramids for only these three pharaohs ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 .
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why is the builders ' quarters so big ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain .
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did n't carbon dating reveal that the pyramids were actually built from top to bottom ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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( the top stones were older by 1000 years than the lower stones ) if so , how was this possible ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court .
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what was found inside the pyramids when they were explored ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller .
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secondly , if you could please , confirm for me that the tangent slope angles for the meidum and khufu structures are the same : both then have a height in ratio to a circle the circumference of which is equal to the perimeter of the pyramid 's base ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court .
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could the pyramids be a power generator for the area ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection .
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on the map , what are boat pits ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection .
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egyptian scientist ( mostafa mahmoud ) suggested that the ancient egyptians built a zone of zero gravity ( just like we did today ) , what do you think about that guyz ?
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one of the seven wonders of the ancient world the last remaining of the seven wonders of the ancient world , the great pyramids of giza are perhaps the most famous and discussed structures in history . these massive monuments were unsurpassed in height for thousands of years after their construction and continue to amaze and enthrall us with their overwhelming mass and seemingly impossible perfection . their exacting orientation and mind-boggling construction has elicited many theories about their origins , including unsupported suggestions that they had extra-terrestrial impetus . however , by examining the several hundred years prior to their emergence on the giza plateau , it becomes clear that these incredible structures were the result of many experiments , some more successful than others , and represent an apogee in the development of the royal mortuary complex . three pyramids , three rulers the three primary pyramids on the giza plateau were built over the span of three generations by the rulers khufu , khafre , and menkaure . each pyramid was part of a royal mortuary complex that also included a temple at its base and a long stone causeway ( some nearly 1 kilometer in length ) leading east from the plateau to a valley temple on the edge of the floodplain . other ( smaller ) pyramids , and small tombs in addition to these major structures , several smaller pyramids belonging to queens are arranged as satellites . a major cemetery of smaller tombs , known as mastabas ( arabic for ‘ bench ’ in reference to their shape—flat-roofed , rectangular , with sloping sides ) , fills the area to the east and west of the pyramid of khufu and were constructed in a grid-like pattern for prominent members of the court . being buried near the pharaoh was a great honor and helped ensure a prized place in the afterlife . a reference to the sun the shape of the pyramid was a solar reference , perhaps intended as a solidified version of the rays of the sun . texts talk about the sun ’ s rays as a ramp the pharaoh mounts to climb to the sky—the earliest pyramids , such as the step pyramid of djoser at saqqara—were actually designed as a staircase . the pyramid was also clearly connected to the sacred ben-ben stone , an icon of the primeval mound that was considered the place of initial creation . the pyramid was considered a place of regeneration for the deceased ruler . construction many questions remain about the construction of these massive monuments , and theories abound as to the actual methods used . the workforce needed to build these structures is also still much discussed . discovery of a town for workers to the south of the plateau has offered some answers . it is likely that there was a permanent group of skilled craftsmen and builders who were supplemented by seasonal crews of approximately 2,000 conscripted peasants . these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller . essay by dr. amy calvert additional resources egyptian art in the age of the pyramids , the metropolitan museum of art giza 3d giza archives , museum of fine arts , boston building the great pyramid , bbc mark lehner , the complete pyramids , thames and hudson , 2008 .
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these crews were divided into gangs of 200 men , with each group further divided into teams of 20 . experiments indicate that these groups of 20 men could haul the 2.5 ton blocks from quarry to pyramid in about 20 minutes , their path eased by a lubricated surface of wet silt . an estimated 340 stones could be moved daily from quarry to construction site , particularly when one considers that many of the blocks ( such as those in the upper courses ) were considerably smaller .
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it says that 20 men could haul 2.5 tons from the quarry to pyramid in 20 minutes with a lubricated path ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared .
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how do you derive the moment of inertia , using calculus ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated .
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i do not understand how rotational inertia increases with increasing distance of mass ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared .
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what 's the idea behind moment of inertia ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ?
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how does frictional torque affect the angular acceleration ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ?
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like if a frictional torque is applied , where does that go in the equation to find angular acceleration of a rod/disk ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis .
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does the rotational inertia of a particular object differ for different axes of rotation ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis .
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can one object have more than one rotational inertia ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ?
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in exercise 3 , why is distance d equal ( 1+0.75 ) /2 ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia .
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why is n't d equal ( 1-0.75 ) /2 ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 .
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why is the moment of inertia of a ring rotated along its center is smaller than a ring rotated along its diameter ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated .
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how do we derive the rotational inertia of complex objects ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion .
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i am confused whether 'g ' term will come in the inertia equation as i=0.5m ( r2+r2 ) /g or not ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) .
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from the figure 3 , how can we calculate rotational inertia in z axis ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia .
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in exercise 3 , is that the rotational inertia for the big disc mr^2 rather than ( mr^2 ) /2 , since it 's a hollow cylinder ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated .
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if rotational inertia increases , does rotational velocity increase or decrease ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation .
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how does this explain a fulcrum when the further the object is from the center , the less force needed to apply to cause an object to move ?
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated . it is a scalar value which tells us how difficult it is to change the rotational velocity of the object around a given rotational axis . rotational inertia plays a similar role in rotational mechanics to mass in linear mechanics . indeed , the rotational inertia of an object depends on its mass . it also depends on the distribution of that mass relative to the axis of rotation . when a mass moves further from the axis of rotation it becomes increasingly more difficult to change the rotational velocity of the system . intuitively , this is because the mass is now carrying more momentum with it around the circle ( due to the higher speed ) and because the momentum vector is changing more quickly . both of these effects depend on the distance from the axis . rotational inertia is given the symbol $ i $ . for a single body such as the tennis ball of mass $ m $ ( shown in figure 1 ) , rotating at radius $ r $ from the axis of rotation the rotational inertia is $ i = mr^2 $ and consequently rotational inertia has si units of $ \mathrm { kg\cdot m^2 } $ . rotational inertia is also commonly known as moment of inertia . it is also sometimes called the second moment of mass ; the 'second ' here refers to the fact that it depends on the length of the moment arm squared . how does rotational inertia relate to newton 's 2ⁿᵈ law ? rotational inertia takes the place of mass in the rotational version of newton 's 2ⁿᵈ law . consider a mass $ m $ attached to one end of a massless rod . the other end of the rod is hinged so that the system can rotate about the central hinge point as shown in figure 2 . we now start rotating the system by applying a tangential force $ f_t $ to the mass . from newton ’ s 2ⁿᵈ law , $ f_t = m a_t $ . this can also be written as $ f_t = m ( r \alpha ) $ . newton 's 2ⁿᵈ law relates force to acceleration . in rotational mechanics torque $ \tau $ takes the place of force . multiplying both sides by the radius gives the expression we want . $ \begin { align } f_t r & amp ; = m ( r \alpha ) r\ \tau & amp ; = m r^2 \alpha \ \tau & amp ; = i \alpha\end { align } $ this expression can now be used to find the behavior of a mass in response to a known torque . exercise 1a : a motor capable of producing a constant torque of $ 100~\mathrm { nm } $ and a maximum rotation speed of $ 150~\mathrm { rad/s } $ is connected to a flywheel with rotational inertia $ 0.1~\mathrm { kg m^2 } $ . what angular acceleration will the flywheel experience as the motor is switched on ? exercise 1b : how long will the flywheel take to reach a steady speed if starting from rest ? how can we calculate rotational inertia in general ? often mechanical systems are made of many masses connected together , or complex shapes . it is possible to calculate the total rotational inertia for any shape about any axis by summing the rotational inertia of each mass . $ \begin { align } i & amp ; = m_1 r_1^2 + m_2 r_2^2 + \ldots \ & amp ; = \sigma m_i r_i^2 \end { align } $ exercise 2a : consider the object shown in figure 3 ( a ) . what is its rotational inertia ? exercise 2b : consider the alternate case of figure 3 ( b ) of the same system rotating about a different axis . what would you expect the rotational inertia to be in this case ? how can we find the rotational inertia of complex shapes ? for more complicated shapes , it is generally necessary to use calculus to find the rotational inertia . however , for many common geometric shapes it is possible to find tables of equations for the rotational inertia in textbooks or other sources . these typically give the moment of inertia for a shape rotated about its centroid ( which often corresponds with the shapes center of mass ) . for example , the rotational inertia of a solid cylinder with radius $ r $ rotated about a central axis is $ i = \frac { 1 } { 2 } m r^2 $ and for a hollow cylinder with inner and outer radii $ r_i $ and $ r_o $ respectively , $ i = \frac { m ( r_i^2 + r_o^2 ) } { 2 } $ expressions for other simple shapes are shown in figure 4 . complex shapes can often be represented as combinations of simple shapes for which there exists a known equation for rotational inertia . we can then combine these rotational inertia to find that of the composite object . the problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape . we can account for this using the parallel axis theorem . the parallel axis theorem allows us to find the moment of inertia of an object about a point $ o $ as long as we known the moment of inertia of the shape around its centroid $ c $ , mass $ m $ and distance $ d $ between points $ o $ and $ c $ . $ \boxed { i_o = i_c + md^2 } $ exercise 3 : if the shape shown in figure 5 is made by welding three $ 10~\mathrm { mm } $ thick steel discs ( each with mass $ 50~\mathrm { kg } $ ) to a steel ring with mass $ 100~\mathrm { kg } $ . if rotated about a central axis ( out of the page ) , what is the rotational inertia of the object ? where else does rotational inertia come up in physics ? rotational inertia is important in almost all physics problems that involve mass in rotational motion . it is used to calculate angular momentum and allows us to explain ( via conservation of angular momentum ) how rotational motion changes when the distribution of mass changes . it also is needed to find the energy which is stored as rotational kinetic energy in a spinning flywheel .
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what is rotational inertia ? rotational inertia is a property of any object which can be rotated .
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what are the units for rotational inertia ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ .
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would 0+0i still be a complex number ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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$ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us .
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what about questions like the square root of -75 times the square root of -2 ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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$ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more !
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in challenge problem 2 , is n't ( 1 + 3i ) ^2 equal to ( 1 + 9i^2 ) = ( 1 + 9* ( -1 ) ) = ( 1 - 9 ) = -8 ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful .
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why is n't dividing complex and imaginary numbers here ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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$ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more !
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in the last problem , how would i know whether to write 3i^2 or 3^2 i^2 ?
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a complex number is any number that can be written as $ \greend { a } +\blued { b } i $ , where $ i $ is the imaginary unit and $ \greend { a } $ and $ \blued { b } $ are real numbers . when multiplying complex numbers , it 's useful to remember that the properties we use when performing arithmetic with real numbers work similarly for complex numbers . sometimes , thinking of $ i $ as a variable , like $ x $ , is helpful . then , with just a few adjustments at the end , we can multiply just as we 'd expect . let 's take a closer look at this by walking through several examples . multiplying a real number by a complex number example multiply $ -4 ( 13+5i ) $ . write the resulting number in the form of $ a+bi $ . solution if your instinct tells you to distribute the $ -4 $ , your instinct would be right ! let 's do that ! $ \begin { align } \teald { -4 } ( 13+5i ) & amp ; =\teald { -4 } ( 13 ) +\teald { ( -4 ) } ( 5i ) \ \ & amp ; =-52-20i \end { align } $ and that 's it ! we used the distributive property to multiply a real number by a complex number . let 's try something a little more complicated . multiplying a pure imaginary number by a complex number example multiply $ 2i ( 3-8i ) $ . write the resulting number in the form of $ a+bi $ . solution again , let 's start by distributing the $ 2i $ to each term in the parentheses . $ \begin { align } \teald { 2i } ( 3-8i ) & amp ; =\teald { 2i } ( 3 ) -\teald { 2i } ( 8i ) \ \ & amp ; =6i-16i^2 \end { align } $ at this point , the answer is not of the form $ a+bi $ since it contains $ i^2 $ . however , we know that $ \goldd { i^2=-1 } $ . let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more ! what follows is the more typical case that you 'll see when you 're asked to multiply complex numbers . multiplying two complex numbers example multiply $ ( 1+4i ) ( 5+i ) $ . write the resulting number in the form of $ a+bi $ . solution in this example , some find it very helpful to think of $ i $ as a variable . in fact , the process of multiplying these two complex numbers is very similar to multiplying two binomials ! multiply each term in the first number by each term in the second number . $ \begin { align } ( \teald { 1 } +\maroond { 4i } ) ( 5+i ) & amp ; = ( \teald { 1 } ) ( 5 ) + ( \teald { 1 } ) ( i ) + ( \maroond { 4i } ) ( 5 ) + ( \maroond { 4i } ) ( i ) \ \ & amp ; =5+i+20i+4i^2\ \ & amp ; =5+21i+4i^2 \end { align } $ since $ \goldd { i^2=-1 } $ , we can replace $ i^2 $ with $ -1 $ to obtain the desired form of $ a+bi $ . $ \begin { align } \phantom { ( \teald { 1 } \maroond { -5 } i ) ( -6+i ) } & amp ; =5+21i+4\goldd { i^2 } \ \ & amp ; =5+21i+4 ( \goldd { -1 } ) \ \ & amp ; =5+21i-4\ \ & amp ; =1+21i \end { align } $ check your understanding problem 3 problem 4 problem 5 problem 6 challenge problems problem 1 problem 2
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let 's substitute and see where that gets us . $ \begin { align } \phantom { \teald { 2i } ( 3-8i ) } & amp ; =6i-16\goldd { i^2 } \ \ & amp ; =6i-16 ( \goldd { -1 } ) \ \ & amp ; =6i+16\ \end { align } $ using the commutative property , we can write the answer as $ 16+6i $ , and so we have that $ 2i ( 3-8i ) =16+6i $ . check your understanding problem 1 problem 2 excellent ! we 're now ready to step it up even more !
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how to find a & b when z=a+bi and z^2=8+6i ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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what were the people of the kingdom of benin called ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin .
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is benin a separate country and a city in nigeria ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin .
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what happened to the monarchy of benin ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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why has the artifacts have to be in a different museum besides nigeria 's ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy .
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how did these peoples record their history ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves .
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why is britain involved in about every country in africa ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin .
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is benin close to togo ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin .
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what happened to the region of the benin city after the british intervention ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast .
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did the britiish rule in nigeria ?
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until the late 19th century , one of the major powers in west africa was the kingdom of benin in what is now southwest nigeria . when european merchant ships began to visit west africa from the 15th century onwards , benin came to control the trade between the inland peoples and the europeans on the coast . the kingdom of benin was also well known to european traders and merchants during the 16th and 17th centuries , when it became wealthy partly due to trading in slaves . a vivid picture when the british tried to expand their own trade in the 19th century , the benin people killed their envoys . so in 1897 the british sent an armed expedition which captured the king of benin , destroyed his palace and took away large quantities of sculpture and regalia , including works in wood , ivory and especially brass . some of these things came from royal altars for the king ’ s ancestors , but among them were a large number of cast brass plaques made to decorate the wooden pillars of the palace . these had been left in the palace storerooms while part of the palace was being rebuilt . as it later emerged , most of them were probably made between about 1550 - 1650 , the people and scenes that they show are so many and varied that they give a vivid picture of the court and kingdom of that time . the plaques were most sought after and were bought by museums across europe and america—you can see the plaques at the british museum , in chicago , vienna , paris and a large collection can be viewed in berlin . a sensation the arrival and the reception of the bronze plaques caused a sensation in europe . scholars struggled to understand how african craftsmen could have made such works of art , putting forward some wild theories to explain them . quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin . they do not show how the ordinary people lived in the villages outside the city as farmers , growing their yams and vegetables in gardens cleared from the tropical forest . nor do they show how most of the townspeople lived , employed in crafts such as the making of the brass plaques themselves . and most striking of all , there are no women or children shown in the plaques , which means that more than half of the people of the king ’ s court are not shown . many of the brass plaques from the king ’ s palace show images of portuguese men and they seem to have been made during the 16th and 17th centuries as their costumes show . although benin had no gold to offer , they supplied the portuguese with pepper , ivory , leopard skins and people , who were taken as slaves to work elsewhere in africa and in the portuguese colonies in brazil . many of these people were captives taken in the wars in which the benin people conquered their neighbors far and wide and made them part of the kingdom , or they were sent by the conquered local chiefs as tribute to the king . © trustees of the british museum
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quickly , however , research showed that the benin bronzes were entirely west african creations without european influence , and they transformed european understanding of african history . the plaques when the son of the deposed king revived the benin monarchy in 1914 , now under british rule , he did his best to restore the palace and continue the ancient traditions of the benin monarchy . because these traditions are followed in the modern city of benin , it is still possible to recognize many of the scenes cast in brass by benin artists about five hundred years ago . as decorations for the halls of the king ’ s palace , the plaques were designed to proclaim and glorify the prestige of the king , his status and achievements , so they give an informative but very one-sided view of the kingdom of benin .
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is benin 's government still run by a monarchy ?
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italian trader at the court of kublai khan at the height of the mongol empire , marco polo served emperor kublai khan in china and returned to venice to write an account of his experiences that would give europeans some of their earliest information about china . background in the 13th century , people who lived in venice , italy , believed that the sun revolved around the earth and that creation occurred exactly 4,484 years before rome was founded . as christians , they considered jerusalem , the place of jesus ’ s crucifixion , to be the so-called navel of the world , and their maps portrayed this . marco polo was born in venice , or possibly croatia , in 1254 . located on the eastern coast of italy , venice served as a gateway to the riches of asia during this era of increasing trade . goods flowed like water through the city . ships from around the eastern mediterranean docked at its port . merchants and traders set sail from venice for constantinople ( now istanbul ) and the black sea to fetch goods from russia and from merchants who traveled the silk roads , a system of trading routes to and from china that crossed the mountains and deserts of central asia . at the time of marco ’ s birth , his father , niccolo , and two uncles , all merchants , were away trading . supposedly they were visiting cities on the black sea , but their adventures had actually taken them all the way to the mongol capital of china , khanbaliq ( city of the khan ) . there they had an audience with the most powerful ruler of the day , kublai khan , grandson of the founding emperor , genghis khan . when the three polo men returned to venice after an absence of 16 years , niccolo found that his wife had died and that he had a 15-year-old son , marco , whom he did not know existed . travels two years later , in 1271 , niccolo polo and his brother , maffeo , set off again , taking the 17-year-old marco with them . this time they aimed directly for the court of kublai khan , to bring him documents from the pope and holy oil from jerusalem that he had requested . even with a gold passport from kublai khan , which enabled the travelers to use lodgings and horses posted by the mongols along the silk road routes , they took three and a half years to arrive . upon reaching the summer palace of kublai khan in 1275 , niccolo presented his son and offered him in service to the emperor . a talented young man , marco had learned several languages along the way , including mongolian ( though not chinese ) , and had mastered four written alphabets . two years before marco ’ s arrival , kublai khan had completed the conquest of all parts of china and needed non-mongol administrators in areas that resisted having mongol authorities . marco took on various sorts of diplomatic and administrative roles for the emperor from his base in dadu , which kublai khan built next to khanbaliq . both dadu and khanbaliq stood at what is now beijing . after more than 16 years in china , the polos begged permission from kublai khan to return home to venice . apparently they had proved so useful to the khan that he did not want them to leave . finally , he agreed for them to escort a mongolian princess , cogatin , to become the bride of a persian khan ; thus they headed back west . this time they traveled by sea in chinese ships and , after many difficulties , succeeded in delivering the princess . before they could reach venice , however , kublai khan died on february 18 , 1294 , which allowed local rulers to reassert themselves and demand payment from traders . consequently , the polos were forced to hand over 4,000 byzantine coins , a significant portion of their fortune , to the local government of a city on the black sea . return the polos returned to venice in 1295 , having been away 24 years . their enthusiastic biographer told stories , which may have been gossip , that when they returned they were wearing mongolian clothing and could hardly remember their native language . their relatives had thought them long dead . but when they produced a small fortune in gems ( rubies , sapphires , garnets , diamonds , and emeralds ) , which had been sewn into the hems of their mongolian garments , they were warmly welcomed . soon venice was at war with its rival city-state , genoa , on the west coast of italy . as was custom for a wealthy merchant , marco polo financed his own war galley . he was captured during a naval battle and ended up in prison in genoa . by chance , one of his cellmates , rusticello from pisa , had experience writing romantic novels . as polo entertained everyone with his tales of traveling to china , rusticello wrote them down in a french dialect . this is how polo ’ s accounts , europe ’ s primary source of information about china until the 19th century , came into existence . in 1299 genoa and venice declared peace ; polo was released and returned to venice to marry donata badoer . the couple had three daughters in quick succession . he spent his remaining days as a businessman , working from home . he died there at almost 70 years of age , on january 8 , 1324 , and was buried under the church of san lorenzo , though his tomb has now vanished . marco polo ’ s book polo might have been forgotten had his book , the travels of marco polo , not engaged widespread interest . it could be circulated only one copy at a time , since printing in europe did not begin until almost 200 years later . about 120 to 140 early manuscripts — hand-printed and fragmentary versions of the travels — survive , and every one of them is different . the earliest readers were scholars , monks , and noblemen . soon translations of the travels appeared , in venetian , german , english , catalan , argonese , gaelic , and latin . it took more than a century for the book to become part of mainstream european consciousness . few texts have provoked more controversy than the travels of marco polo . the authorship is not clear — is it polo or rusticello ? sometimes the text is in the first-person voice , sometimes in the third-person . how much of the text is based on polo ’ s firsthand experience and how much did the author ( s ) insert secondhand accounts by others ? certainly it ’ s a mix . what was reported seemed so bizarre to stay-at-home europeans that the readers often assumed that everything was made up . yet historians have largely confirmed the facts in polo ’ s account of the height of the mongol dynasty . polo proved an engaging storyteller . he found mongolian customs fascinating and reported them enthusiastically , such as the use of paper for money and the burning of coal for heat ( see excerpts below ) . paper money had been utilized in china for several hundred years , and coal had been burned in parts of china since the beginning of agriculture . polo also missed a few unfamiliar practices , notably the books being sold in quinsa ( now hangzhou ) , the capital city of the earlier song dynasty in southern china . books were widely available there because they were printed with moveable type made of wood , clay , or tin . moveable type was missing in europe until 1440 , when johannes gutenberg , a german printer , invented it there . when christopher columbus set sail on august 3 , 1492 , hoping to find a route by sea to china , he carried with him a heavily annotated copy of the travels of marco polo , expecting it to be useful . from the travels of marco polo : book 2 , chapter 18 of the kind of paper money issued by the grand khan , and made to pass current throughout his dominions in this city of cambalu [ another spelling for khanbaliq ] is the mint of the grand khan , who may truly be said to possess the secret of the alchemists , as he has the art of producing money by the following process . he causes bark to be stripped from those mulberry-trees the leaves of which are used for feeding silk-worms , and takes from it that thin inner ring which lies between the coarser bark and the wood of the tree . this being steeped , and afterwards pounded in a mortar , until reduced to a pulp , is made into paper , resembling that which is made from cotton , but quite black . when ready for use , he has it cut into pieces of money of different sizes , nearly square , but somewhat longer than they are wide ... the coinage of this paper money is authenticated with as much form and ceremony as if it were actually of pure gold or silver ; for to each note a number of officers , specially appointed , not only subscribe their names , but affix their signets also ; and when this has been regularly done by the whole of them , the principal officer , deputed by his majesty , having dipped into vermilion the royal seal committed to his custody , stamps with it the piece of paper , so that the form of the seal tinged with the vermilion remains impressed upon it , by which it receives full authenticity as current money , and the act of counterfeiting it is punished as a capital offence . when thus coined in large quantities , this paper currency is circulated in every part of the grand khan ’ s dominions ; nor dares any person , at the peril of his life , refuse to accept it in payment . all his subjects receive it without hesitation , because wherever their business may call them , they can dispose of it again in the purchase of merchandise they may have occasion for ; such as pearls , jewels , gold , or silver . with it , in short , every article may be procured ... all his majesty ’ s armies are paid with this currency , which is to them of the same value as if it were gold or silver . upon these grounds , it may certainly be affirmed that the grand khan has a more extensive command of treasure than any other sovereign in the universe . ( pp . 145–147 ) book 2 , chapter 23 of the kind of wine made in the province of cathay — and of the stones used there for burning in the manner of charcoal the greater part of the inhabitants of the province of cathay [ now china ] drink a sort of wine made from rice mixed with a variety of spices and drugs . this beverage , or wine as it may be termed , is so good and well flavoured that they do not wish for better . it is clear , bright , and pleasant to the taste , and being made very hot , has the quality of inebriating sooner than any other . throughout this province there is found a sort of black stone , which they dig out of the mountains , where it runs in veins . when lighted , it burns like charcoal , and retains the fire much better than wood ; inso- much that it may be preserved during the night , and in the morning be found still burning . these stones do not flame , excepting a little when first lighted , but during their ignition give out a considerable heat . it is true there is no scarcity of wood in the country , but the multitude of inhabitants is so immense , and their stoves and baths , which they are continually heating , so numerous , that the quantity could not supply the demand ; for there is no person who does not frequent the warm bath at least three times in the week , and during the winter daily , if it is in their power . every man of rank or wealth has one in his house for his own use ; and the stock of wood must soon prove inadequate to such consumption ; whereas these stones may be had in the greatest abundance , and at a cheap rate . ( p. 155 ) by cynthia stokes brown for further discussion what are some similarities and differences between ibn battuta and marco polo ’ s travels ? share one similarity and one difference in the questions area below .
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few texts have provoked more controversy than the travels of marco polo . the authorship is not clear — is it polo or rusticello ? sometimes the text is in the first-person voice , sometimes in the third-person . how much of the text is based on polo ’ s firsthand experience and how much did the author ( s ) insert secondhand accounts by others ?
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could it be mijiu , a clear rice wine from china which is also drank warm , like japanese sake is drank warm sometimes ?
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italian trader at the court of kublai khan at the height of the mongol empire , marco polo served emperor kublai khan in china and returned to venice to write an account of his experiences that would give europeans some of their earliest information about china . background in the 13th century , people who lived in venice , italy , believed that the sun revolved around the earth and that creation occurred exactly 4,484 years before rome was founded . as christians , they considered jerusalem , the place of jesus ’ s crucifixion , to be the so-called navel of the world , and their maps portrayed this . marco polo was born in venice , or possibly croatia , in 1254 . located on the eastern coast of italy , venice served as a gateway to the riches of asia during this era of increasing trade . goods flowed like water through the city . ships from around the eastern mediterranean docked at its port . merchants and traders set sail from venice for constantinople ( now istanbul ) and the black sea to fetch goods from russia and from merchants who traveled the silk roads , a system of trading routes to and from china that crossed the mountains and deserts of central asia . at the time of marco ’ s birth , his father , niccolo , and two uncles , all merchants , were away trading . supposedly they were visiting cities on the black sea , but their adventures had actually taken them all the way to the mongol capital of china , khanbaliq ( city of the khan ) . there they had an audience with the most powerful ruler of the day , kublai khan , grandson of the founding emperor , genghis khan . when the three polo men returned to venice after an absence of 16 years , niccolo found that his wife had died and that he had a 15-year-old son , marco , whom he did not know existed . travels two years later , in 1271 , niccolo polo and his brother , maffeo , set off again , taking the 17-year-old marco with them . this time they aimed directly for the court of kublai khan , to bring him documents from the pope and holy oil from jerusalem that he had requested . even with a gold passport from kublai khan , which enabled the travelers to use lodgings and horses posted by the mongols along the silk road routes , they took three and a half years to arrive . upon reaching the summer palace of kublai khan in 1275 , niccolo presented his son and offered him in service to the emperor . a talented young man , marco had learned several languages along the way , including mongolian ( though not chinese ) , and had mastered four written alphabets . two years before marco ’ s arrival , kublai khan had completed the conquest of all parts of china and needed non-mongol administrators in areas that resisted having mongol authorities . marco took on various sorts of diplomatic and administrative roles for the emperor from his base in dadu , which kublai khan built next to khanbaliq . both dadu and khanbaliq stood at what is now beijing . after more than 16 years in china , the polos begged permission from kublai khan to return home to venice . apparently they had proved so useful to the khan that he did not want them to leave . finally , he agreed for them to escort a mongolian princess , cogatin , to become the bride of a persian khan ; thus they headed back west . this time they traveled by sea in chinese ships and , after many difficulties , succeeded in delivering the princess . before they could reach venice , however , kublai khan died on february 18 , 1294 , which allowed local rulers to reassert themselves and demand payment from traders . consequently , the polos were forced to hand over 4,000 byzantine coins , a significant portion of their fortune , to the local government of a city on the black sea . return the polos returned to venice in 1295 , having been away 24 years . their enthusiastic biographer told stories , which may have been gossip , that when they returned they were wearing mongolian clothing and could hardly remember their native language . their relatives had thought them long dead . but when they produced a small fortune in gems ( rubies , sapphires , garnets , diamonds , and emeralds ) , which had been sewn into the hems of their mongolian garments , they were warmly welcomed . soon venice was at war with its rival city-state , genoa , on the west coast of italy . as was custom for a wealthy merchant , marco polo financed his own war galley . he was captured during a naval battle and ended up in prison in genoa . by chance , one of his cellmates , rusticello from pisa , had experience writing romantic novels . as polo entertained everyone with his tales of traveling to china , rusticello wrote them down in a french dialect . this is how polo ’ s accounts , europe ’ s primary source of information about china until the 19th century , came into existence . in 1299 genoa and venice declared peace ; polo was released and returned to venice to marry donata badoer . the couple had three daughters in quick succession . he spent his remaining days as a businessman , working from home . he died there at almost 70 years of age , on january 8 , 1324 , and was buried under the church of san lorenzo , though his tomb has now vanished . marco polo ’ s book polo might have been forgotten had his book , the travels of marco polo , not engaged widespread interest . it could be circulated only one copy at a time , since printing in europe did not begin until almost 200 years later . about 120 to 140 early manuscripts — hand-printed and fragmentary versions of the travels — survive , and every one of them is different . the earliest readers were scholars , monks , and noblemen . soon translations of the travels appeared , in venetian , german , english , catalan , argonese , gaelic , and latin . it took more than a century for the book to become part of mainstream european consciousness . few texts have provoked more controversy than the travels of marco polo . the authorship is not clear — is it polo or rusticello ? sometimes the text is in the first-person voice , sometimes in the third-person . how much of the text is based on polo ’ s firsthand experience and how much did the author ( s ) insert secondhand accounts by others ? certainly it ’ s a mix . what was reported seemed so bizarre to stay-at-home europeans that the readers often assumed that everything was made up . yet historians have largely confirmed the facts in polo ’ s account of the height of the mongol dynasty . polo proved an engaging storyteller . he found mongolian customs fascinating and reported them enthusiastically , such as the use of paper for money and the burning of coal for heat ( see excerpts below ) . paper money had been utilized in china for several hundred years , and coal had been burned in parts of china since the beginning of agriculture . polo also missed a few unfamiliar practices , notably the books being sold in quinsa ( now hangzhou ) , the capital city of the earlier song dynasty in southern china . books were widely available there because they were printed with moveable type made of wood , clay , or tin . moveable type was missing in europe until 1440 , when johannes gutenberg , a german printer , invented it there . when christopher columbus set sail on august 3 , 1492 , hoping to find a route by sea to china , he carried with him a heavily annotated copy of the travels of marco polo , expecting it to be useful . from the travels of marco polo : book 2 , chapter 18 of the kind of paper money issued by the grand khan , and made to pass current throughout his dominions in this city of cambalu [ another spelling for khanbaliq ] is the mint of the grand khan , who may truly be said to possess the secret of the alchemists , as he has the art of producing money by the following process . he causes bark to be stripped from those mulberry-trees the leaves of which are used for feeding silk-worms , and takes from it that thin inner ring which lies between the coarser bark and the wood of the tree . this being steeped , and afterwards pounded in a mortar , until reduced to a pulp , is made into paper , resembling that which is made from cotton , but quite black . when ready for use , he has it cut into pieces of money of different sizes , nearly square , but somewhat longer than they are wide ... the coinage of this paper money is authenticated with as much form and ceremony as if it were actually of pure gold or silver ; for to each note a number of officers , specially appointed , not only subscribe their names , but affix their signets also ; and when this has been regularly done by the whole of them , the principal officer , deputed by his majesty , having dipped into vermilion the royal seal committed to his custody , stamps with it the piece of paper , so that the form of the seal tinged with the vermilion remains impressed upon it , by which it receives full authenticity as current money , and the act of counterfeiting it is punished as a capital offence . when thus coined in large quantities , this paper currency is circulated in every part of the grand khan ’ s dominions ; nor dares any person , at the peril of his life , refuse to accept it in payment . all his subjects receive it without hesitation , because wherever their business may call them , they can dispose of it again in the purchase of merchandise they may have occasion for ; such as pearls , jewels , gold , or silver . with it , in short , every article may be procured ... all his majesty ’ s armies are paid with this currency , which is to them of the same value as if it were gold or silver . upon these grounds , it may certainly be affirmed that the grand khan has a more extensive command of treasure than any other sovereign in the universe . ( pp . 145–147 ) book 2 , chapter 23 of the kind of wine made in the province of cathay — and of the stones used there for burning in the manner of charcoal the greater part of the inhabitants of the province of cathay [ now china ] drink a sort of wine made from rice mixed with a variety of spices and drugs . this beverage , or wine as it may be termed , is so good and well flavoured that they do not wish for better . it is clear , bright , and pleasant to the taste , and being made very hot , has the quality of inebriating sooner than any other . throughout this province there is found a sort of black stone , which they dig out of the mountains , where it runs in veins . when lighted , it burns like charcoal , and retains the fire much better than wood ; inso- much that it may be preserved during the night , and in the morning be found still burning . these stones do not flame , excepting a little when first lighted , but during their ignition give out a considerable heat . it is true there is no scarcity of wood in the country , but the multitude of inhabitants is so immense , and their stoves and baths , which they are continually heating , so numerous , that the quantity could not supply the demand ; for there is no person who does not frequent the warm bath at least three times in the week , and during the winter daily , if it is in their power . every man of rank or wealth has one in his house for his own use ; and the stock of wood must soon prove inadequate to such consumption ; whereas these stones may be had in the greatest abundance , and at a cheap rate . ( p. 155 ) by cynthia stokes brown for further discussion what are some similarities and differences between ibn battuta and marco polo ’ s travels ? share one similarity and one difference in the questions area below .
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he died there at almost 70 years of age , on january 8 , 1324 , and was buried under the church of san lorenzo , though his tomb has now vanished . marco polo ’ s book polo might have been forgotten had his book , the travels of marco polo , not engaged widespread interest . it could be circulated only one copy at a time , since printing in europe did not begin until almost 200 years later .
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was it marco polo who gave to chinese ceramics name `` porcelain '' , said to derive from italian `` porcellana '' or cowrie shell , please ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity .
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why is it that only the end product blocks the earliest step of the pathway and not the intermediate products of the metabolic pathway ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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what is an allosteric activator ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site .
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whats the difference between non competitive inhibition and allosteric regulation ( involving inhibitor ) ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate .
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does the non competitive inhibitors actually change the shape of the active site ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors .
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what does it mean to `` stabilize '' the enzyme ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors .
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the competitive inhibator has a limit of time in the enzyme or make the enzyme useless ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate .
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is the substrate here the inhibitor/activator ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well .
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what is 'immobilising enzymes ' ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
|
in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme .
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and why some says that the 'immobilising enzymes ' are more tolerant to temperature and ph and does not denature easily ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site .
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what is a good example of allosteric regulation ( it can be inhibition or activation ) , its pathway and the name of the enzyme involved ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment .
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can a non competitive inhibitor also be an irreversible inhibitor ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell .
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what is a kinase about , what it is ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle .
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why does vitamin c look like a monosaccharide ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well .
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so , is it that , in the case of inhibition , conformational change happens only to allosteric enzymes ( because they have multiple subunits , each undergoing a conformational change at the active site ) ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors .
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what do an activator do to boost the activity of an enzyme ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available .
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what is an example of a noncompetitive inhibitor ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) .
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does this mean that there is allosteric competitive inhibition and allosteric non-competitive inhibition ?
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introduction the cells of your body are capable of making many different enzymes , and at first you might think : great , let ’ s crank all of those enzymes up and metabolize as fast as possible ! as it turns out , though , you really don ’ t want to produce and activate all of those enzymes at the same time , or in the same cell . needs and conditions vary from cell to cell and change in individual cells over time . for instance , stomach cells need different enzymes than fat storage cells , skin cells , blood cells , or nerve cells . also , a digestive cell works much harder to process and break down nutrients during the time that follows a meal as compared with many hours after a meal . as these cellular demands and conditions changes , so do the amounts and functionality of different enzymes . because enzymes guide and regulate the metabolism of a cell , they tend to be carefully controlled . in this article , we ’ ll take a look at factors that can affect or control enzyme activity . these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors . many enzymes are only active when bound to non-protein helper molecules known as cofactors . compartmentalization . storing enzymes in specific compartments can keep them from doing damage or provide the right conditions for activity . feedback inhibition . key metabolic enzymes are often inhibited by the end product of the pathway they control ( feedback inhibition ) . in the rest of this article , we 'll examine these factors one at a time , seeing how each can affect enzyme activity . regulatory molecules enzymes can be regulated by other molecules that either increase or reduce their activity . molecules that increase the activity of an enzymes are called activators , while molecule that decrease activity of an enzyme are called inhibitors . there are many kinds of molecules that block or promote enzyme function , and that affect enzyme function by different routes . competitive vs. noncompetitive in many well-studied cases , an activator or inhibitor 's binding is reversible , meaning that the molecule does n't permanently attach to the enzyme . some important types of drugs act as reversible inhibitors . for example , the drug tipranivir , which is used to treat hiv , is a reversible inhibitor. $ ^1 $ it blocks activity of a viral enzyme that helps the virus make more copies of itself . reversible inhibitors are divided into groups based on their binding behavior . we wo n't discuss all of the types here , but we will look at two important groups : competitive and noncompetitive inhibitors . an inhibitor may bind to an enzyme and block binding of the substrate , for example , by attaching to the active site . this is called competitive inhibition , because the inhibitor “ competes ” with the substrate for the enzyme . that is , only the inhibitor or the substrate can be bound at a given moment . in noncompetitive inhibition , the inhibitor does n't block the substrate from binding to the active site . instead , it attaches at another site and blocks the enzyme from doing its job . this inhibition is said to be `` noncompetitive '' because the inhibitor and substrate can both be bound at the same time . competitive and non-competitive inhibitors can be told apart by how they affect an enzyme 's activity at different substrate concentrations . if an inhibitor is competitive , it will decrease reaction rate when there 's not much substrate , but can be `` out-competed '' by lots of substrate . that is , the enzyme can still reach its maximum reaction rate given enough substrate . in that case , almost all the active sites of almost all the enzyme molecules will be occupied by the substrate rather than the inhibitor . if an inhibitor is noncompetitive , the enzyme-catalyzed reaction will never reach its normal maximum rate even with a lot of substrate . this is because the enzyme molecules with the noncompetitive inhibitor bound are `` poisoned '' and ca n't do their job , regardless of how much substrate is available . on a graph of reaction velocity ( y-axis ) at different substrate concentrations ( x-axis ) , you can tell these two types of inhibitors apart by the shape of the curves : not familiar with this type of graph ? no worries ! the basics of enzyme kinetics graphs article has a step-by-step walkthrough . allosteric regulation allosteric regulation , broadly speaking , is just any form of regulation where the regulatory molecule ( an activator or inhibitor ) binds to an enzyme someplace other than the active site . the place where the regulator binds is called the allosteric site . pretty much all cases of noncompetitive inhibition ( along with some cases of competitive inhibition , the ones where the inhibitor binds elsewhere than the active site ) are forms of allosteric regulation . however , some enzymes that are allosterically regulated have a set of unique properties that set them apart . these enzymes , which include some of our key metabolic regulators , are often given the name of allosteric enzymes $ ^2 $ . allosteric enzymes typically have multiple active sites located on different protein subunits . when an allosteric inhibitor binds to an enzyme , all active sites on the protein subunits are changed slightly so that they work less well . there are also allosteric activators . some allosteric activators bind to locations on an enzyme other than the active site , causing an increase in the function of the active site . also , in a process called cooperativity , the substrate itself can serve as an allosteric activator : when it binds to one active site , the activity of the other active sites goes up. $ ^ { 3 } $ this is considered allosteric regulation because the substrate affects active sites far from its binding site . cofactors and coenzymes many enzymes don ’ t work optimally , or even at all , unless bound to other non-protein helper molecules called cofactors . these may be attached temporarily to the enzyme through ionic or hydrogen bonds , or permanently through stronger covalent bonds.common cofactors include inorganic ions such as iron $ \text { ( fe } ^ { 2+ } ) $ and magnesium $ ( \text { mg } ^ { 2+ } ) $ . for example , the enzyme that builds dna molecules , dna polymerase , requires magnesium ions to function. $ ^4 $ coenzymes are a subset of cofactors that are organic ( carbon-based ) molecules . the most common sources of coenzymes are dietary vitamins . some vitamins are precursors to coenzymes and others act directly as coenzymes . for example , vitamin c is a coenzyme for several enzymes that take part in building the protein collagen , a key part of connective tissue . enzyme compartmentalization enzymes are often compartmentalized ( stored in a specific part of the cell where they do their job ) -- for instance , in a particular organelle . compartmentalization means that enzymes needed for specific processes can be kept in the places where they act , ensuring they can find their substrates readily , do n't damage the cell , and have the right microenvironment to work well . for instance , digestive enzymes of the lysosome work best at a ph around $ 5.0 $ , which is found in the acidic interior of the lysosome ( but not in the cytosol , which has a ph of about $ 7.2 $ ) . lysosomal enzymes have low activity at the ph of the cytosol , which may serve as `` insurance '' for the cell : even if a lysosome bursts and spills its enzymes , the enzymes will not begin digesting the cell , because they will no longer have the right ph to function. $ ^5 $ feedback inhibition of metabolic pathways in the process of feedback inhibition , the end product of a metabolic pathway acts on the key enzyme regulating entry to that pathway , keeping more of the end product from being produced . this may seem odd – why would a molecule want to turn off its own pathway ? but it ’ s actually a clever way for the cell to make just the right amount of the product . when there ’ s little of the product , the enzyme will not be inhibited , and the pathway will go full steam ahead to replenish the supply . when there ’ s lots of the product sitting around , it will block the enzyme , preventing the production of new product until the existing supply has been used up . typically , feedback inhibition acts at the first committed step of the pathway , meaning the first step that ’ s effectively irreversible . however , feedback inhibition can sometimes hit multiple points along a pathway as well , particularly if the pathway has lots of branch points . the pathway steps regulated by feedback inhibition are often catalyzed by allosteric enzymes. $ ^ { 6 } $ for example , the energy carrier molecule atp is an allosteric inhibitor of some of the enzymes involved in cellular respiration , a process that makes atp to power cellular reactions . when there is lots of atp , this feedback inhibition keeps more atp from being made . this is useful because atp is an unstable molecule . if too much atp were made , much of it might go to waste , spontaneously breaking back down into its components ( adp and p $ _i $ ) . adp , on the other hand , serves as a positive allosteric regulator ( an allosteric activator ) for some of the same enzymes that are inhibited by atp . for instance , adp may act by binding to an enzyme and changing its shape so that it becomes more active. $ ^ { 7 } $ thanks to this pattern of regulation , when adp levels are high compared to atp levels , cellular respiration enzymes become very active and will make more atp through cellular respiration .
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these include ph and temperature ( discussed in the active site article ) , as well as : regulatory molecules . enzyme activity may be turned `` up '' or `` down '' by activator and inhibitor molecules that bind specifically to the enzyme . cofactors .
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in the second to last paragraph , does atp bind to activate an enzyme , or adp ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ .
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disorder is the molecular movement of particles in general ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive .
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and when heat leaves the surroundings into the system , should n't q be negative ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system .
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does n't spontaneity depend on enthalpy too ( not just entropy ) based on the equation for gibb 's free energy ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ .
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is n't it correct to say that if the change in entropy is negative , a reaction can still be spontaneous if temperature is low enough and the change in enthalpy is positive ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin .
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if entropy is joule/kelvin and absolute zero is 0 kelvin , then why entropy at this temperature is 0 ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ?
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any given energy/0 should n't be rather infinity or undefined ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ .
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can someone explain what is the maximum value of heat capacity ratio ( kappa ) ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j .
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i have seen that most of ideal gases have a ratio ranging from 1 to 1.67 , so i was wondering if that value can be higher than those in thermodynamics tables ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work .
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at room temperature , if i touch a ball made of iron with one hand & a wooden ball from another hand why the iron ball feels colder than the wooden one ?
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law of thermodynamics thermodynamics is a very important branch of both physics and chemistry . it deals with the study of energy , the conversion of energy between different forms and the ability of energy to do work . as you go through this article , i am pretty sure that you will begin to appreciate the importance of thermodynamics and you will start noticing how laws of thermodynamics operate in your daily lives ! there are essentially four laws of thermodynamics . zeroth law of thermodynamics “ if two systems are in thermal equilibrium with a third system , then they are in thermal equilibrium with one another ” let ’ s first define what ‘ thermal equilibrium ’ is . when two systems are in contact with each other and no energy flow takes place between them , then the two systems are said to be in thermal equilibrium with each other . in simple words , thermal equilibrium means that the two systems are at the same temperature . thermal equilibrium is a concept that is so integral to our daily lives . for instance , let 's say you have a bowl of hot soup and you put it in the freezer . what will happen to the soup ? the soup will , of course , start cooling down with time . you all know that . and you also probably know that the soup will continue to cool down until it reaches the same temperature as the freezer . even if you are familiar with this concept , what you may not realize is that this is an excellent example of thermal equilibrium . here , heat flows from the system at a higher temperature ( bowl of soup ) to the system at a lower temperature ( freezer ) . heat flow stops when the two systems reach the same temperature . in other words , now the two systems are in thermal equilibrium with each other and there is no more heat flow taking place between the two systems . let ’ s assume we have three systems - system 1 , system 2 and system 3 . their temperatures are t $ _1 $ , t $ _2 $ and t $ _3 $ respectively . the zeroth law states that if the temperature of system 1 is equal to temperature of system 3 , and the temperature of system 2 is equal to temperature of system 3 ; then the temperature of system 1 should be equal to the temperature of system 2 . the three systems are said to be in thermal equilibrium with each other . that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ . first law of thermodynamics this law is essentially the ‘ law of conservation of energy ’ . energy can neither be created nor destroyed ; it can just be converted from one form to another . in simple words , the first law of thermodynamics states that whenever heat energy is added to a system from outside , some of that energy stays in the system and the rest gets consumed in the form of work . energy that stays in the system increases the internal energy of the system . this internal energy of the system can be manifested in various different forms – kinetic energy of molecules , potential energy of molecules or heat energy ( that simply raises the temperature of the system ) . what is internal energy ? it is defined as the sum total of kinetic energy , which comes from motion of the molecules , and potential energy which comes from the chemical bonds that exist between the atoms and any other intermolecular forces that may be present . first law of thermodynamics is thus conventionally stated as : “ the change in internal energy of a closed system is equal to the energy added to it in the form of heat ( q ) plus the work ( w ) done on the system by the surroundings. ” mathematically , this can be put as ∆e $ _ { internal } $ = q + w conventional definition of the first law is based on the system gaining heat and the surrounding doing work . the opposite scenario can occur too , in which case the ‘ signs ’ in the equation will have to be changed appropriately . this will be discussed shortly . lots of times you will notice that ∆e $ _ { internal } $ is also denoted as ∆u . now you must be wondering what is meant by a ‘ closed system ’ . let ’ s try to understand this through a simple example . imagine we have two saucepans containing water - 1 ) with a lid 2 ) without a lid . both are kept on a heated stove . both the saucepans shown above will absorb heat from the stove and get heated up . so there is exchange of energy taking place in both the cases from the stove ( surroundings ) to the system ( water ) . but do you notice a difference ? saucepan , with the lid , prevents any addition of mass to it or removal of mass from it ; whereas in the case of the saucepan , without the lid , we can easily add coffee and sugar from outside and thus change the mass of the contents . basically , the lid is preventing matter from entering the saucepan and leaving the saucepan . here , the saucepan with a lid is an example of a closed system ; while the saucepan without a lid is an example of an open system . thus , an ‘ open system ’ can be defined as a system that freely exchanges both energy and matter with its surroundings ; while a ‘ closed system ’ is a system that exchanges only energy with its surroundings , not matter . ps : coming back to the sign conventions for the first law of thermodynamics ( ∆e $ _ { internal } $ = q + w ) ; let ’ s be ‘ very very ’ clear of the following norms - if heat flows out of the system , then q will be negative if heat flows into the system , then q will be positive if work is done by the system , then w will be negative if work is done on the system , then w will be positive let ’ s look at the following example : we have a gas in a sealed container ( closed system ; no matter exchange can take place with the surroundings ) . a piston is attached , on top of which is placed a block of wood . we provide heat ( q ) from outside to this system . this heat energy leads to expansion of the gas , which in turn pushes the piston up . so , the gas does work ( w ) in expanding itself , which results in pushing of the piston . if you recall from the ideal gas laws ; for an ideal gas , work ( w ) = pv = nrt let ’ s now mathematically define the change in the internal energy of the above system . change in internal energy of a system ( ∆e ) = q + w let ’ s try to apply the rules we talked about earlier , in this example , *heat flows into the system , so q will be positive and the work is done by the system ( gas in this case ) , so w will be negative * thus , ( ∆e ) = q – w = q - p∆v [ q is the external energy provided , p is the pressure of the gas , and ∆v is the change in volume of the gas ] now let ’ s attempt a couple of problems dealing with the first law of thermodynamics . always be sure to use the correct units while solving any numerical ! ! ! problem 1 : in an exothermic process , the volume of a gas expanded from 186 ml to 1997 ml against a constant pressure of 745 torr . during the process , 18.6 calories of heat energy were given off . what was the internal energy change for the system in joules ? also , ( 1 l atm = 101.3 j ) q = heat given off by system = 18.6 cal = 18.6 x 4.184 j ( remember : 1 cal = 4.184 j ) = 77.82 j since heat flows out of the system , q will be negative . so q = -77.82 j work ( w ) = p∆v , where p = constant pressure of gas , ∆v = change in volume of gas let ’ s first convert pressure and volume into the correct units 760 torr = 1 atm , so 745 torr of pressure = 745/ 760 = 0.98 atm volume should be in litres ( l ) , thus ∆v = ( 1997 – 186 ) ml = 1811 ml = 1811 x 10 $ ^ { -3 } $ l thus , w = p∆v = 0.98 atm x 1.811 l = 1.77 atm l also , the problem statement gives conversion between atm l and joules ( 1 l atm = 101.3 j ) . so , 1.77 atm l = 1.77 x 101.3 = 179.30 j in this example , work is being done by the system in expansion of the gas , so w is negative ( remember : if work is done by the system , then w will be negative ) . therefore , w = -179.30 j so , net change in internal energy of the system ( ∆u ) = q + w = -77.82 + ( -179.30 ) = -257.12 j this result indicates that the energy of the gas is decreases by 257.12 j . this means , at the end of the process the gas has less energy than it had in the beginning . problem 2 : the work done when a gas is compressed in a cylinder is 820 j . at the same time , the system lost 320 j of heat to the surrounding . what is the energy change of this system ? here the gas is the system . first you must decide the signs of ‘ w ’ and ‘ q ’ using the convention discussed earlier . work is done on the system , so w = + 820 j and heat is lost by the system , so q = - 320 j . therefore ∆e = q + w = - 320 j + 820 j = 500 j this result indicates that the energy of the gas is increased by 500 j . this implies , at the end of the process the gas has more energy than it had in the beginning . second law of thermodynamics this law states “ the total change in entropy of a system plus its surroundings will always increase for a spontaneous process ” entropy is defined as the “ measure of disorder or randomness of a system ” . every system wants to achieve a state of maximum disorder or randomness . a commonly observed daily life example of something constantly moving towards a state of randomness is a ‘ kid ’ s room ’ . every time mom cleans up the room , within minutes the room looks like this this is the natural state in which a kid ’ s room wants to exist ☺ another commonly encountered entropy driven process is the melting of ice into water . this happens spontaneously as soon as ice is left at room temperature . ice is a solid with an ordered crystalline structure as compared to water , which is a liquid in which molecules are more disordered and randomly distributed . all natural processes tend to proceed in a direction which leads to a state that has more random distribution of matter and energy . all of these processes take place spontaneously , meaning that once they start , they will proceed to the end if there is no external intervention . you will never witness the reverse of this process , in which water converts back to ice at room temperature . in other words , it would be inconceivable that this process could be reversed without tampering with the external conditions ( you will have to put water in the freezer to force it to form ice ) . so what determines the direction in which a process will go under a given set of conditions ? now you know the answer - all these processes are driven by entropy . mathematically , the second law of thermodynamics can be stated as ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ & gt ; 0 where , ∆s $ _ { universe } $ = net change in entropy of the universe ∆s $ _ { system } $ = net change in entropy of the system ∆s $ _ { surroundings } $ = net change in entropy of the surroundings take home message : “ entropy of the universe is constantly increasing ” take home message : “ entropy of the universe is constantly increasing ” entropy is mathematically calculated as q/ t ( heat absorbed or released by the system or surroundings divided by the temperature of the system or surroundings ) . entropy is expressed in joules per kelvin ( j/ k ) . why is the second law of thermodynamics so important ? second law of thermodynamics is very important because it talks about entropy and as we have discussed , ‘ entropy dictates whether or not a process or a reaction is going to be spontaneous ’ . i want you to realize that any natural process happening around you is driven by entropy ! ! let ’ s take a daily life example : we drink coffee every day . what happens to our cup of hot coffee in say 10 minutes ? the coffee starts getting cold , or in thermodynamic terms you will tell me that the hot coffee gives out heat to the surroundings and in turn the coffee cools down . you are 100 % correct , but the thing you might not have realized is that this very obvious daily life phenomenon is governed by “ entropy ” . let ’ s try to prove this mathematically . as shown below , the following two scenarios are possible the temperature of the surroundings and the coffee are 25 $ ^o $ c and 45 $ ^o $ c respectively . scenario 1 : 10 j of heat is absorbed ( from the surroundings ) by coffee , so surroundings lose 10 j and the system ( coffee ) gains 10 j . thus , q $ { system } $ = + 10 j and q $ { surroundings } $ = -10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = 10/ ( 45 + 273 ) + ( -10 ) / ( 25 + 273 ) [ temperatures are to be converted into kelvin ] = -0.0021 joules/ kelvin this violates the second law of thermodynamics ( ∆s $ _ { universe } $ should be greater than zero ) , so the above process can not occur spontaneously . scenario 2 : 10 j of heat is released ( to the surroundings ) by hot coffee , so surroundings gain 10 j and system ( coffee ) loses 10 j . thus , q $ { system } $ = - 10 j and q $ { surroundings } $ = +10 j ∆s $ { universe } $ = ∆s $ { system } $ + ∆s $ _ { surroundings } $ = q $ { system } $ / t $ { system } $ + q $ { surroundings } $ / t $ { surroundings } $ = -10/ ( 45 + 273 ) + 10/ ( 25 + 273 ) [ temperatures have to be converted into kelvin ] = +0.0021 joules/ kelvin this obeys the second law of thermodynamics ( ∆s $ _ { universe } $ & gt ; 0 ) , so the above process occurs spontaneously . in the case of a cup of coffee this was pretty intuitive . but this is not true for chemical reactions . just by looking at a chemical reaction , we can not predict if it will take place spontaneously or not . so , calculating the entropy change for that particular reaction becomes important . gibb ’ s free energy ( g ) : predictor of spontaneity of a chemical reaction gibb ’ s free energy is defined as ‘ the energy associated with a chemical reaction that can be used to do work. ’ the free energy ( g ) of a system is the sum of its enthalpy ( h ) minus the product of the temperature ( t ) and the entropy ( s ) of the system : g = h - ts for details on ‘ enthalpy ’ , refer to the article on ‘ endothermic and exothermic reactions ’ . gibbs free energy combines the effect of both enthalpy and entropy . the change in free energy ( δg ) is equal to the sum of the change of enthalpy ( ∆h ) minus the product of the temperature and the change of entropy ( ∆s ) of the system . ∆g = ∆h - t∆s *δg predicts the direction in which a chemical reaction will go under two conditions : ( 1 ) constant temperature and ( 2 ) constant pressure . * rule of thumb : if δg is positive , then the reaction is not spontaneous ( it requires the input of external energy to occur ) and if it is negative , then it is spontaneous ( occurs without the input of any external energy ) . let ’ s attempt a problem involving δg calculate δg for the following reaction at 25 $ ^o $ c nh $ _3 $ ( g ) + hcl ( g ) → nh $ _4 $ cl ( s ) but first we need to convert the units for δs into kj/ k ( or convert δh into j ) and temperature into kelvin . so , δs = −284.8 j/ k = −0.284.8 kj/ k t = 273.15 k + 25 = 298 k * ( 1 kj = 1000 j ) now , δg = δh − tδs δg = −176.0 kj − ( 298 k ) ( −0 . 284.8 kj/ k ) δg = −176.0 kj − ( −84.9 kj ) δg = −91.1 kj answer : yes , this reaction is spontaneous at room temperature since δg is negative . the beauty of the gibb ’ s free energy equation is its ability to determine the relative importance of the enthalpy ( δh ) and the entropy ( δs ) of the system . the change in free energy of the system measures the balance between the two driving forces ( δh and δs ) , which together determine whether a reaction is spontaneous or not . let us tabulate this information to make it easier to comprehend δg = δh − tδs favorable reaction conditions | unfavorable reaction conditions : - : | : - : ∆h & lt ; 0 | ∆h & gt ; 0 ∆s & gt ; 0 | ∆s & lt ; 0 ∆g & lt ; 0 | ∆g & gt ; 0 if ∆h & lt ; 0 and ∆s & gt ; 0 , without even doing any calculations you can say that the reaction will be spontaneous because δg = δh – tδs will be negative if ∆h & gt ; 0 and ∆s & lt ; 0 , without even doing any calculations you can say that the reaction will not be spontaneous because δg = δh – tδs will be positive actual calculations become necessary when out of the two parameters , ∆h and ∆s , one is favorable and the other is not . in such a case , δg has to be calculated to predict the spontaneity of the reaction third law of thermodynamics “ the entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. ” whenever i think of this law , i am reminded of the beautiful documentary made on the survival tactics of penguins ‘ march of the penguins ’ . those who have watched this documentary will recall : in order to survive the extremely cold weathers of antarctica ( where temperatures approach −80 °f or 210.92 k ) , penguins form colonies consisting of a group of huddles ; and in each colony the penguins are tightly packed and don ’ t move at all , and all the penguins face in the same direction as shown in the image on the right . now assume these penguins to be atoms . analogous to the penguins , at a temperature of zero kelvin the atoms in a pure crystalline substance get aligned perfectly and do not move around . matter is in a state of maximum order ( least entropy ) when the temperature approaches absolute zero ( 0 kelvin ) . in other words , the entropy of a perfect crystal approaches zero when the temperature of the crystal approaches 0 kelvin . this is , in fact , the third law of thermodynamics . the consequence of this law is that any thermal motion ceases in a perfect crystal at 0 k. conversely , if there will be any thermal motion within the crystal at 0 k , it will lead to disorder in the crystal because atoms will start moving around , violating the third law of thermodynamics .
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that is ; if t $ _1 $ = t $ _3 $ and t $ _2 $ = t $ _3 $ , then t $ _1 $ = t $ _2 $ the zeroth law is analogous to the basic rule in algebra , if a=c and b=c , then a=b . this law points to a very important fact - ‘ temperature affects the direction of heat flow between systems. ’ heat always flows from high temperature to low temperature . heat flow is mathematically denoted as ‘ q ’ .
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is entropy related to temperature ?
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key points communication is when one animal transmits information to another animal causing some kind of change in the animal that gets the information . communication is usually between animals of a single species , but it can also happen between two animals of different species . animals communicate using signals , which can include visual ; auditory , or sound-based ; chemical , involving pheromones ; or tactile , touch-based , cues . communication behaviors can help animals find mates , establish dominance , defend territory , coordinate group behavior , and care for young . introduction have you ever wondered how ants follow what seem to be invisible trails leading to food ? why male dogs mark their territory by peeing on bushes and lampposts when you take them for a walk ? what birds are saying to one another when they chirp outside your window ? if so , you 're in the right place ! in this article , we 'll take a look at these—and many other—forms of communication used in the animal kingdom . communication takes many forms communication—when we 're talking about animal behavior—can be any process where information is passed from one animal to another causing a change or response in the receiving animal . communication most often happens between members of a species , though it can also take place between different species . for instance , your dog may bark at you to ask for a treat ! some species are very social , living in groups and interacting all the time ; communication is essential for keeping these groups cohesive and organized . however , even animals that are relative loners usually have to communicate at least a little , if only to find a mate . what forms can communication behaviors take ? well , animal sensory systems vary quite a great deal . for instance , a dog 's sense of smell is 40 times more acute than ours ! $ ^2 $ because of this sensory diversity , different animals communicate using a wide range of stimuli , known collectively as signals . below are some common types of signals : pheromones—chemicals auditory cues—sounds visual cues tactile cues—touch in some cases , signals can even be electric ! where does this diversity of communication behaviors come from ? like other traits , communication behaviors—and/or the capacity for learning these behaviors—arise through natural selection . heritable communication behaviors that increase an organism 's likelihood of surviving and reproducing will tend to persist and become common in a population or species . in the rest of the article , we 'll look at some examples of the many ways that animals can communicate with one another . pheromones a pheromone is a secreted chemical signal used to trigger a response in another individual of the same species . pheromones are especially common among social insects , such as ants and bees . pheromones may attract the opposite sex , raise an alarm , mark a food trail , or trigger other , more complex behaviors . the diagram below shows pheromone trails laid down by ants to direct others in the colony to sources of food . when a food source is rich , ants will deposit pheromone on both the outgoing and return legs of their trip , building up the trail and attracting more ants . when the food source is about to run out , the ants will stop adding pheromone on the way back , letting the trail fade out $ ^ { 3,4 } $ . ants also use pheromones to communicate their social status , or role , in the colony , and ants of different `` castes '' may respond differently to the same pheromone signals $ ^3 $ . a squashed ant will also release a burst of pheromones that warns nearby ants of danger—and may incite them to swarm and sting $ ^ { 5,6 } $ . dogs also communicate using pheromones . they sniff each other to collect this chemical information , and many of the chemicals are also released in their urine . by peeing on a bush or post , a dog leaves a mark of its identity that can be read by other passing dogs and may stake its claim to nearby territory $ ^ { 7,8 } $ . auditory signals auditory communication—communication based on sound—is widely used in the animal kingdom . auditory communication is particularly important in birds , who use sounds to convey warnings , attract mates , defend territories , and coordinate group behaviors . some birds also produce birdsong , vocalizations that are relatively long and melodic and tend to be similar among the members of a species . many non-bird species also communicate using sound : monkeys cry out a warning when a predator is near , giving the other members of the troop a chance to escape . vervet monkeys even have different calls to indicate different predators . bullfrogs croak to attract female frogs as mates . in some frog species , the sounds can be heard up to a mile away ! gibbons use calls to mark their territory , keeping potential competitors away . a paired male and female , and even their offspring , may make the calls together . water , like air , can carry sound waves , and marine animals also use sound to communicate . dolphins , for instance , produce various noises—including whistles , chirps , and clicks—and arrange them in complex patterns . the idea that this might represent a form of language is intriguing but controversial $ ^9 $ . visual signals visual communication involves signals that can be seen . examples of these signals include gestures , facial expressions , body postures , and coloration . gesture and posture are widely used visual signals . for instance , chimpanzees communicate a threat by raising their arms , slapping the ground , or staring directly at another chimpanzee . gestures and postures are commonly used in mating rituals and may place other signals—such as bright coloring—on display . facial expressions are also used to convey information in some species . for instance , what is known as the fear grin—shown on the face of the young chimpanzee below—signals submission . this expression is used by young chimpanzees when approaching a dominant male in their troop to indicate they accept the male 's dominance . changes in coloration also serve as visual signals . for instance , in some species of monkeys , the skin around a female ’ s reproductive organs becomes brightly colored when the female is in the fertile stage of her reproductive cycle . the color change signals that the female can be approached by suitors . an organism 's general coloration—rather than a change in color—may also act as a visual signal $ ^1 $ . for instance , the bright coloration of some toxic species , such as the poison dart frog , acts as a do-not-eat warning signal to predators . tactile signals—touch tactile signals are more limited in range than the other types of signals , as two organisms must be right next to each other in order to touch $ ^ { 10 } $ . still , these signals are an important part of the communication repertoire of many species . tactile signals are fairly common in insects . for instance , a honeybee forager that 's found a food source will perform an intricate series of motions called a waggle dance to indicate the location of the food . since this dance is done in darkness inside the nest , the other bees interpret it largely through touch $ ^ { 11,12 } $ . tactile signals also play an important role in social relationships . for instance , in many primate species , members of a group will groom one another—removing parasites and performing other hygiene tasks $ ^ { 13 } $ . this largely tactile behavior reinforces cooperation and social bonds among group members $ ^ { 14 } $ . tactile stimuli also play a role in the survival of very young organisms . for instance , newborn puppies will instinctively knead at their mother 's mammary glands , causing the release of the hormone oxytocin and production of milk $ ^ { 15 } $ . what is communication used for ? as the examples above illustrate , animals communicate using many different types of signals , and they also use these signals in a wide range of contexts . here are some of the most common functions of communication : obtaining mates . many animals have elaborate communication behaviors surrounding mating , which may involve attracting a mate or competing with other potential suitors for access to mates . establishing dominance or defending territory . in many species , communication behaviors are important in establishing dominance in a social hierarchy or defending territory . coordinating group behaviors . in social species , communication is key in coordinating the activities of the group , such as food acquisition and defense , and in maintaining group cohesion . caring for young . among species that provide parental care to offspring , communication coordinates parent and offspring behaviors to help ensure that the offspring will survive . as these examples show , communication helps organisms interact to carry out basic life functions , such as surviving , obtaining mates , and caring for young .
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still , these signals are an important part of the communication repertoire of many species . tactile signals are fairly common in insects . for instance , a honeybee forager that 's found a food source will perform an intricate series of motions called a waggle dance to indicate the location of the food .
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do all animals have common type of signals in them ?
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background formal definition of divergence in two-dimensions flux in three-dimensions it is a short step between these two prerequisites , and understanding the formal definition of divergence in three dimensions . for that reason , i 'm going to keep this article relatively short , assuming that you have the intuition behind both of those pieces of background knowledge . what we 're building to the goal is to capture the intuition of outward fluid flow at a point in a mathematical formula . in three-dimensions , divergence is defined using the following limit : $ \begin { align } \text { div } \ , \bluee { \textbf { f } } \golde { ( x , y , z ) } = \lim_ { |\rede { r } { \golde { ( x , y , z ) } } | \to 0 } ! ! ! ! \overbrace { \dfrac { 1 } { |\rede { r } { \golde { ( x , y , z ) } } | } ! ! ! ! ! \underbrace { \iint_\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ , \rede { d\sigma } } _ { \text { flux through the surface of $ \rede { r } $ } } } ^ { \text { average outward flow from $ \rede { r } $ per unit volume } } \end { align } $ there is quite a lot going on in this definition , but most of the complexity lies in that flux integral . if you understand that part , the rest comes from taking the limit with respect to a region shrinking around a point . from a region to a point let 's say you have a three-dimensional vector field . $ \bluee { f } ( x , y , z ) \quad \leftarrow \text { three-dimensional vector field } $ as always , think of this vector field as representing a fluid flow . the divergence $ \text { div } \bluee { f } $ tries to measure the `` outward flow '' of this fluid at each point . however , it does n't quite make sense to talk about what it means for fluid to flow out of a point . what does make sense is the idea of fluid flowing out of region . specifically , picture some region $ \rede { r } $ in the vector field . let 's name the surface of this region `` $ \rede { s } $ '' . in the article on flux in three dimensions , i showed how you can measure the rate at which fluid is leaving this region by taking the flux of $ \bluee { \textbf { f } } $ over the surface $ \rede { s } $ : $ \displaystyle \underbrace { -\dfrac { d ( \text { fluid mass in $ \rede { r } $ } ) } { dt } } { \text { rate at which fluid exits $ \rede { r } $ } } = \underbrace { \iint\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ ; \rede { d\sigma } } _ { \text { flux surface integral } } $ here , $ \greene { \hat { \textbf { n } } } ( x , y , z ) $ is a vector-valued function which returns the outward facing unit normal vector at each point on $ \rede { s } $ . divergence itself is concerned with the change in fluid density around each point , as opposed mass . we can get the change in fluid density of $ \rede { r } $ by dividing the flux integral by the volume of $ \rede { r } $ . to denote the volume of $ \rede { r } $ , put bars around it : $ |\rede { r } | \quad \leftarrow \text { volume of $ \rede { r } $ } $ so here 's what rate at which fluid density changes inside $ \rede { r } $ looks like : $ \displaystyle -\dfrac { d ( \text { fluid $ \bluee { \text { density } } $ in $ \rede { r } $ } ) } { dt } = \dfrac { 1 } { |\rede { r } | } \iint_\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ ; \rede { d\sigma } $ the divergence of $ \bluee { \textbf { f } } $ at a point $ \golde { ( x , y , z ) } $ is defined as the limit of this change-in-fluid-density expression as the region shrinks around the point $ \golde { ( x , y , z ) } $ . $ \displaystyle \text { div } \ , \bluee { \textbf { f } } \golde { ( x , y , z ) } = ! ! ! ! ! ! ! ! ! ! \underbrace { \lim_ { \rede { r } \to \golde { ( x , y , z ) } } } { \rede { r } \text { shrinks around } \golde { ( x , y , z ) } } ! ! ! ! \dfrac { 1 } { |\rede { r } | } \iint\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ ; \rede { d\sigma } $ in that equation , i wrote $ \rede { r } \to \golde { ( x , y , z ) } $ to communicate the idea of $ \rede { r } $ shrinking around the point $ \golde { ( x , y , z ) } $ . at the end of the day , all this notation is just a desperate attempt to communicate a heavily visual idea with symbols . you will see different authors use different notation . if you prefer , you could alternatively start by saying $ \rede { r } _ { \golde { ( x , y , z ) } } $ is a region which contains the point $ \golde { ( x , y , z ) } $ , then write the following : $ \displaystyle \text { div } \ , \bluee { \textbf { f } } \golde { ( x , y , z ) } = \lim_ { |\rede { r } \golde { ( x , y , z ) } | \to 0 } \dfrac { 1 } { |\rede { r } \golde { ( x , y , z ) } | } \iint_\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ ; \rede { d\sigma } $ i have a slight preference for this last notation , just because it makes it a bit easier to see the connection between $ \golde { ( x , y , z ) } $ on the left hand side and the right hand side without relying so heavily on the context in which all the terms are defined . congratulations ! if you are at the point where you can understand this ( rather complicated ) definition , it is a good sign that you have a solid mental grasp of both divergence and surface integrals . it also means you are in a strong position to understand the divergence theorem , which connects this idea to that of triple integrals .
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$ \displaystyle \text { div } \ , \bluee { \textbf { f } } \golde { ( x , y , z ) } = ! ! ! ! ! ! ! ! ! ! \underbrace { \lim_ { \rede { r } \to \golde { ( x , y , z ) } } } { \rede { r } \text { shrinks around } \golde { ( x , y , z ) } } ! ! ! ! \dfrac { 1 } { |\rede { r } | } \iint\rede { s } \bluee { \textbf { f } } \cdot \greene { \hat { \textbf { n } } } \ ; \rede { d\sigma } $ in that equation , i wrote $ \rede { r } \to \golde { ( x , y , z ) } $ to communicate the idea of $ \rede { r } $ shrinking around the point $ \golde { ( x , y , z ) } $ .
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is r ( x , y , z ) supposed to indicate surface area or volume ?
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antibiotics are a type of medicine which are used to treat bacterial infections . everyday we come into contact with thousands of bacterial cells . we are colonized with lots of different types of bacteria which live on us , and inside of us ; everywhere from the grooves of your fingerprint , to the nooks and crannies of your intestines . if you count up all of the bacteria , they actually outnumber us ( by `` us '' we mean our human cells ) about 10 to 1 . to stay healthy , we need to maintain a healthy ecosystem of bacteria , called normal flora ( not all bacteria is bad ! ) , while selectively getting rid of the harmful , “ pathogenic ” bacteria which can cause an infection . pathogenic bacteria is a relative term . some bacteria can cause illness in you no matter what . other bacteria cause illness when they wander from their normal location ( e.g . intestines ) and try to live in a new location ( e.g . bladder ) , which is what happens when you develop a urinary tract infection ( uti ) . the body ’ s immune system responds to an infection by trying to fight and destroy the invading bacteria ! what are antibiotics ? to help the immune system , we sometimes use antibiotics , which are chemicals ( specifically a swarm of small molecules ) that enter and stick to important parts ( think of targets ) of the bacterial cell , and interfere with its ability to survive and multiply . if the bacteria are susceptible to the antibiotic , then they will stop growing or simply die . these important parts include : proteins/sugars in the bacterial wall important enzymes that make new bacterial dna or proteins when an antibiotic molecule sticks to its target , it will disable or destroy that protein or enzyme . if enough of the antibiotic is present , the bacterial cell is crippled and either stops growing ( bacterio-static effect ) or simply dies ( bacteri-cidal effect ) . just to be clear , antibiotics don ’ t affect viruses , fungi , or parasites - they only bind to bacterial cell targets so they only affect bacterial cells . in fact , they specifically target bacteria rather than human cells . how were antibiotics discovered ? back in 1928 ( right before the great depression ) , alexander fleming first discovered the antibiotic penicillin when he noticed that bacteria in his lab wouldn ’ t grow near some fungus , which had accidentally found its way into his experiments . the fungus was making a small molecule which leaked into the petri gel around it , and fleming called the stuff - “ mold juice ” . he realized that the mold juice was killing the bacteria in the area ! the next big surprise for mr. fleming came when he later found out that the fungus was the same bluish-green fungus that grows on old bread . the discovery earned him the nobel prize in 1945 , and helped humanity develop a key antibiotic which has saved countless lives . in his nobel prize acceptance speech , fleming warned the world of the dangers of misusing antibiotics . he had already noted bacteria in his lab becoming resistant to penicillin , just a few years after its discovery ! after decades of antibiotic misuse , today we find ourselves facing bacteria which has become resistant to most , if not all antibiotics . how do antibiotics work ? let 's take a look at a couple of examples of antibiotics : penicillin and azithromycin . penicillin penicillin is a fabulous antibiotic because it is n't toxic to humans at concentrations that can kill bacteria and it can kill a lot of different types of bacteria . so how does it work ? penicillin weakens the bacterial wall by : deactivating a bacterial enzyme ( transpeptidase ) that builds and repairs the bacteria wall . activating a bacterial enzyme ( autolysin ) that cuts open parts of the bacterial wall , an enzyme normally only activated when the bacteria is multiplying . in short , penicillin causes the bacteria to weaken its own cell wall ( imagine being forced to punch yourself ! ) , and prevents the bacteria from being able to repair itself . with a weak wall , water seeps in , and the bacteria swells up and explodes . azithromycin azithromycin is a broad spectrum antibiotic which is often used to treat a wide variety of infections ; everything from pneumonia to sexually transmitted diseases . so how does it work ? azithromycin prevents the bacteria from multiplying by : blocking the cell 's ability to create proteins by attaching to ribosomes in the cell . in short , azithromycin prevents bacteria from multiplying , making it much easier for the immune system to handle the infection . antibiotic development over the years , a number of antibiotics have been discovered in nature or synthesized in the lab . some antibiotics target only specific bacteria and are called “ narrow spectrum ” antibiotics , whereas other antibiotics target many types of bacteria and are called “ broad spectrum ” antibiotics . developing completely new classes of antibiotics ( as opposed to variations on existing antibiotics ) is very difficult . it ’ s easy to find chemicals that kill bacteria , but not so easy to find substances that could be used as medicines , even if researchers were given infinite resources ! researchers are basically shooting in the dark . in fact , the most recent discovery of a novel antibiotic class was in 1987 , almost 30 years ago ( silver , l. , 2011 ) ! while there are a few new antibiotics currently in development , researchers don ’ t know if they ’ ll ever become usable as medicine . this void in the discovery of new antibiotics is problematic . when a bacteria becomes resistant to a specific drug within a drug class , it gains some level of resistance to drugs within the same class . for example , if a bacteria became resistant to ampicillin , it would also have some level of resistance to other penicillin-like antibiotics .
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antibiotic development over the years , a number of antibiotics have been discovered in nature or synthesized in the lab . some antibiotics target only specific bacteria and are called “ narrow spectrum ” antibiotics , whereas other antibiotics target many types of bacteria and are called “ broad spectrum ” antibiotics . developing completely new classes of antibiotics ( as opposed to variations on existing antibiotics ) is very difficult .
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what happens if bacteria evolves beyond what antibiotics can treat ?
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antibiotics are a type of medicine which are used to treat bacterial infections . everyday we come into contact with thousands of bacterial cells . we are colonized with lots of different types of bacteria which live on us , and inside of us ; everywhere from the grooves of your fingerprint , to the nooks and crannies of your intestines . if you count up all of the bacteria , they actually outnumber us ( by `` us '' we mean our human cells ) about 10 to 1 . to stay healthy , we need to maintain a healthy ecosystem of bacteria , called normal flora ( not all bacteria is bad ! ) , while selectively getting rid of the harmful , “ pathogenic ” bacteria which can cause an infection . pathogenic bacteria is a relative term . some bacteria can cause illness in you no matter what . other bacteria cause illness when they wander from their normal location ( e.g . intestines ) and try to live in a new location ( e.g . bladder ) , which is what happens when you develop a urinary tract infection ( uti ) . the body ’ s immune system responds to an infection by trying to fight and destroy the invading bacteria ! what are antibiotics ? to help the immune system , we sometimes use antibiotics , which are chemicals ( specifically a swarm of small molecules ) that enter and stick to important parts ( think of targets ) of the bacterial cell , and interfere with its ability to survive and multiply . if the bacteria are susceptible to the antibiotic , then they will stop growing or simply die . these important parts include : proteins/sugars in the bacterial wall important enzymes that make new bacterial dna or proteins when an antibiotic molecule sticks to its target , it will disable or destroy that protein or enzyme . if enough of the antibiotic is present , the bacterial cell is crippled and either stops growing ( bacterio-static effect ) or simply dies ( bacteri-cidal effect ) . just to be clear , antibiotics don ’ t affect viruses , fungi , or parasites - they only bind to bacterial cell targets so they only affect bacterial cells . in fact , they specifically target bacteria rather than human cells . how were antibiotics discovered ? back in 1928 ( right before the great depression ) , alexander fleming first discovered the antibiotic penicillin when he noticed that bacteria in his lab wouldn ’ t grow near some fungus , which had accidentally found its way into his experiments . the fungus was making a small molecule which leaked into the petri gel around it , and fleming called the stuff - “ mold juice ” . he realized that the mold juice was killing the bacteria in the area ! the next big surprise for mr. fleming came when he later found out that the fungus was the same bluish-green fungus that grows on old bread . the discovery earned him the nobel prize in 1945 , and helped humanity develop a key antibiotic which has saved countless lives . in his nobel prize acceptance speech , fleming warned the world of the dangers of misusing antibiotics . he had already noted bacteria in his lab becoming resistant to penicillin , just a few years after its discovery ! after decades of antibiotic misuse , today we find ourselves facing bacteria which has become resistant to most , if not all antibiotics . how do antibiotics work ? let 's take a look at a couple of examples of antibiotics : penicillin and azithromycin . penicillin penicillin is a fabulous antibiotic because it is n't toxic to humans at concentrations that can kill bacteria and it can kill a lot of different types of bacteria . so how does it work ? penicillin weakens the bacterial wall by : deactivating a bacterial enzyme ( transpeptidase ) that builds and repairs the bacteria wall . activating a bacterial enzyme ( autolysin ) that cuts open parts of the bacterial wall , an enzyme normally only activated when the bacteria is multiplying . in short , penicillin causes the bacteria to weaken its own cell wall ( imagine being forced to punch yourself ! ) , and prevents the bacteria from being able to repair itself . with a weak wall , water seeps in , and the bacteria swells up and explodes . azithromycin azithromycin is a broad spectrum antibiotic which is often used to treat a wide variety of infections ; everything from pneumonia to sexually transmitted diseases . so how does it work ? azithromycin prevents the bacteria from multiplying by : blocking the cell 's ability to create proteins by attaching to ribosomes in the cell . in short , azithromycin prevents bacteria from multiplying , making it much easier for the immune system to handle the infection . antibiotic development over the years , a number of antibiotics have been discovered in nature or synthesized in the lab . some antibiotics target only specific bacteria and are called “ narrow spectrum ” antibiotics , whereas other antibiotics target many types of bacteria and are called “ broad spectrum ” antibiotics . developing completely new classes of antibiotics ( as opposed to variations on existing antibiotics ) is very difficult . it ’ s easy to find chemicals that kill bacteria , but not so easy to find substances that could be used as medicines , even if researchers were given infinite resources ! researchers are basically shooting in the dark . in fact , the most recent discovery of a novel antibiotic class was in 1987 , almost 30 years ago ( silver , l. , 2011 ) ! while there are a few new antibiotics currently in development , researchers don ’ t know if they ’ ll ever become usable as medicine . this void in the discovery of new antibiotics is problematic . when a bacteria becomes resistant to a specific drug within a drug class , it gains some level of resistance to drugs within the same class . for example , if a bacteria became resistant to ampicillin , it would also have some level of resistance to other penicillin-like antibiotics .
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if enough of the antibiotic is present , the bacterial cell is crippled and either stops growing ( bacterio-static effect ) or simply dies ( bacteri-cidal effect ) . just to be clear , antibiotics don ’ t affect viruses , fungi , or parasites - they only bind to bacterial cell targets so they only affect bacterial cells . in fact , they specifically target bacteria rather than human cells .
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since antibiotics do not kill fungi , parasites and viruses , what is the normal treatment of fungi , parasites and viruses ?
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antibiotics are a type of medicine which are used to treat bacterial infections . everyday we come into contact with thousands of bacterial cells . we are colonized with lots of different types of bacteria which live on us , and inside of us ; everywhere from the grooves of your fingerprint , to the nooks and crannies of your intestines . if you count up all of the bacteria , they actually outnumber us ( by `` us '' we mean our human cells ) about 10 to 1 . to stay healthy , we need to maintain a healthy ecosystem of bacteria , called normal flora ( not all bacteria is bad ! ) , while selectively getting rid of the harmful , “ pathogenic ” bacteria which can cause an infection . pathogenic bacteria is a relative term . some bacteria can cause illness in you no matter what . other bacteria cause illness when they wander from their normal location ( e.g . intestines ) and try to live in a new location ( e.g . bladder ) , which is what happens when you develop a urinary tract infection ( uti ) . the body ’ s immune system responds to an infection by trying to fight and destroy the invading bacteria ! what are antibiotics ? to help the immune system , we sometimes use antibiotics , which are chemicals ( specifically a swarm of small molecules ) that enter and stick to important parts ( think of targets ) of the bacterial cell , and interfere with its ability to survive and multiply . if the bacteria are susceptible to the antibiotic , then they will stop growing or simply die . these important parts include : proteins/sugars in the bacterial wall important enzymes that make new bacterial dna or proteins when an antibiotic molecule sticks to its target , it will disable or destroy that protein or enzyme . if enough of the antibiotic is present , the bacterial cell is crippled and either stops growing ( bacterio-static effect ) or simply dies ( bacteri-cidal effect ) . just to be clear , antibiotics don ’ t affect viruses , fungi , or parasites - they only bind to bacterial cell targets so they only affect bacterial cells . in fact , they specifically target bacteria rather than human cells . how were antibiotics discovered ? back in 1928 ( right before the great depression ) , alexander fleming first discovered the antibiotic penicillin when he noticed that bacteria in his lab wouldn ’ t grow near some fungus , which had accidentally found its way into his experiments . the fungus was making a small molecule which leaked into the petri gel around it , and fleming called the stuff - “ mold juice ” . he realized that the mold juice was killing the bacteria in the area ! the next big surprise for mr. fleming came when he later found out that the fungus was the same bluish-green fungus that grows on old bread . the discovery earned him the nobel prize in 1945 , and helped humanity develop a key antibiotic which has saved countless lives . in his nobel prize acceptance speech , fleming warned the world of the dangers of misusing antibiotics . he had already noted bacteria in his lab becoming resistant to penicillin , just a few years after its discovery ! after decades of antibiotic misuse , today we find ourselves facing bacteria which has become resistant to most , if not all antibiotics . how do antibiotics work ? let 's take a look at a couple of examples of antibiotics : penicillin and azithromycin . penicillin penicillin is a fabulous antibiotic because it is n't toxic to humans at concentrations that can kill bacteria and it can kill a lot of different types of bacteria . so how does it work ? penicillin weakens the bacterial wall by : deactivating a bacterial enzyme ( transpeptidase ) that builds and repairs the bacteria wall . activating a bacterial enzyme ( autolysin ) that cuts open parts of the bacterial wall , an enzyme normally only activated when the bacteria is multiplying . in short , penicillin causes the bacteria to weaken its own cell wall ( imagine being forced to punch yourself ! ) , and prevents the bacteria from being able to repair itself . with a weak wall , water seeps in , and the bacteria swells up and explodes . azithromycin azithromycin is a broad spectrum antibiotic which is often used to treat a wide variety of infections ; everything from pneumonia to sexually transmitted diseases . so how does it work ? azithromycin prevents the bacteria from multiplying by : blocking the cell 's ability to create proteins by attaching to ribosomes in the cell . in short , azithromycin prevents bacteria from multiplying , making it much easier for the immune system to handle the infection . antibiotic development over the years , a number of antibiotics have been discovered in nature or synthesized in the lab . some antibiotics target only specific bacteria and are called “ narrow spectrum ” antibiotics , whereas other antibiotics target many types of bacteria and are called “ broad spectrum ” antibiotics . developing completely new classes of antibiotics ( as opposed to variations on existing antibiotics ) is very difficult . it ’ s easy to find chemicals that kill bacteria , but not so easy to find substances that could be used as medicines , even if researchers were given infinite resources ! researchers are basically shooting in the dark . in fact , the most recent discovery of a novel antibiotic class was in 1987 , almost 30 years ago ( silver , l. , 2011 ) ! while there are a few new antibiotics currently in development , researchers don ’ t know if they ’ ll ever become usable as medicine . this void in the discovery of new antibiotics is problematic . when a bacteria becomes resistant to a specific drug within a drug class , it gains some level of resistance to drugs within the same class . for example , if a bacteria became resistant to ampicillin , it would also have some level of resistance to other penicillin-like antibiotics .
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antibiotic development over the years , a number of antibiotics have been discovered in nature or synthesized in the lab . some antibiotics target only specific bacteria and are called “ narrow spectrum ” antibiotics , whereas other antibiotics target many types of bacteria and are called “ broad spectrum ” antibiotics . developing completely new classes of antibiotics ( as opposed to variations on existing antibiotics ) is very difficult .
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if antibiotics kill bacteria , do they affect the good bacteria we contain in our bodies ?
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