Questions and Problems

Transcription

1 668 Chapter 15 Thermodynamics II Q = 0 and so U = 2W. For process a S b we have U 7 0 (the internal energy increases because the temperature increases) and W 7 0 (the gas expands), so Q = U + W is positive and the process cannot be adiabatic. For process a S c we have U = 0 (the internal energy remains the same because the temperature is constant) and W 7 0 (the gas expands), so again Q = U + W is positive and the process cannot be adiabatic. For process a S e U 6 0 (the internal energy decreases because the temperature decreases) and W = 0 (the volume does not change and so the gas does zero work), so Q = U + W is negative and the process cannot be adiabatic. The only process that could be adiabatic is a S d, for which U 6 0 (the internal energy decreases because the temperature decreases) and W 7 0 (the gas expands). For the process the quantity Q = U + W could be adiabatic (b) For the first, constant-volume process the relationship between heat and temperature change is Q = nc V T, while for the second, constant-pressure process the relationship is Q = nc p T (see Equations 15-11). The relationship C p 2 C V = R (Equation 15-15) tells us that C p is greater than C V, so for a given quantity of heat Q the temperature change T will be less for a constant-pressure process. You can get the same result from the first law of thermodynamics, U = Q 2 W or Q = U + W. For the constant-volume process W = 0 and Q = U: All of the heat goes into increasing the internal energy of the gas and so into raising its temperature. But for the constant-pressure process, the expanding gas must do positive work W on the piston. Some of the heat goes into doing this work, so only a fraction of Q is available to increase the internal energy of the gas (c) From Equations the relationship between heat and temperature change for these constant-pressure processes is Q = nc p T. Table 15-1 shows that the molar specific heat at constant pressure C p has a smaller value for He than for N 2, so for a given quantity of heat Q the temperature change T is greater for He than for N 2. Equation tells us that the work done by an ideal gas in a constant-pressure process is W = nr T; the number of moles n is the same for both gases and R is the ideal gas constant, so more work is done by the gas that undergoes the greater temperature change T (in this example, helium) No. A gasoline engine uses ambient temperature (about 20 C or 293 K) as the cold temperature. The engine your fellow student has designed uses a hot temperature that must be less than 1941 K, the melting temperature of titanium, or else the cylinders would melt. The efficiency of a Carnot cycle operating between T C = 293 K and T H = 1941 K is e Carnot = 1-1T C >T H 2 = K2 > K2 4 = = 0.849, or 84.9%. Your fellow student is claiming an even higher efficiency, which is impossible because no heat engine can have greater efficiency than a Carnot engine. This would be a poor investment! 15-7 (b) Both melting and vaporization take place at a constant temperature, so we can use Equation 15-33, S = Q>T, to calculate the entropy change in each process. For melting at 0 C or T = K, Q = ml F = (1.00 kg)(3.34 * 10 5 J>kg) = 3.34 * 10 5 J and S melting = Q>T = * 10 5 J2 > K2 = 1.22 * 10 3 J>K. For vaporization at 100 C or T = ( ) K = K, Q = ml V = kg * 10 6 J>kg2 = 2.26 * 10 6 J and S vaporization = Q>T = * 10 6 J2 > K2 = 6.06 * 10 3 J>K. The entropy change is about five times greater for vaporization than for melting, which agrees with the idea that entropy is a measure of disorder. The molecules of liquid water are able to move while those of ice cannot, so the entropy of liquid water is greater than that of ice. But the molecules of water vapor are free to move over a much greater volume, and so the entropy of water vapor is very much greater than that of liquid water. Questions and Problems In a few problems, you are given more data than you actually need; in a few other problems, you are required to supply data from your general knowledge, outside sources, or informed estimate. Interpret as significant all digits in numerical values that have trailing zeros and no decimal points. For all problems, use g = 9.80 m>s 2 for the free-fall acceleration due to gravity. Neglect friction and air resistance unless instructed to do otherwise. Basic, single-concept problem Intermediate-level problem, may require synthesis of concepts and multiple steps Challenging problem SSM Solution is in Student Solutions Manual Conceptual Questions 1. Clearly define and give an example of each of the following thermodynamic processes: (a) isothermal, (b) adiabatic, (c) isobaric, and (d) isochoric. SSM 2. Can a system absorb heat without increasing its internal energy? Explain. 3. Why does the temperature of a gas increase when it is quickly compressed? 4. Why is it possible for the temperature of a system to remain constant even though heat is released or absorbed by the system? 5. When we say engine, we think of something mechanical with moving parts. In such an engine, friction always reduces the engine s efficiency. Why? SSM 6. There are people who try to keep cool on a hot summer day by leaving the refrigerator door open, but you can t cool your kitchen this way! Why not? 7. If the coefficient of performance is greater than 1, do we get more energy out than we put in, violating conservation of energy? Why or why not? 8. How does the time required to freeze water vary with each of the following parameters: mass of water, power of the refrigerator, and temperature of the outside air? 9. By how much is the entropy of the universe changed when heat is released from a hotter object to a colder one? In what sense does this correspond to energy becoming unavailable for doing work? SSM 10. In a slow, steady isothermal expansion of an ideal gas against a piston, the work done is equal to the heat input. Is this consistent with the first law of thermodynamics? 11. If a gas expands freely into a larger volume in an insulated container so that no heat is added to the gas, its entropy increases. Using the definition of S, explain this statement. Freed_c15_ _st_hr.indd 668

2 Questions and Problems Why do engineers designing a steam-electric generating plant always try to design for as high a feed-steam temperature as possible? 13. Conduction across a temperature difference is an irreversible process, but the object that lost heat can always be rewarmed, and the one that gained heat can be recooled. An object sliding across a rough table slows down and warms up as mechanical energy dissipates. This process is irreversible, but the object can be cooled and set moving again at its original speed. So in just what sense are these processes irreversible? SSM 14. The frictional drag of the atmosphere causes an orbiting satellite to move closer to Earth and to gain kinetic energy. In what way does energy become unavailable for doing work in this irreversible process? 15. Is a process necessarily reversible if there is no exchange of heat between the system in which the process takes place and its surroundings? 16. Is the operation of an automobile engine reversible? 17. In discussing the Carnot cycle, we say that extracting heat from a reservoir isothermally does not change the entropy of the universe. In a real process, this is a limiting situation that can never quite be reached. Why not? What is the effect on the entropy of the universe? SSM 18. A pot full of hot water is placed in a cold room, and the pot gradually cools. How does the entropy of the water change? 19. If you drop a glass cup on the floor, it will shatter into fragments. If you then drop the fragments on the floor, why will they not become a glass cup? 20. Why is the entropy of 1 kg of liquid iron greater than that of 1 kg of solid iron? Explain your answer. Multiple-Choice Questions 21. An ideal gas trapped inside a thermally isolated cylinder expands slowly by pushing back against a piston. The temperature of the gas A. increases. B. decreases. C. remains the same. D. increases if the process occurs quickly. E. remains the same if the process occurs quickly. SSM 22. A gas is compressed adiabatically by a force of 800 N acting over a distance of 5.0 cm. The net change in the internal energy of the gas is A J. B. +40 J. C J. D. 240 J. E An ideal gas is contained in a cylinder of fixed length and diameter. Eighty joules of heat is added while the piston is held in place. The work done by the gas on the walls of the cylinder is A. 80 J. B. 0 J. C. less than 80 J. D. more than 80 J. E. not specified by the information given. 24. In an isothermal process, there is no change in D. heat. E. internal energy and pressure. 25. In an isobaric process, there is no change in D. internal energy. E. internal energy and pressure. SSM 26. In an isochoric process, there is no change in D. internal energy. E. internal energy and pressure. 27. A gas quickly expands in an isolated environment. During the process, the gas exchanges no heat with its surroundings. The process is A. isothermal. B. isobaric. C. isochoric. D. adiabatic. E. isotonic. 28. The statement that no process is possible in which heat is absorbed from a cold reservoir and transferred completely to a hot reservoir is A. not always true. B. only true for isothermal processes. C. the first law of thermodynamics. D. the second law of thermodynamics. E. the zeroth law of thermodynamics. 29. Carnot s heat engine employs A. two adiabatic processes and two isothermal processes. B. two adiabatic processes and two isobaric processes. C. two adiabatic processes and two isochoric processes. D. two isothermal processes and two isochoric processes. E. two isothermal processes and two isobaric processes. SSM 30. Compare two methods to improve the theoretical efficiency of a heat engine: lower T C by 10 K or raise T H by 10 K. Which one is better? A. Lower T C by 10 K. B. Raise T H by 10 K. C. Both changes would give the same result. D. The better method would depend on the difference between T C and T H. E. There is nothing you can do to improve the theoretical efficiency of a heat engine. Estimation/Numerical Analysis 31. (a) Estimate the work (in J) done in raising a book from the floor to the table. (b) Estimate the temperature rise in a glass of water if that amount of energy were added to it. 32. (a) Estimate the work (in J) done in driving a car across America. (b) If the energy required to do that work were added to an Olympic-sized swimming pool, how much would the temperature of the water rise? 33. Estimate the internal energy increase in a 1.00-L sample of oxygen that increases in temperature from 20 C to 100 C. Assume that the volume of this ideal gas is constant in the process. SSM Freed_c15_ _st_hr.indd 669

3 670 Chapter 15 Thermodynamics II 34. Estimate the pressure acting on a 2-L sample of nitrogen, an ideal gas, when it is held at 300 K. 35. Biology Estimate how far up a granite monolith a 70-kg student can climb if she uses 50% of the energy from a 4000-kcal meal to scale the cliff. (The other 50% supports her resting metabolic rate.) Is your answer reasonable? 36. Estimate the efficiency of an average internal combustion engine in Canada. 37. Estimate the distance a car can be driven on a tank of gas. Assume that the gas releases 125,000 BTU of energy per gallon. SSM 38. Estimate the amount of energy that is wasted each day in Europe due to an additional inefficiency of 5% (on top of the thermodynamic efficiency) from cars that are not lubricated properly. You will have to make some assumptions about how many cars are poorly maintained, how far Europeans drive each day, and so on. 39. Biology Estimate the efficiency of the human body acting as a heat engine. Problems 15-1 The laws of thermodynamics involve energy and entropy 15-2 The first law of thermodynamics relates heat flow, work done, and internal energy change 40. If 800 J of heat is added to a system that does no external work, how much does the internal energy of the system increase? 41. Five hundred joules of heat is absorbed by a system that does 200 J of work on its surroundings. What is the change in the internal energy of the system? 15-3 A graph of pressure versus volume helps to describe what happens in a thermodynamic process 42. Calculate the amount of work done on a gas that undergoes a change of state described by the pv diagram shown in Figure p(10 2 Pa) V(m 3 ) Figure Problem Calculate the amount of work done on a gas that undergoes a change of state described by the pv diagram shown in Figure p(10 2 Pa) V(m 3 ) Figure Problem A gas is heated and is allowed to expand such that it follows a horizontal line path on a pv diagram from its initial state (1.0 * 10 5 Pa, 1.0 m 3 ) to its final state (1.0 * 10 5 Pa, 2.0 m 3 ). Calculate the work done by the gas on its surroundings. 45. A gas is heated such that it follows a vertical line path on a pv diagram from its initial state (1.0 * 10 5 Pa, 3.0 m 3 ) to its final state (2.0 * 10 5 Pa, 3.0 m 3 ). Calculate the work done by the gas on its surroundings. SSM 46. A sealed cylinder has a piston and contains 8000 cm 3 of an ideal gas at a pressure of 8.0 atm. Heat is slowly introduced, and the gas isothermally expands to 16,000 cm 3. How much work does the gas do on the piston? 47. An ideal gas expands isothermally, performing 8.80 kj of work in the process. Calculate the heat absorbed during the expansion. SSM 48. Heat is added to 8.00 m 3 of helium gas in an expandable chamber that increases its volume by 2.00 m 3. If in the isothermal expansion process 2.00 kj of work is done by the gas, what was its original pressure? 49. A cylinder that has a piston contains 2.00 mol of an ideal gas and undergoes a reversible isothermal expansion at 400 K from an initial pressure of 12.0 atm down to 3.00 atm. Determine the amount of work done by the gas. 50. A gas contained in a cylinder that has a piston is kept at a constant pressure of 2.80 * 10 5 Pa. The gas expands from m 3 to 1.50 m 3 when 300 kj of heat is added to the cylinder. What is the change in internal energy of the gas? 51. The pressure in an ideal gas is slowly reduced to 1>4 its initial value, while being kept in a container with rigid walls. In the process, 800 kj of heat leaves the gas. What is the change in internal energy of the gas during this process? SSM 52. An ideal gas is compressed adiabatically to half its volume. In doing so, 1888 J of work is done on the gas. What is the change in internal energy of the gas? 53. Two moles of an ideal monatomic gas expand adiabatically, performing 8.00 kj of work in the process. What is the change in temperature of the gas during the expansion? 15-4 More heat is required to change the temperature of an ideal gas isobarically than isochorically 54. One mole of an ideal monatomic gas (g = 1.66), initially at a temperature of 0.00 C, undergoes an adiabatic expansion from a pressure of 10.0 atm to a pressure of 2.00 atm. How much work is done on the gas? 55. A container holds 32.0 g of oxygen gas at a pressure of 8.00 atm. How much heat is required to increase the temperature by 100 C at constant pressure? 56. A container holds 32.0 g of oxygen gas at a pressure of 8.00 atm. How much heat is required to increase the temperature by 100 C at constant volume? 57. The temperature of 4.00 g of helium gas is increased at constant volume by 1.00 C. Using the same amount of heat, the temperature of what mass of oxygen gas will increase at constant volume by 1.00 C? SSM 58. Heat is added to 1.00 mol of air at constant pressure, resulting in a temperature increase of 100 C. If the same amount of heat is instead added at constant volume, what is the temperature increase? The molar specific heat ratio g = C p >C V for the air is The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.6. What is the molar specific heat ratio g = C p >C V? Freed_c15_ _st_hr.indd 670

4 Questions and Problems The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. By what factor does the temperature increase? 61. What ratio of initial volume to final volume, V i >V f, will raise the temperature of air from 27.0 C to 857 C in an adiabatic process? The molar specific heat ratio g = C p >C V for air is 1.4. SSM 62. A monatomic ideal gas at a pressure of 1.00 atm expands adiabatically from an initial volume of 1.50 m 3 to a final volume of 3.00 m 3. What is the new pressure? 15-5 The second law of thermodynamics describes why some processes are impossible 63. An engine doing work takes in 10 kj and exhausts 6 kj. What is the efficiency of the engine? SSM 64. What is the theoretical maximum efficiency of a heat engine operating between 100 C and 500 C? 65. A heat engine operating between 473 K and 373 K runs at about 70% of its theoretical maximum efficiency. What is its efficiency? 66. An engine operates between 10.0 C and 200 C. At the very best, how much heat should we be prepared to supply in order to output 1000 J of work? 67. A furnace supplies 28.0 kw of thermal power at 300 C to an engine and exhausts waste energy at 20.0 C. At the very best, how much work could we expect to get out of the system per second? SSM 68. A kitchen refrigerator extracts 75.0 kj per second of energy from a cool chamber while exhausting 100 kj per second to the room. What is its coefficient of performance? 69. What is the coefficient of performance of a Carnot refrigerator operating between 0.00 C and 80.0 C? 70. An electric refrigerator removes 13.0 MJ of heat from its interior for each kilowatt-hour of electric energy used. What is its coefficient of performance? 71. A certain refrigerator requires 35.0 J of work to remove 190 J of heat from its interior. (a) What is its coefficient of performance? (b) How much heat is ejected to the surroundings at 22.0 C? (c) If the refrigerator cycle is reversible, what is the temperature inside the refrigerator? SSM 15-6 The entropy of a system is a measure of its disorder 72. A reservoir at a temperature of 400 K gains 100 J of heat from another reservoir. What is its entropy change? 73. What is the minimum change of entropy that occurs in kg of ice at 273 K when 6.68 * 10 4 J of heat is added so that it melts to water? SSM 74. If, in a reversible process, enough heat is added to change a 500-g block of ice to water at a temperature of 273 K, what is the change in the entropy of the ice/water system? 75. A room is at a constant 295 K maintained by an air conditioner that pumps heat out. What is the entropy change of the room for each 5.00 kj of heat removed? 76. One mole of ideal gas expands isothermally from 1.00 m 3 to 2.00 m 3. What is the entropy change for the gas? 77. An 1800-kg car traveling at 80.0 km>h crashes into a concrete wall. If the temperature of the air is 27.0 C, what is the entropy change of the universe as a result of the crash? Assume all of the car s kinetic energy is converted into heat. SSM 78. A 1000-kg rock at 20.0 C falls 100 m into a large lake, also at 20.0 C. Assuming that all of the rock s kinetic energy on entering the lake converts to thermal energy absorbed by the lake, what is the change in entropy of the lake? 79. Astronomy The surface of the Sun is about 5700 K, and the temperature of Earth s surface is about 293 K. What entropy change occurs when 8000 J of energy is transferred by heat from the Sun to Earth? 80. You have a cup containing 220 g of freshly brewed coffee which, at 75.0 C, is too warm to drink. If you cool the coffee a little by pouring 60.0 g of tap water at 26.0 C into the cup, estimate how much the entropy of the universe increases. 81. In a vacuum bottle, 350 g of water and 150 g of ice are initially in equilibrium at 0.00 C. The bottle is not a perfect insulator. Over time, its contents come to thermal equilibrium with the outside air at 25.0 C. How much does the entropy of universe increase in the process? SSM General Problems 82. A vertical metal cylinder contains an ideal gas. The top of the cylinder is closed off by a piston of mass m that is free to move up and down with no appreciable friction. The piston is a height h above the bottom of the cylinder when the gas alone supports it. Sand is now very slowly poured onto the piston until the weight of the sand is equal to the weight of the piston. Find the new height of the piston (in terms of h) if the ideal gas in the cylinder is (a) oxygen O 2, (b) helium He, or (c) hydrogen H A Carnot engine on a ship extracts heat from seawater at 18.0 C and exhausts the heat to evaporating dry ice at C. If the ship s engines are to run at 8000 horsepower, what is the minimum amount of dry ice the ship must carry for the ship to run for a single day? SSM 84. A Carnot engine removes 1200 J of heat from a high-temperature source and dumps 600 J to the atmosphere at 20.0 C. (a) What is the efficiency of the engine? (b) What is the temperature of the hot reservoir? 85. A certain engine has a second-law efficiency of 85.0%. During each cycle, it absorbs 480 J of heat from a reservoir at 300 C and dumps 300 J of heat to a cold temperature reservoir. (a) What is the temperature of the cold reservoir? (b) How much more work could be done by a Carnot engine working between the same two reservoirs and extracting the same 480 J of heat in each cycle? 86. A refrigerator is rated at 370 W. Its interior is at 0 C, and its surroundings are at 20 C. If the second law efficiency of its cycle is 66%, how much heat can it remove from its interior in 1 min? 87. Medical During a high fever, a 60.0-kg-patient s normal metabolism is increased by 10.0%. This results in an increase of 10.0% in the heat given off by the person. When the person slowly walks up five flights of stairs (20.0 m), she normally releases 100 kj of heat. Compare her efficiency when she has a fever to when her temperature is normal. SSM 88. A rigid 5.50-L pressure cooker contains steam initially at 100 C under a pressure of 1.00 atm. Consult Table 15-1 as needed and assume that the values given there remain constant. The mass of a water molecule is 2.99 * kg. (a) To what temperature (in C) would you have to heat the steam so that its pressure was 1.25 atm? (b) How much heat would you need in part (a)? (c) Calculate the specific heat of the steam in part (a) in units of J> 1kg K). Freed_c15_ _st_hr.indd 671

5 672 Chapter 15 Thermodynamics II 89. You have a cup containing 220 g of freshly brewed coffee which, at 75 C, is too warm to drink. If you cool the coffee a little by pouring 60 g of tap water at 26 C into the cup, estimate how much the entropy of the universe increases. 90. A certain electric generating plant produces electricity by using steam that enters its turbine at a temperature of 320 C and leaves it at 40 C. Over the course of a year, the plant consumes 4.40 * J of heat and produces an average electric power output of 600 MW. What is its second-law efficiency? 91. As we drill down into the rocks of Earth s crust, the temperature typically increases by 3.0 C for every 100 m of depth. Oil wells are commonly drilled to depths of 1830 m. If water is pumped into the shaft of the well, it will be heated by the hot rock at the bottom and the resulting heated steam can be used as a heat engine. Assume that the surface temperature is 20 C. (a) Using such a 1830-m well as a heat engine, what is the maximum efficiency possible? (b) If a combination of such wells is to produce a 2.5-MW power plant, how much energy will it absorb from the interior of Earth each day? SSM 92. The energy efficiency ratio (or rating) the EER for air conditioners, refrigerators, and freezers is defined as the ratio of the input rate of heat ( Q C >t, in BTU>h) to the output rate of work (W>t, in W): EER = Q C>t1BTU>hr2. (a) Show W>t1W2 that the EER can be expressed as Q C 1BTU2 W 1W # and is therefore h2 nothing more than the coefficient of performance CP expressed in mixed units. (b) Show that the EER is related to the coefficient of performance CP by the equation CP = EER> (c) Typical home freezers have EER ratings of about 5.1 and operate between an interior freezer temperature of 0.00 F and an outside kitchen temperature of about 70.0 F. What is the coefficient of performance for such a freezer, and how does it compare to the coefficient of performance of the best possible freezer operating between those temperatures? (d) What is the EER of the best possible freezer in part (c)? 93. Your energy efficient home freezer has an EER of 6.50 (see Problem 15-98). In preparation for a picnic, you put 1.50 L of water at 20.0 C into the freezer to make ice at 0.00 C for your ice chest. (See Tables 11-1, 14-3, and 14-4 as needed.) (a) How much electrical energy (which runs the freezer) is required to make the ice? Express your answer in J and kwh. (b) How much heat is ejected into your kitchen, which is at 22.0 C? (c) How much does making the ice change the entropy of your kitchen? 94. Biology The volume of air taken in during a typical breath is 0.5 L. The inhaled air is heated to 37 C (the internal body temperature) as it enters the lungs. Because air is about 80% nitrogen N 2, we can model it as an ideal gas. Suppose that the outside air is at room temperature (20 C) and that you take two breaths every 3.0 s. Assume that the pressure does not change during the process. (a) How many joules of heat does it take to warm the air in a single breath? (b) How many food calories (kcal) are used up per day in heating the air you breathe? Is this a significant amount of typical daily caloric intake? 95. A heat engine works in a cycle between reservoirs at 273 K and 490 K. In each cycle, the engine absorbs 1250 cal of heat from the high-temperature reservoir and does 475 J of work. (a) What is its efficiency? (b) By how much is the entropy of the universe changed when the engine goes through one full cycle? (c) How much energy becomes unavailable for doing work when the engine goes through one full cycle? SSM 96. You have a cabin on the plains of central Saskatchewan. It is built on a 8.50-m by 12.5-m rectangular foundation with walls 3.00 m tall. The wooden walls and flat roof are made of white pine that is 9.00 cm thick. To conserve heat, the windows are negligibly small. The floor is well insulated so you lose negligible heat through it. The cabin is heated by an electrically powered heat pump operating on the Carnot cycle between the inside and outside air. When the outside temperature is a frigid F, how much electrical energy does the heat pump consume per second to keep the interior temperature a steady and toasty 70.0 F? Assume that the surfaces of the walls and roof are at the same temperature as the air with which they are in contact and neglect radiation. (Consult Table 14-5 as needed.) 97. Sports In an international diving competition, divers fall from a platform 10.0 m above the surface of the water into a very large pool. The diver leaves the platform with negligible initial speed. What is the maximum change in the entropy of the water in the pool at 25.0 C when a 75.0-kg diver executes his dive? Does the pool s entropy increase or decrease? 98. A heat engine works in a cycle between reservoirs at 273 K and 490 K. In each cycle the engine absorbs 1250 J of heat from the high-temperature reservoir and does 475 J of work. (a) What is its efficiency? (b) What is the change in entropy of the universe when the engine goes through one complete cycle? (c) How much energy becomes unavailable for doing work when the engine goes through one complete cycle? 99. Biology A 68.0-kg person typically eats about 2250 kcal per day, 20.0% of which goes to mechanical energy and the rest to heat. If she spends most of her time in her apartment at 22.0 C, how much does the entropy of her apartment change in one day? Does entropy increase or decrease? SSM 100. Consider an engine in which the working substance is 1.23 mol of an ideal gas for which g = The engine runs reversibly in the cycle shown on the pv diagram (Figure 15-23). The cycle consists of an isobaric (constant-pressure) expansion a at a pressure of 15.0 atm, during which the temperature of the gas increases from 300 K to 600 K, followed by an isothermal expansion b until its pressure becomes 3.00 atm. Next is an isobaric compression c at a pressure of 3.00 atm, during which the temperature decreases from 600 K to 300 K, followed by an isothermal compression d until its pressure returns to 15 atm. Find the work done by the gas, the heat absorbed by the gas, the internal energy change, and the entropy change of the gas, first for each part of the cycle and then for the complete cycle. p T 1 T 2 a p 1 p 2 d V 1 V 4 V 2 V 3 V Figure Problem 100 c 15 atm b 3 atm 600 K 300 K Freed_c15_ _st_hr.indd 672