Entropy & the Second Law of Thermodynamics

PHYS102 Previous Exam Problems CHAPTER 20 Entropy & the Second Law of Thermodynamics Entropy gases Entropy solids & liquids Heat engines Refrigerators Second law of thermodynamics 1. The efficiency of a car engine is 20% when the engine does 1.2 kj of work per cycle. What is the energy Q L the engine loses per cycle as heat? (Ans: 4.8 kj) 2. The freezing compartment of a Carnot refrigerator is at 269 K while the outside air in the room is at 298 K. If the power of refrigerator motor is 150 W, what is the maximum amount of energy that can be extracted as heat from the freezing compartment in 10.0 min? (Ans: 8.35 10 5 J) 3. Calculate the change in entropy of 1.0 kg of ice at 0.0 C when its temperature is increased to 20.0 C. [L f, ice= 333 kj/kg; c water= 4190 J/kg.K] (Ans: 1.5 10 3 J/K) 4. In an isolated container, a 0.10-kg block of aluminum initially at 600 K is brought into thermal contact with a very large block of iron at 200 K until thermal equilibrium is reached. The iron block is so large that we can assume that its temperature does not change. What is the change in entropy of the iron block? [specific heat of iron is 0.11 kcal/kg.k and specific heat of aluminum is 0.22 kcal/kg.k] (Ans: 44 cal/k) 5. A Carnot engine completes 4 cycles per second. In every cycle, it delivers a power 120 W and discharges 40 J. what is the efficiency of the engine? (Ans: 43%) 6. A refrigerator converts 7.0 kg of water at 0 o C into ice at 0 o C in one hour. What is the coefficient of performance of the refrigerator if its power input is 300 W? [Heat of fusion for water is 333 kj/kg] (Ans: 2.2) 7. As shown in figure 1, container A, of volume 1.0 L, holds 2.0 moles of oxygen. Container B, of volume 4.0 L, holds 2.0 moles of nitrogen. Both containers are isolated and are at the same temperature. The valve between the two containers is open and the molecules of each gas spread to fill the whole volume of the two containers. Treat the process as free expansion. What is the total entropy change in the process? (Ans: 30 J/K) 8. An 8.0-MW electric power plant has an efficiency of 30 %. It loses its waste heat to the environment. How much heat is lost to the environment per second? (Ans: 19 MJ) 9. A Carnot heat engine operates between reservoirs at temperatures of 700 K and 300 K. In one cycle, it absorbs 1500 J of heat. How much work is done by the engine? (857 J) 10. A Carnot refrigerator operating between -20 o C and +20 o C extracts heat from the cold reservoir at the rate 200 J/s. What is the rate at which work is done on the refrigerator? (Ans: 32 J/s) 11. What is the change in entropy for melting 6.0 kg of a solid which melts at 27 o C? [The latent heat of fusion of the solid is 2.5 10 4 J/kg] (Ans: + 500 J/K) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 1

12. A Carnot heat engine operates between two reservoirs at temperatures of 500 K and 375 K. If the engine extracts 6.0 10 7 J/cycle, find the heat rejected per cycle. (Ans: 4.5 10 7 J/cycle) 13. A Carnot heat engine operates between two reservoirs at temperatures of 400 K and 500 K. What is the ratio of the work done by the engine to the heat expelled to the low-temperature reservoir? (Ans: 0.25) 14. Liquid water having a mass of 50 grams was initially at 0 o C. Heat was added to the water so that its entropy increases by 94.0 J/K, what is the final temperature of the water? (Ans: 428 K) 15. A 2.50-mole sample of an ideal monatomic gas was initially at 300 K. The gas is compressed isobarically to half of its original volume, what is the change of entropy of the gas? (Ans: 36.0 J/K) 16. A 100-g block of ice at -10 o C is placed in a lake whose temperature is 20 o C. Calculate the change in entropy of the lake. [c w = 4190 J/kg.K, c i = 2220 J/kg.K, L F = 333 kj/kg] (Ans: 150 J/K) 17. The temperature of 2.0 mole of a monatomic ideal gas is raised reversibly from 100 K to 300 K, with its volume kept constant. What is the entropy change for the gas? (Ans: 27 J/K) 18. Two moles of an ideal monatomic gas are taken around the cycle shown in figure 2. If T a = 60K, T b = 30K and T c = 38K, find the efficiency? [C v = 12.5 and C p = 20.75J/mol.K] (Ans: 56%) 19. Two moles of an ideal gas undergo an adiabatic free expansion from an initial volume of 0.6 L to 1.3 L. Calculate the change in entropy of gas. (Ans: 12.9 J/K) 20. System A (one kilogram of ice at 0 o C) is added to system B (one kilogram of water at 100 o C) in an insulator container. Calculate the total change in entropy of system A. (Ans: 1.37 kj/k) 21. One mole of a monatomic ideal gas is taken from an initial state (i) to a final state (f), as shown in figure 3. The curved line is an isotherm. Calculate the increase in entropy of the gas for this process. (Ans: 36.5 J/K) 22. One mole of a diatomic ideal gas is taken through the cycle shown in figure 4. Process b c is adiabatic, P a = 0.30 atm, P b = 3.0 atm, V b = 1.0 10-3 m 3, and V c = 5.2 10-3 m 3. What is the efficiency of the cycle? (Ans: 35%) 23. You mix two samples of water, A and B. Sample A is 100 g at 20 o C and sample B is also 100 g but at 80 o C. Calculate the change in the entropy of sample B. (Ans: - 8.9 cal/k) 24. Five moles of an ideal gas undergo a reversible isothermal compression from volume V to volume V/2 at temperature 30 o C. What is the change in the entropy of the gas? (Ans: -29 J/K) 25. An automobile engine operates with an overall efficiency of 20%. How many gallons of gasoline is wasted for each 10 gallons burned? (Ans: 8) 26. 240 grams of water at 8 o C are cooled to ice at - 5 o C. Calculate the change in entropy of the water. [c ice = 2090 J/kg.K, c water = 4186 J/kg.K, L f = 3.33 10 5 J/Kg] (Ans: -331 J/K) 27. An ideal monatomic gas is confined to a cylinder by a piston. The piston is slowly pushed in so that the gas temperature remains at 27 o C. During the compression, 750 J of work is done on the gas. What is the change in the entropy of the gas? (Ans: - 2.5 J/K) 28. An ideal engine, whose low-temperature reservoir is at 27 o C, has an efficiency of 20 %. By how much should the temperature of the high-temperature reservoir be increased to increase the efficiency to 50 %? (Ans: 225 K) 29. What is the change in entropy of 200 g of water as its temperature increases from 0 o C to 50 o C? [For water: the specific heat = 4.19 kj/(kg.k), and the latent heat of fusion = 333 kj/kg] (Ans: 1.41 10 2 J/K) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 2

30. What is the coefficient of performance of a refrigerator that absorbs 40 cal/cycle at low temperature and expels 51 cal/cycle at high temperature? (Ans: 3.6) 31. A heat engine absorbs 8.71 kj per cycle from a hot reservoir with an efficiency of 25% and executes 3.15 cycles per second. What is the power output of the heat engine? (Ans: 6.86 kw) 32. Figure 5 shows a cycle for a heat engine for which Q H = 35 J. What is the thermal efficiency of the engine? (Ans: 29%) 33. Two moles of an ideal monatomic gas undergo the reversible process shown in figure 6. How much energy is absorbed as heat by the gas during this process? (Ans: 13.5 kj) 34. A freezer has a coefficient of performance of 3.8 and uses 200 W of power. How long would it take to freeze 600 g of water at 0 C? [Heat of fusion of ice = 3.33 10 5 J/kg] (Ans: 4.4 minutes) 35. A Carnot heat engine absorbs 70.0 kj as heat and expels 55.0 kj as heat in each cycle. If the lowtemperature reservoir is at 120 o C, find the temperature of the high-temperature reservoir. (Ans: 227 o C) 36. One mole of an ideal gas is taken through the reversible cycle shown in figure 8, with Q 1 = 6.0 kj, Q 2 = 30 kj, Q 3 = 18 kj and Q 4 = 10 kj. What is the efficiency of this cycle? (Ans: 0.22) 37. A heat engine operates between 800 K and 300 K, but its efficiency is only 80% of the maximum possible. What is the actual efficiency of the engine? (Ans: 50%) 38. An ideal freezer has a coefficient of performance of 5.0. If the temperature inside the freezer is 20 o C, what is the temperature at which heat is rejected? (Ans: 31 o C) 39. If 3200 J of heat flows from a hot reservoir at 500 K to another reservoir at 300 K though a conducting metal rod, find the change in entropy of the universe (i.e. the change in entropy of the two reservoirs plus the rod). Assume steady state. (Ans: +4.27 J/K) 40. A 200 g of aluminum at 100 o C is mixed with 50.0 g of water at 20.0 o C, with the mixture thermally isolated. The aluminum-water system comes to equilibrium at 57.0 o C. What is the entropy change of the aluminum-water system? [specific heat of aluminum = 900 J/kg K] (Ans: + 2.86 J/K) 41. Figure 9 shows T versus S diagram of 4.00 moles of an ideal monatomic gas undergoing a reversible cyclic process. How much energy is absorbed as heat by the gas during the process from A to B? (Ans: 900 J) 42. A heat engine operates between a hot reservoir at 1500 K and a cold reservoir at 500 K. During each cycle, 1.0 10 5 J of heat is absorbed from the hot reservoir and 5.0 10 4 J of work is performed. What is the actual efficiency of this engine? (Ans: 75 % of the maximum efficiency) 43. A system consists of two thermal reservoirs in contact with each other, one at a temperature of 300 o C and the other at a temperature of 200 o C. If 6000 J of heat is transferred from the 300 o C reservoir to the 200 o C reservoir, what is the change in entropy of this system? (Ans: +2.2 J/K) 44. A Carnot heat engine operates between two reservoirs at temperatures of 300 K and 500 K. The work done in one cycle is 1200 J. What is the change in the entropy of the hot reservoir? (Ans: 6.0 J/K) 45. A heat engine is connected to two heat reservoirs: one is steam at 100 o C, and the other is ice at 0.0 o C. The engine runs by condensing 1.0 g of steam and melting 5.0 g of ice. What is the efficiency of this engine? (Ans: 0.26) 46. One kg of copper, initially at 20.0 o C, absorbs 5.00 kj of heat. What is the change of entropy of copper? The specific heat of copper is 390 J/kg.K. (Ans: 16.7 J/K) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 3

47. A Carnot heat pump transfers energy as heat to a house with inside temperature at 21 C when the outdoor temperature is 15 C. For each joule of electric energy required to operate the pump, how much heat energy is transferred to the building? (Ans: 8.2 J) 48. Two moles of an ideal gas undergoes the expansion shown in figure 17. What is the change in the entropy of the gas as it expands from state i to state f? (Ans: +11.5 J/K) A B C D E Conceptual Problems 1. A heat engine operates between 600 K and 300 K. In each cycle, it takes 100 J from the hot reservoir, loses 25 J to the cold reservoir, and does 75 J of work. This heat engine violates: A. The second law but not the first law of thermodynamics. B. Both, the first law and the second law of thermodynamics. C. The first law but not the second law of the thermodynamics. D. Neither the first law nor the second law. E. Conservation of energy. 2. Which of the following statements are wrong? 1. The efficiency of the ideal engine is greater than one. 2. The change in entropy is zero for reversible isothermal processes. 3. In cyclic processes, the change in entropy is zero. 4. If steam is condensed, its entropy will decrease. 5. If ice is melted, its entropy will decrease. (Ans: 1, 2 and 5) 3. Which one of the following statements is wrong? A. The total entropy of a system increases only if it absorbs heat. B. After a system has gone through a reversible cyclic process, its total entropy does not change. C. A refrigerator works like a heat engine in reverse. D. Thermal energy cannot be transferred spontaneously from a cold object to a hot object. E. No heat engine has higher efficiency than Carnot efficiency. 4. A system consists of an equilibrium mixture of ice and water at constant pressure. On heating the system, some of the ice melts, then A. the entropy increases. B. the entropy decreases. C. the temperature decreases. D. the internal energy decreases. E. the temperature increases. 5. Choose the correct answer: If a process occurs in a closed system, the entropy of the system A. increases for an irreversible process. B. decreases for a reversible process. C. remains constant for an irreversible process. D. increases for a reversible process. E. decreases for an irreversible process. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 4

6. Find the wrong statement. A. The entropy of an isolated system can decrease. B. Perfect heat engines are not possible. C. Perfect refrigerators are not possible. D. Entropy is not a conserved quantity. E. A refrigerator requires work as input to make heat flow from a cold reservoir to a hot reservoir. 7. A hot object and a cold object are placed in thermal contact and the combination is isolated. They transfer energy until they reach a final equilibrium temperature. The change in the entropy of the hot object (ΔS h), the change in the entropy of the cold object (ΔS c), and the change in the entropy of the combination (ΔS total) are: A. ΔSh < 0, ΔSc > 0, ΔStotal > 0 B. ΔSh > 0, ΔSc > 0, ΔStotal > 0 C. ΔSh < 0, ΔSc > 0, ΔStotal = 0 D. ΔSh > 0, ΔSc < 0, ΔStotal > 0 E. ΔSh > 0, ΔSc < 0, ΔStotal < 0 8. Which of the following statements is correct? A. For an adiabatic process the change in entropy is zero if it is done reversibly. B. For an adiabatic process the change in entropy is negative if it is done irreversibly. C. For an isothermal expansion the change in entropy of an ideal gas is zero. D. A Carnot engine does not reject any heat as waste. E. The efficiency of a Carnot engine is 100%. 9. Consider the following reversible processes in which the temperatures of two identical gases (A and B) with the same number of moles are increased from the same initial temperature to the same final temperature. For gas A, the process is carried out at constant volume while for gas B it is carried out at constant pressure. The change in entropy A. is greater for B. B. is greater for A only if the initial temperature is high. C. is greater for A. D. is the same for A and B. E. is greater for A only if the initial temperature is low. 10. A sample of an ideal monatomic gas undergoes the reversible process A to B displayed in the T-S diagram shown in figure 7. The process is A. an isothermal expansion. B. an isothermal compression. C. a constant-volume process. D. a free expansion. E. a change of phase. 11. The change in entropy is zero for A. reversible adiabatic processes. B. reversible isothermal processes. C. reversible isobaric processes. D. reversible processes during which no work is done. E. all adiabatic processes. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 5

12. When an ideal gas is subjected to a reversible adiabatic compression, which of the following is correct? A. The entropy of the gas does not change. B. The internal energy of the gas does not change. C. No work is done on the gas. D. The gas absorbs heat. E. The gas ejects heat. 13. Which of the processes on an ideal gas shown in figure 10 results in the minimum change in entropy of the gas in changing the gas from state S to state F? A. All processes B. Only process A C. Only process B D. Only process C E. Only process D 14. In four experiments, 3 moles of an ideal gas undergo reversible isothermal expansions, starting from the same volume but at different temperatures. The corresponding p-v plots are shown in figure 11. Rank the four situations a, b, c, and d according to the change in the entropy of the gas, greatest first. A.(a and c) tie, then (b and d) tie. B. a, then b, then c, then d. C. d, then c, then b, then a. D.(b and d) tie, then (a and c) tie. E.(a and d) tie, then (b and c) tie 15. The initial state of a monatomic ideal gas is represented by the dot in figure 12. Arrows 1 through 4 represent isobaric, isothermal, and isochoric processes that the sample can undergo. Which process corresponds to the highest increase in the entropy of the gas? A.4 B.3 C.2 D.1 E. All processes are the same. 16. A sample of an ideal gas expands from state A to state B. Let ΔSI denote the change in entropy of the gas for an irreversible expansion. Let ΔSR denote the change in entropy of the gas for a reversible expansion. Then: A. ΔSI = ΔSR B. ΔSI > ΔSR C. ΔSI < ΔSR D. ΔSI < 0 E. ΔSR < 0 17. A monatomic gas can be taken through one of the two thermodynamical processes A or B. Process A is at constant volume and process B is at constant pressure. Both processes are shown in a PV diagram in figure 13. The change in entropy: A. is greater for process B than for process A B. is greater for process A than for process B C. is the same for both processes A and B D. is greater for process A than for process B only if the initial temperature is low E. is greater for process A than for process B only if the initial temperature is high Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 6

18. An ideal monatomic gas at initial temperature T o expands from initial volume V o to volume 2V o by each of the five processes shown in the T-V diagram shown in figure 14. In which process is the change of entropy of the gas zero? A. Process AF. B. Process AB. C. Process AC. D. Process AD. E. Process AE. 19. A real heat engine is represented by the diagram shown in figure 15. The heat expelled to the lowtemperature reservoir can be A. 60 J B. 40 J C. 20 J D. 10 J E. zero 20. Point i in figure 16 represents the initial state of an ideal gas at temperature T. Rank the entropy changes that the gas undergoes as it moves reversibly from point i to points a, b, c, and d, greatest first. A. b, a, c, d B. a, b, c, d C. b, d, a, c D. (b and d tie), (a and c tie) E. (b and d tie), a, c 21. In which of the following, is the entropy change per cycle negative? A) a perfect refrigerator B) a Carnot refrigerator C) a real refrigerator D) a Carnot heat engine E) none of the other answers Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 7

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 8

Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 20 Page 9