Download Chapter 18

Heat Engines, Entropy,
and the Second Law
of Thermodynamics
1. The Second Law of Thermodynamics states that
a. we can get more out of a process than we put in.
b. we can not get as much out of a process as we put in.
c. we can get out of a process exactly what we put in.
d. two bodies are in thermal equilibrium when they both have the same temperature.
e. work and temperature are the same thing.
ANS: b
2. What happens to the temperature of an insulated room when a refrigerator in the middle of the room is
plugged in and left running with its door open?
a. It increases.
b. It decreases.
c. It remains the same.
d. It doubles.
e. It is cut in half.
ANS: a
3. A device that converts thermal energy to other useful forms is a
a. heat engine.
b. refrigerator.
c. heat pump.
d. electric motor.
e. induction motor.
ANS: a
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Heat Engines, Entropy, and the Second Law of Thermodynamics
4. Thermal efficiency can be described mathematically as
QQ
a. 1 2 .
Q3
W
b.
.
Qh
Q Q
c. h c .
Qh
Qh  Qc
d.
.
Qh
Q
e. 1  h .
Qc
ANS: b
5. A heat engine burns 2500 J of heat and exhausts 1200 J of heat. What is its efficiency?
a. 0.52
b. 0.81
c. 0.34
d. 0.61
e. 0.49
ANS: a
6. What is the thermal efficiency of a Carnot engine?
W
a. 1  1
W2
T
b. 1  h
Tc
Tc
c. 1 
Th
T
d. 1  c
Th
T
e. 1  h
Tc
ANS: d
7. When compared to a Carnot engine operating between the same two temperatures, real engines are
a. more efficient.
b. less efficient.
c. hotter.
d. colder.
e. less theoretical.
ANS: b
Chapter 18
8. A Carnot engine has a 0.36 efficiency and an exhaust temperature of 270 K. What is the combustion
temperature of the engine in K?
a. 420
b. 390
c. 430
d. 380
e. 440
ANS: a
9. The coefficient of performance of a heat pump is
W
a.
.
Qh
W  W2
b. 1
.
Qh
T  Tc
c. h
.
Th
T  Tc
d. h
.
Th
Q
e. h .
W
ANS: e
10. Change in entropy is
dQ r
a.
.
T
dT
b.
.
Qr
dT
c.
.
dQ r
dQ c
d.
.
dQ r
dQ c
e.
.
Qr
ANS: a
11. The total change of entropy in one cycle of a Carnot engine is
a. e.
b. e1 .
Q
c. r .
T
d. zero.
e. ln T c .
ANS: d
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Heat Engines, Entropy, and the Second Law of Thermodynamics
12. What is the change in entropy in J/K of 0.356 kg of solid lead when it melts at 327°C if the latent heat of
fusion of lead is 24.5 kJ/kg?
a. 24.3
b. 14.5
c. 13.8
d. 12.9
e. 15.1
ANS: b
13. In any real process,
Q
Q
a.

 0.
W h Th
T T
b. c  h  0 .
Q Q
Q Q
c.

 0.
Tc Th
Q Q
d.

 0.
Tc Th
Q Q
e.

 0.
Tc Th
ANS: e
14. 923 J of heat is transferred from a body at 383 K to a body at 283 K. What is the minimum change in
entropy in J/K?
a. 0.742
b. 0.797
c. 0.713
d. 0.852
e. 0.738
ANS: d
15. What is the change in entropy in J/K of 2.51 mol of an ideal gas due to a free expansion to 3.62 times its
original volume? ( R  8.31 J mol  K )
a. 25.2
b. 24.1
c. 27.3
d. 24.6
e. 26.8
ANS: e
Chapter 18
16. 1.23 kg of water at 273 K is mixed with 1.23 kg of water at 373 K. 323 K is the equilibrium temperature.
What is the change in entropy in J/K of the system if c  4186 J kg  K ?
a. 125
b. 110
c. –740
d. 360
e. 210
ANS: a
17. Entropy is defined as
a. k B ln T .
b. k B ln V .
c. k B ln W .
d. k B ln k .
e. k B ln c .
ANS: c
18. Ten kg of water at 0°C is mixed with ten kg of water at 100°C. The change in entropy in cal/K of the
system is
a. 1000.
b. 480.
c. –720.
d. 240.
e. –168.
ANS: d
19. A vessel containing 10 kg of water is left out where it evaporates. Assuming the temperature remains
constant at 20°C, what is the change in entropy in kcal/K? (The latent heat of vaporization at 20°C is 585
cal/g.)
a. 30
b. 10
c. 20
d. 40
e. 290
ANS: c
20. One kg of ice at 0°C is added to one kg of boiling water. The mixture comes to equilibrium. What is the
change in entropy in cal/K of the system? ( L f  80 cal g  C )
a. 300
b. 100
c. 200
d. 50
e. 25
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Heat Engines, Entropy, and the Second Law of Thermodynamics
ANS: d
Chapter 18
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21. The change in entropy of mass m of a solid that melts at temperature T with latent heat of fusion L is
LT
a.
.
m
b. mL ln T .
c. mLT.
mL
d.
.
T
L
e.
.
mT
af
ANS: d
22. The change in entropy in cal/K when 1 kg of ice melts is ( L f  80 cal g  C )
a. 144.
b. 293.
c. 312.
d. 516.
e. 80.
ANS: b
23. If n moles of an ideal gas are compressed isothermally from an initial volume V 1 to a final volume V 2 , the
change in entropy is
V
a. nR ln 2 .
V1
F
IJ
G
HK
FV I
b. nRT ln G J.
HV K
FV I
c. nk ln G J.
HV K
2
1
2
1
d. n C v
z
dT
.
T
C
e. n v .
T
ANS: a
24. If 5 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm 3 to a final
volume of 20 cm 3 , the change in entropy in J/K is ( R  8.31 J mol  K )
a. –191.
b. –52.
c. –71.
d. –67.
e. –208.
ANS: d
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Heat Engines, Entropy, and the Second Law of Thermodynamics
25. An ideal gas is allowed to undergo a free expansion. If the initial volume is V 1 and its final volume is V 2 ,
the change in entropy is
V
a. nR ln 2 .
V1
F
IJ
G
HK
FV I
b. nRT ln G J.
HV K
FV I
c. nk ln G J.
HV K
2
1
2
1
d. 0.
e. nR
V2
.
V1
ANS: a
26. Five moles of an ideal gas is allowed to undergo a free expansion. If the initial volume is 20 cm 3 and the
final volume is 100 cm 3 , find the change in entropy in J/K if R  8.31 J mol  K .
a. 71
b. 52
c. 67
d. 191
e. 208
ANS: c
27. An automobile engine operates with an overall efficiency of 12%. How much energy in gallons of gasoline
is delivered as waste heat for each 10 gallons of fuel burned?
a. 1.2
b. 8.8
c. 6.5
d. 4.7
e. 7.5
ANS: b
28. An engine is designed to obtain energy from the temperature gradient of the ocean. What is the
thermodynamic efficiency of such an engine if the temperature of the surface of the water is 59°F (15°C) and
the temperature well below the surface is 41°F (5°C)?
a. 3.5%
b. 67%
c. 31%
d. 17%
e. 96%
ANS: a
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29. A vessel containing 5 kg of water at 10°C is put into a refrigerator. The 1/7 HP motor (1 HP = 746 W) runs
for 5 minutes to cool the liquid to the refrigerator’s low temperature, 0°C. What is the COP of the refrigerator?
(1 cal = 4.186 J)
a. 5.7
b. 4.6
c. 6.6
d. 7.2
e. 3.6
ANS: c
30. 500 grams of ice is melted at a temperature of 32°F. The change in entropy in J/K is ( L f  333 J g )
a. 3.21.
b. 146.
c. 512.
d. 610.
e. 5230.
ANS: d
31. The change in entropy of mass m of water having a mass m that is heated from an absolute temperature T1
to T 2 is
F
T I
G
HT J
K.
FT I
b. cm G J.
HT K
FT  T IJ.
c. cm G
HT K
FT  T IJ.
d. cm G
HT K
FT  T IJ.
e. cm G
HT  T K
2
a. cm ln
1
2
1
2
1
1
2
1
2
2
1
2
1
ANS: a
32. An 800 MW electric power plant has an efficiency of 30%. It loses its waste heat in large cooling towers.
Approximately how much waste heat in MJ is discharged to the atmosphere per second?
a. 1200
b. 1900
c. 800
d. 560
e. 240
ANS: d
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Heat Engines, Entropy, and the Second Law of Thermodynamics
33. Nuclear power plants have an overall efficiency of around 34% instead of the 41% for plants that burn
fossil fuel. The reason for this is
a. the temperature of the steam is lower than that of a fossil fuel plant.
b. there is not as much energy available from nuclear energy.
c. there is more waste energy with nuclear energy.
d. the high cost of nuclear waste.
e. cooling towers cannot be used at nuclear plants.
ANS: a
34. A homeowner has a new oil furnace that has an efficiency of 60%. For every 100 barrels of oil needed to
heat his house, how many barrels of oil go up the chimney as waste heat?
a. 20
b. 60
c. 40
d. 80
e. 10
ANS: c
35. A lawnmower has a 6 horsepower engine (1 HP = 750 watts). If the engine has an efficiency of 20%, and
the throttle is such that the engine cycles 10 times a second, the heat in J that is expelled in one cycle is
a. 360.
b. 200.
c. 220.
d. 240.
e. 225.
ANS: a
36. A steam engine has an efficiency of 60%. If the waste heat has a temperature of 100°F (38°C), what is the
lowest possible temperature of the boiler in °C?
a. 350
b. 94
c. 225
d. 505
e. 778
ANS: d
37. A company that produces pulsed gas heaters claims its efficiency is approximately 90%. If the engine
operates between 250°C and 25°C, what percentage is its thermodynamic efficiency?
a. 83%
b. 65%
c. 43%
d. 90%
e. 56%
Chapter 18
ANS: c
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Heat Engines, Entropy, and the Second Law of Thermodynamics
38. A heat engine absorbs 2500 J of heat from a hot reservoir and expels 1000 J to a cold reservoir. When it is
run in reverse with the same reservoirs, the engine pumps 2500 J of heat to the hot reservoir, requiring 1500 J
of work to do so. Find the ratio of the work done by the heat engine to the work done by the pump. Is the
heat engine reversible?
a. 1 (no)
b. 1 (yes)
c. 1.5 (yes)
d. 1.5 (no)
e. 2.5 (no)
ANS: b
39. On a cold day, a homeowner uses a heat pump to absorb heat from the outside air of 15°F (–10°C) and
transfers it into his home at a temperature of 85°F (30°C). The COP of the heat pump is
a. 0.2.
b. 4.4.
c. 0.5.
d. 7.6.
e. 6.7.
ANS: d
40. A new electric power plant has an efficiency of 42%. For every 100 barrels of oil needed to run the turbine,
how many are essentially lost as waste heat to the environment in barrels of oil?
a. 21
b. 42
c. 58
d. 10
e. 79
ANS: c
41. A gasoline engine absorbs 2500 J of heat and performs 500 J of mechanical work in each cycle. The amount
of heat in J expelled in each cycle is
a. 1000.
b. 1500.
c. 2000.
d. 500.
e. 3000.
ANS: c
42. A heat pump has a coefficient of performance of 4. If the heat pump absorbs 20 cal of heat from the cold
outdoors in each cycle, the heat expelled in cal to the warm indoors is
a. 34.
b. 27.
c. 36.
d. 40.
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e. 80.
ANS: b
43. A refrigerator has a COP of 4. If the refrigerator absorbs 30 cal of heat from the cold reservoir in each
cycle, the heat expelled in cal into the heat reservoir is
a. 40.
b. 37.5.
c. 36.
d. 34.
e. 22.5.
ANS: b
44. The COP of refrigerators is often expressed commercially as an energy efficiency ratio “E.E.R.”, the ratio
of the rate at which heat is removed (in BTU/hr) to the electrical power required (in watts). Assume a heat
pump has an E.E.R. of 12. What is its COP? (1 BTU = 1054 J)
a. 3.5
b. 3.0
c. 4.5
d. 6.0
e. 5.0
ANS: a
45. What is the maximum efficiency of a heat engine operating between 500 K and 200 K?
a. 70%
b. 60%
c. 50%
d. 40%
e. 30%
ANS: b
46. Entropy changes can be measured in
a. J K .
b. N  K .
c. cal  K .
d. J S .
e. J K .
ANS: e
47. What happens when an ice cube melts?
a. The temperature decreases.
b. Entropy increases.
c. Entropy decreases.
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Heat Engines, Entropy, and the Second Law of Thermodynamics
d. Entropy stays constant.
e. Work is converted to energy.
ANS: b
Chapter 18
48. An isentropic process occurs when
a. no thermal energy enters or leaves the system.
b. the entropy of the system increases.
c. the entropy of the system decreases.
d. work is converted to energy.
e. work is performed on or by the system.
ANS: a
49. When a process occurs in an isolated system, the
a. temperature increases.
b. temperature decreases.
c. entropy stays the same.
d. entropy decreases.
e. entropy increases.
ANS: e
50. The second law of thermodynamics states that
a. it is impossible to construct a heat engine that, operating in a cycle, produces no other effect than
absorption of energy from a reservoir and the performance of an equal amount of work.
b. energy does not flow spontaneously from a cold object to a hot object.
c. the entropy of the universe increases in all natural processes.
d. all of the above are correct.
e. only (b) and (c) above are correct.
ANS: d
51. A reversible process is one for which
a. the initial state can be reached from the final state with every point being an equilibrium state.
b. the final state can be reached from the initial state by a Carnot engine as well as by the actual process.
c. the system can be returned to its initial conditions along the same path.
d. the system can be returned to its initial conditions along the same path with every point being an
equilibrium state.
e. the final state is the same as the initial state.
ANS: d
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Heat Engines, Entropy, and the Second Law of Thermodynamics
52. Three engines operate between reservoirs separated in temperature by 200 K. The reservoir temperatures
are:
engine A: Th  600 K ; Tc  400 K .
engine B: Th  500 K ; Tc  300 K .
engine C: Th  550 K ; Tc  350 K .
Rank the engines in the order of their maximum possible efficiencies, from lowest to highest.
a. A, B, C
b. A, C, B
c. B, C, A
d. B, A, C
e. C, A, B
ANS: b
53. More energy than you pay for in electricity costs can be
a. removed from a house in summer by a heat pump.
b. delivered to a house in winter by a heat pump.
c. removed from the inside of a refrigerator by its motor.
d. removed or delivered by all of the above.
e. removed or delivered by (a) and (b) only.
ANS: d
54. The most probable macrostate is the one with
a. the smallest number of microstates.
b. the largest number of microstates.
c. the smallest probability.
d. the least disorder.
e. the smallest ln W .
ANS: b
55. The solar constant, the radiant energy received from the sun per unit area per second, is 1.4 kW m 2 . The
Earth’s mean radius is 6.37  10 6 m . The efficiency of the atmosphere as a heat engine is 0.8%. The energy in J
that the atmosphere converts into prevailing winds in a 24 hour period of time is approximately
a. 1.2  10 20 .
b. 2.5  10 20 .
c. 4.9  10 20 .
d. 6.4  10 24
e. 1.4  1015 .
ANS: a
Chapter 18
56. One mole of an ideal gas undergoes an adiabatic free expansion to 3 times its initial volume. Which
statement is correct?
a. Q  0 ; S  0 .
b. T  S  0 .
c. Eint  S  0 .
d. T  0 ; S  0 .
e. W  0 ; S  0 .
ANS: d
57. The most probable macrostate for a pair of six-sided dice is
a. 5.
b. 6.
c. 7.
d. 8.
e. either 7 or 8.
ANS: c
58. The minimum change in entropy in the universe in J/K when a human body processes a 2000 calorie
(8400 J) daily diet at a body temperature of 37°C is
a. 3.2.
b. 6.5.
c. 14.
d. 27.
e. 227.
ANS: d
59. When a body undergoes a reversible adiabatic process,
a. Q  0 ; S  0 .
b. Q  0 , S  0 .
c. Q  0 ; S  0 .
d. Q  0 ; S  0 .
e. Q  0 ; S  0 .
ANS: b
60. A schematic representation of a heat engine includes
a. a hot reservoir at T h and a cold reservoir at Tc .
b. a working substance.
c. work done by the heat engine.
d. (a) and (b) above.
e. (a), (b) and (c) above.
ANS: e
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Heat Engines, Entropy, and the Second Law of Thermodynamics
61. In the formula for the maximum possible efficiency of a heat engine, e  1 
Tc
, the temperatures must be
Th
in
a. Celsius degrees.
b. Kelvins.
c. Fahrenheit degrees.
d. (a) or (b) above.
e. (a), (b) or (c) above.
ANS: b
62. Real heat engines are less efficient than Carnot engines because
a. they operate irreversibly.
b. they complete a cycle in a relatively brief time interval.
c. they do not have the cold reservoir at absolute zero.
d. (a) and (b) above are correct.
e. (a), (b) and (c) above are correct.
ANS: d
63. Which answer below is not a statement of the second law of thermodynamics?
a. Real processes proceed in a preferred direction.
b. Energy does not flow spontaneously by heat from a cold to a hot reservoir.
c. The entropy of the universe increases in all natural processes.
d. In theory, heat engines working in a cycle employ reversible processes.
e. You cannot construct a heat engine, operating in a cycle that does nothing but take heat from a reservoir
and perform an equal amount of work.
ANS: d
64. If a movie shows a person rising out of a swimming pool feet first and landing back on the diving board,
you know it is being played backwards because it violates
a. the zeroth law of thermodynamics.
b. the first law of thermodynamics.
c. the second law of thermodynamics.
d. the law of conservation of energy.
e. the law of conservation of momentum.
ANS: c
65. In calculating the minimum change in entropy in a portion of a real process, we use
a. the heat dQ transferred in that process.
b. the heat dQ absorbed in that process.
c. the heat dQ r transferred in a portion of a reversible process.
d. dU, the internal energy change in that process.
e. dU c , the internal energy change in one cycle of the heat engine.
Chapter 18
ANS: c
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Heat Engines, Entropy, and the Second Law of Thermodynamics
66. You have 50 red and 50 green marbles in a bag. You take out one marble at a time, check its color, return it
to the bag and shake the bag. If you take out 4 marbles, the most probable color macrostate is
a. all red.
b. one red, three green.
c. two red, two green.
d. three red, one green.
e. all green.
ANS: c
67. The change in entropy, S , is largest in a(n)
a. constant volume process.
b. constant pressure process.
c. adiabatic process.
d. process in which no heat is transferred.
e. process in which no work is performed.
ANS: b