Deck 19: Heat Engines and Refrigerators

Question 1

A heat engine with an efficiency of 30.0% performs 2500 J of work. How much heat is discharged to the lower temperature reservoir?

A) 5830 J
B) 8330 J
C) 750 J
D) 1350 J
E) 7080 J

Answer 1

5830 J

Question 2

A heat engine takes 2.0 moles of an ideal gas through the reversible cycle abca, on the pV diagram shown in the figure. The path bc is an isothermal process. The temperature at c is 820 K, and the volumes at a and c are 0.010 m³ and 0.16 m³, respectively. The molar heat capacity at constant volume, of the gas, is 37 J/mol·K, and the ideal gas constant is R = 8.314 J/(mol∙K). The thermal efficiency of the engine is closest to

A) 0.26.
B) 0.026.
C) 0.33.
D) 0.40.
E) 0.53.

Answer 2

0.26.

Question 3

A refrigerator removes heat from the freezing compartment at the rate of 20 kJ and ejects 24 kJ into a room per cycle. How much work is required in each cycle?

A) 4 kJ
B) 20 kJ
C) 22 kJ
D) 24 kJ
E) 44 kJ

Answer 3

4 kJ

Question 4

A refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the refrigerator in order to remove 250 J of heat from the interior?

A) 60 J
B) 120 J
C) 250 J
D) 480 J
E) 1050 J

Question 5

The entropy of an isolated system must be conserved, so it never changes.

Question 6

According to the second law of thermodynamics, the entropy of any system always increases.

Question 7

Is it possible to transfer heat from a hot reservoir to a cold reservoir?

A) No; this is forbidden by the second law of thermodynamics.
B) Yes; this will happen naturally.
C) Yes, but work will have to be done.
D) Theoretically yes, but it hasn't been accomplished yet.

Question 8

An engine manufacturer makes the claim that the engine they have developed will, on each cycle, take 100 J of heat out of boiling water at 100°C, do mechanical work of 80 J, and exhaust 20 J of heat at 10°C. What, if anything, is wrong with this claim?

A) The heat exhausted must always be greater than the work done according to the second law of thermodynamics.
B) This engine violates the first law of thermodynamics because 100 J + 20 J ≠ 80 J.
C) An engine would operate by taking in heat at the lower temperature and exhausting heat at the higher temperature.
D) The efficiency of this engine is greater than the ideal Carnot cycle efficiency.
E) There is nothing wrong with this claim because 100 J = 20 J + 80 J.

Question 9

A certain engine extracts 1300 J of heat from a hot temperature reservoir and discharges 700 J of heat to a cold temperature reservoir. What is the efficiency of this engine?

A) 46%
B) 54%
C) 86%
D) 27%
E) 13%

Question 10

During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?

A) 712 J
B) 586 J
C) 460 J
D) 310 J
E) 126 J

Question 11

An ice cube at 0°C is placed in a very large bathtub filled with water at 30°C and allowed to melt, causing no appreciable change in the temperature of the bath water. Which one of the following statements is true?

A) The entropy gained by the ice cube is equal to the entropy lost by the water.
B) The entropy lost by the ice cube is equal to the entropy gained by the water.
C) The net entropy change of the system (ice plus water) is zero because no heat was added to the system.
D) The entropy of the system (ice plus water) increases because the process is irreversible.
E) The entropy of the water does not change because its temperature did not change.

Question 12

A hot piece of iron is thrown into the ocean and its temperature eventually stabilizes. Which of the following statements concerning this process is correct? (There may be more than one correct choice.)

A) The entropy lost by the iron is equal to the entropy gained by the ocean.
B) The entropy gained by the iron is equal to the entropy lost by the ocean.
C) The change in the entropy of the iron-ocean system is zero.
D) The ocean gains more entropy than the iron loses.
E) The ocean gains less entropy than the iron loses.

Question 13

A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of 650 K and 270 K, performs 4.3 kJ of net work and rejects 8.0 kJ of heat in a single cycle. The thermal efficiency of this heat engine is closest to

A) 0.35
B) 0.31
C) 0.28
D) 0.38
E) 0.42

Question 14

A nuclear fission power plant has an actual efficiency of 39%. If 0.25 MW of power are produced by the nuclear fission, how much electric power does the power plant output?

A) 0.098 MW
B) 9.8 MW
C) 35 MW
D) 0.35 MW

Question 15

As a result of any natural process, the total entropy of any system plus that of its environment

A) never decreases.
B) sometimes decreases.
C) never increases.
D) always stays the same.

Question 16

The second law of thermodynamics leads us to conclude that

A) the total energy of the universe is constant.
B) disorder in the universe is increasing with the passage of time.
C) it is theoretically impossible to convert work into heat with 100% efficiency.
D) the total energy in the universe is increasing with time.
E) the total energy in the universe is decreasing with time.

Question 17

The graph in the figure shows a cycle for a heat engine for which Q_H=35 J. What is the thermal efficiency of this engine?

A) 29 %
B) 57 %
C) 14 %
D) 23 %

Question 18

A heat engine performs the reversible cycle abca with 9.0 moles of an ideal gas, as shown in the figure. Path ca is an adiabatic process. The temperatures at points a and b are 300 K and 500 K, respectively. The volume at point c is 0.20 m³. The adiabatic constant of the gas is 1.60. The thermal efficiency of this engine is closest to

A) 0.070.
B) 0.10.
C) 0.13.
D) 0.16.
E) 0.19.

Question 19

Is it possible to transfer heat from a cold reservoir to a hot reservoir?

A) No; this is forbidden by the second law of thermodynamics.
B) Yes; this will happen naturally.
C) Yes, but work will have to be done.
D) Theoretically yes, but it hasn't been accomplished yet.

Question 20

An automobile engine takes in 4000 J of heat and performs 1100 J of mechanical work in each cycle.
(a) Calculate the engine's efficiency.
(b) How much heat is "wasted" in each cycle?

Question 21

What is the maximum theoretical efficiency possible for a heat engine operating between a reservoir in which ice and water coexist, and a reservoir in which water and steam coexist? The pressure is constant at 1.0 atmosphere for both reservoirs.

A) 27%
B) 45%
C) 73%
D) 17%

Question 22

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power. How much power is it discharging to the outdoors?

A) 30 kW
B) 75 kW
C) 105 kW
D) 135 kW
E) 210 kW

Question 23

A Carnot refrigerator takes heat from water at 0°C and rejects heat to a room at 12°C. Suppose that 92.0 grams of water at 0°C are converted to ice at 0°C by the refrigerator. Calculate the mechanical energy that must be supplied to the refrigerator. The heat of fusion of water is 3.34 × 10⁵ J/kg.

Question 24

A refrigerator has a coefficient of performance of 1.15, and it extracts 7.95 J of heat from the cold reservoir during each cycle.
(a) How much work is done on the gas in each cycle?
(b) How much heat is exhausted into the hot reservoir in each cycle?

Question 25

A perfect Carnot engine operates between the temperatures of 300K and 700K, drawing 60 kJ of heat from the 700K reservoir in each cycle. How much heat is dumped into the 300K reservoir in each cycle?

A) 38 kJ
B) 34 kJ
C) 30 kJ
D) 26 kJ
E) 42 kJ

Question 26

A Carnot engine operates between reservoirs at 550K and 300K, discarding 1500 J of heat in each cycle.
(a) What is the engine's efficiency?
(b) How much heat is supplied to the engine by the hot reservoir in each cycle?

Question 27

An ideal reversible refrigerator keeps its inside compartment at 9.0°C. What is the high temperature, T_h, needed to give this refrigerator a coefficient of performance of 3.7?

A) 85°C
B) 1052°C
C) 11°C
D) 42°C

Question 28

A Carnot engine is operated as a heat pump to heat a room in the winter. The heat pump delivers heat to the room at the rate of 34 kJ per second and maintains the room at a temperature of 293 K when the outside temperature is 229 K. The power requirement for the heat pump under these operating conditions is closest to

A) 7500 W.
B) 6000 W.
C) 17,000 W.
D) 13,000 W.
E) 9600 W.

Question 29

A Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C. How much energy does it need to remove 2000 J of heat from the interior of the house?

A) 105 J
B) 130 J
C) 780 J
D) 520 J
E) 340 J

Question 30

One of the most efficient engines built so far has the following characteristics:
combustion chamber temperature = 1900°C
exhaust temperature = 430°C
7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour, where 1 cal = 4.19 J
(a) What is the actual efficiency of this engine?
(b) What is the Carnot efficiency of the engine?
(c) What is the power output of this engine?

Question 31

You want to design an ideal Carnot heat engine that wastes only 35.0% of the heat that goes into it. The lowest cold-reservoir temperature available to you is +15.0°C. If 150.0 J of work is done per cycle, the heat input per cycle is closest to

A) 203 J
B) 231 J
C) 248 J
D) 429 J
E) 760 J

Question 32

An ideal Carnot engine operates between reservoirs having temperatures of 125°C and -20°C. Each cycle the heat expelled by this engine is used to melt 30.0 g of ice at 0.00°C. The heat of fusion of water is 3.34 × 10⁵ J/kg and the heat of vaporization of water is 2.25 × 10⁶ J/kg.
(a) How much work does this engine do each cycle?
(b) How much heat per cycle does this engine absorb at the hot reservoir?

Question 33

A Carnot engine operates between a high temperature reservoir at 435 K and a river with water at 280 K. If it absorbs 3700 J of heat each cycle, how much work per cycle does it perform?

A) 1318 J
B) 2382 J
C) 1449 J
D) 2251 J

Question 34

A certain Carnot heat pump transfers energy from the outside of a house, where the temperature is -15°C, to the inside of a room where the temperature is 21°C. If this heat pump runs off of electricity, what is the minimum rate at which it uses electrical energy to deliver 150 W to the inside room?

Question 35

A Carnot refrigerator has a coefficient of performance of 2.5. The refrigerator consumes 50 W of power. How much heat is removed from the interior of the refrigerator in 1 hour?

A) 7.5 kJ
B) 450 kJ
C) 180 kJ
D) 720 kJ
E) 72 kJ

Question 36

The temperature inside a Carnot refrigerator placed in a kitchen at 22.0°C is 2.0°C. The heat extracted from the refrigerator is 89 MJ/h. What power is needed to operate this refrigerator?

A) 1.7 kW
B) 1.8 kW
C) 1.5 kW
D) 1.9 kW
E) 1.6 kW

Question 37

A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 10⁶ kg of coal each day. The heat produced by the combustion of coal is 3.3 × 10⁷ J/kg. The steam that drives the turbines is at a temperature of 300°C, and the exhaust water is at 37°C.
(a) What is the overall efficiency of the plant for generating electric power?
(b) What is the maximum efficiency that this plant could possibly have using the same temperature extremes that it presently uses?
(c) How much thermal energy is exhausted each day by this plant?

Question 38

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C. If the engine is required to output 20.0 kJ of work per cycle, how much heat must the high temperature reservoir transfer to the engine during each cycle?

A) 27.5 kJ
B) 73.2 kJ
C) 39.2 kJ
D) 800 kJ
E) 20.5 kJ

Question 39

The compressor in a certain Carnot refrigerator performs 480 J of work to remove 150 J of heat from the interior of the refrigerator. How much heat must the coils behind the refrigerator discharge into the kitchen?

A) 110 J
B) 150 J
C) 330 J
D) 480 J
E) 630 J

Question 40

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts 10.0 J of heat from the mercury and does 8.0 J of work during each cycle. What is the temperature of the colder reservoir?

A) 47 K
B) 186 K
C) 163 K
D) 207 K

Question 41

A system consists of two very large thermal reservoirs in contact with each other, one at temperature 300°C and the other at temperature 200°C. When 600 J of heat transfers from the 300°C reservoir to the 200°C reservoir, what is the change in entropy of this system?

A) 0.221 J/K
B) 1.00 J/K
C) 5.00 J/K
D) -1.00 J/K
E) -2.31 J/K

Question 42

A 610-g quantity of an ideal gas undergoes a reversible isothermal compression at a temperature of 330 K. The compression reduces the volume of the gas from 0.40 m³ initially, to 0.21 m³ finally. The molecular mass of the gas is 33.0 g/mol and the ideal gas constant is R = 8.314 J/(mol∙K). The entropy change for the gas is closest to

A) -99 J/K.
B) -81 J/K.
C) 99 J/K.
D) 81 J/K.
E) 0.00 J/K.

Question 43

A 2.00-kg block of ice at 0.00°C is dropped into a very large lake at 25.0°C and completely melts. For water, the heat of fusion is 3.35 × 10⁵ J/kg, the heat of vaporization is 2.25 × 10⁵ J/kg, and the specific heat is 4190 J/kg∙K. The net change in entropy of the system consisting of the ice and the lake due to this melting process is closest to

A) 2.45 × 10³ J/K.
B) 2.24 × 10³ J/K.
C) 2.06 × 10² J/K.
D) -2.45 × 10³ J/K.
E) -2.06 × 10² J/K.

Question 44

A brass rod, 75.0 cm long and having a cross-sectional area of 2.50 cm², conducts heat from a large furnace at 375°C into a very large cold water bath at 10.0°C without losing any heat at the lateral surface of the rod. Steady state has been established, and the thermal conductivity of brass is 109 W/m∙K. The rate at which the entropy of the system (furnace plus water) is changing is closest to

A) 2.05 × 10^-2 W/K.
B) 2.64 × 10^-2 W/K.
C) 3.54 × 10^-2 W/K.
D) 4.69 × 10^-2 W/K.
E) 6.74 × 10^-2 W/K.

Question 45

What is the change in entropy of 10.0 moles of ideal monatomic gas that reversibly undergoes the isothermal expansion shown in the figure? The ideal gas constant is R = 8.314 J/(mol∙K).

A) 221 J/K
B) 104 J/K
C) 63.1 J/K
D) 45.2 J/K
E) 90.8 J/K

Question 46

At atmospheric pressure, 45 moles of liquid helium are vaporized at its boiling point of 4.22 K. The heat of vaporization of helium, at atmospheric pressure, is 2.09 × 10⁴ J/kg, and the atomic weight of helium is 4.00 g/mol. The change in the entropy of the helium, as it vaporizes, is closest to

A) 890 J/K.
B) 14,000 J/K.
C) 18,000 J/K.
D) -9400 J/K.
E) -14,000 J/K.

Question 47

A 2.0-kg block of aluminum at 50°C is dropped into 5.0 kg of water at 20°C and the temperature is allowed to stabilize. What is the total change in entropy during this process, assuming no heat is exchanged with the environment? The specific heat of aluminum is 910 J/(kg∙K) and the specific heat of water is 4190 J/(kg∙K).

A) 8.2 J/K
B) 10 J/K
C) 3.3 × 10^-2 J/K
D) 3.8 × 10^-3 J/K
E) 2.4 × 10^-3 J/K

Question 48

A 2.00 kg piece of lead at 40.0°C is placed in a very large quantity of water at 10.0°C, and thermal equilibrium is eventually reached. Calculate the entropy change of the lead that occurs during this process. The specific heat of lead is 130 J/(kg∙K).

A) -12.5 J/K
B) 86.0 J/K
C) -26.2 J/K
D) -86.0 J/K
E) -6.24 J/K

Question 49

A 2.00 kg piece of lead at 40.0°C is placed in a very large quantity of water at 10.0°C, and thermal equilibrium is eventually reached. Calculate the TOTAL change in entropy that occurs during this process. The specific heat of lead is 130 J/(kg∙K).

A) 190 J/K
B) 100 J/K
C) 6.6 J/K
D) 6.2 J/K
E) 1.4 J/K

Question 50

A 810-g quantity of ethanol, in the liquid state at its melting point of -114°C, is frozen at atmospheric pressure. The heat of fusion of ethanol is 1.04 × 10⁵ J/kg, the molecular mass is 46.1 g/mol, and the ideal gas constant is R = 8.314 J/(mol∙K). The change in the entropy of the ethanol as it freezes is closest to

A) -540 J/K.
B) -490 J/K.
C) -600 J/K.
D) 490 J/K.
E) 540 J/K.