Question 1

Carnot engine: 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.

Accepted Answer

The efficiency of a Carnot engine is determined by the temperatures of the heat reservoirs, and it is impossible for any real or theoretical engine operating between two temperatures to have an efficiency greater than that of a Carnot cycle. The claim of doing 80 J of work with only 20 J exhausted at a lower temperature suggests an efficiency that exceeds the maximum possible defined by the Carnot efficiency, which is a violation of the second law of thermodynamics.

Question 2

Heat engines: 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.

Accepted Answer

B

Question 3

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

Accepted Answer

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. However, it does not state that the entropy of any system always increases; in a non-isolated system, entropy can decrease locally as long as the total entropy of the system plus its surroundings increases.

Question 4

Heat engines: 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.

Accepted Answer

Yes, transferring heat from a cold reservoir to a hot reservoir is possible, but it requires work to be done on the system. This process is the principle behind refrigerators and heat pumps, where work (usually in the form of electrical energy) is used to move heat against its natural flow from a cooler to a warmer place. This does not violate the second law of thermodynamics, which states that the entropy of an isolated system can never decrease over time. The work input compensates for the decrease in entropy associated with moving heat from a colder to a hotter body.

Question 5

Heat engines: 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.

Accepted Answer

The answer of Heat engines: A heat engine performs the...

Question 6

Heat engines: A nuclear fission power plant has an actual efficiency of 39%. If  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

Accepted Answer

The answer of Heat engines: A nuclear fission power plant...

Question 7

Entropy: 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.

Accepted Answer

When a hot piece of iron is thrown into the ocean, the system (iron + ocean) undergoes an irreversible process towards thermal equilibrium. The entropy of the system increases because the process is not reversible. The ocean gains more entropy than the iron loses because the dispersion of energy (heat) into the much larger mass of the ocean results in a greater increase in entropy for the ocean compared to the decrease in entropy of the iron as it cools.

Question 8

Heat engines: 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%

Accepted Answer

The efficiency of a heat engine is calculated using the formula: Efficiency = (Work output / Heat input) * 100%. The work output is the difference between the heat extracted from the hot reservoir and the heat discharged to the cold reservoir, which is 1300 J - 700 J = 600 J. Therefore, the efficiency is (600 J / 1300 J) * 100% = 46%.

Question 9

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

Accepted Answer

The entropy of an isolated system can actually increase over time, as it tends towards a state of maximum entropy. This is known as the Second Law of Thermodynamics. However, the entropy of the entire universe (including all isolated systems) is always increasing.

Question 10

Refrigerators: 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

Accepted Answer

The work required in each cycle is the difference between the heat ejected into the room and the heat removed from the freezing compartment, which is 24 kJ - 20 kJ = 4 kJ.

Question 11

Heat engines: 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.

Accepted Answer

The answer of Heat engines: A heat engine takes 2.0...

Question 12

Entropy: 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.

Accepted Answer

The process of an ice cube melting in a bathtub of water at a higher temperature is irreversible, leading to an increase in the total entropy of the system. This is because the heat transfer from the warmer water to the melting ice increases the disorder of the system.

Question 13

Entropy: 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.

Accepted Answer

The Second Law of Thermodynamics states that the total entropy of a closed system will never decrease, as entropy always tends to increase over time. Therefore, the total entropy of any system plus that of its environment A) never decreases.

Question 14

Refrigerators: 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

Accepted Answer

The coefficient of performance (COP) for a refrigerator is defined as the ratio of the heat removed from the interior (Q_c) to the work done on the refrigerator (W), COP = Q_c / W. Rearranging this formula to solve for work gives W = Q_c / COP. Substituting the given values, W = 250 J / 4.2 = approximately 60 J.

Question 15

Heat engines: 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

Accepted Answer

The efficiency of a heat engine is given by the ratio of work output to heat input, which is 30% or 0.30 in this case. If the engine performs 2500 J of work, the heat input (Q_in) can be calculated as work divided by efficiency: Q_in = 2500 J / 0.30 = 8333.33 J. The heat discharged (Q_out) is the difference between the heat input and the work output: Q_out = Q_in - Work = 8333.33 J - 2500 J = 5833.33 J, which is approximately 5830 J.

Question 16

Heat engines: 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?

Accepted Answer

The answer of Heat engines: An automobile engine takes in...

Question 17

Heat engines: The graph in the figure shows a cycle for a heat engine for which  = 35 J. What is the thermal efficiency of this engine? 
A) 29 %
B) 57 %
C) 14 %
D) 23 %

Accepted Answer

The answer of Heat engines: The graph in the figure...

Question 18

Entropy: 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.

Accepted Answer

The second law of thermodynamics states that the entropy (disorder) of the universe is increasing with time. This means that things naturally tend to go from a state of order to a state of disorder, and that it takes energy to create order. This idea helps to explain why some things are irreversible, such as heat flowing from a hot object to a cold object, but not from a cold object to a hot object. Choice A is incorrect because the first law of thermodynamics tells us that energy cannot be created or destroyed, only transformed. Choice C is a separate concept related to the efficiency of energy conversion. Choice D and E are also incorrect as the total energy in the universe is constant, as per the first law of thermodynamics.

Question 19

Heat engines: A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of  and  performs 2.4 kJ of net work and rejects  of heat in a single cycle. The thermal efficiency of this heat engine is closest to
A) 0.21.
B) 0.19.
C) 0.17.
D) 0.23.
E) 0.25.

Accepted Answer

The answer of Heat engines: A real (non-Carnot) heat engine,...

Question 20

Refrigerators: 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

Accepted Answer

The work input required is the difference between the heat expelled to the room and the heat absorbed from the freezer. Therefore, Work = 356 J - 230 J = 126 J.

Quiz 15: Mechanical Waves

Carnot engine: 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?

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

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

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

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

Entropy: 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.)

Heat engines: 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?

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

Refrigerators: 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?

Entropy: 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?

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

Refrigerators: 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?

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

Heat engines: 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?

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

Entropy: The second law of thermodynamics leads us to conclude that

Heat engines: A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of and performs 2.4 kJ of net work and rejects of heat in a single cycle. The thermal efficiency of this heat engine is closest to

Refrigerators: 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?