Deck 20: Entropy and the Second Law of Thermodynamics

Question 1

Consider the following processes: The temperatures of two identical gases are increased from the same initial temperature to the same final temperature. Reversible processes are used. 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 the same for A and B
B) is greater for A
C) is greater for B
D) is greater for A only if the initial temperature is low
E) is greater for A only if the initial temperature is high

Answer 1

is greater for B

Question 2

Rank from smallest to largest, the changes in entropy of a pan of water on a hot plate, as the temperature of the water

A) 1, 2, 3, 4
B) 3, 4, 1, 2
C) 1 and 2 tie, then 3 and 4 tie
D) 3 and 4 tie, then 1 and 2 tie
E) 4, 3, 2, 1

Answer 2

4, 3, 2, 1

Question 3

The temperature of n moles of a gas is increased from T_i to T_f at constant pressure. If the molar specific heat at constant pressure is C_p and is independent of temperature, then change in the entropy of the gas is:

A) nC_p ln(T_f/T_i)
B) nC_p ln(T_i/T_f)
C) nC_p ln(T_f - T_i)
D) nC_p ln(1 - T_i/T_f)
E) nC_p (T_f - T_i)

Answer 3

nC_p ln(T_f/T_i)

Question 4

For all adiabatic processes:

A) the entropy does not change
B) the entropy increases
C) the entropy decreases
D) the entropy does not increase
E) the entropy does not decrease

Question 5

An ideal gas expands into a vacuum in a rigid vessel. As a result there is:

A) a change in entropy
B) an increase of pressure
C) a change in temperature
D) a decrease of internal energy
E) a change in phase

Question 6

An ideal gas, consisting of n moles, undergoes an irreversible process in which the temperature has the same value at the beginning and end. If the volume changes from V_i to V_f, the change in entropy is given by:

A) n R(V_f - V_i)
B) n R ln(V_f - V_i)
C) n R ln(V_i/V_f)
D) n R ln(V_f/V_i)
E) none of the above (entropy can't be calculated for an irreversible process)

Question 7

Possible units of entropy are:

A) J
B) J/K
C) J^-1
D) liter.atm
E) cal/mol

Question 8

For all irreversible processes involving a system and its environment:

A) the entropy of the system does not change
B) the entropy of the system increases
C) the total entropy of the system and its environment does not change
D) the total entropy of the system and its environment increases
E) none of the above

Question 9

Consider all possible isothermal contractions of an ideal gas. The entropy of the gas:

A) does not change for any of them
B) does not decrease for any of them
C) does not increase for any of them
D) increases for all of them
E) decreases for all of them

Question 10

In a reversible process the system:

A) is always close to equilibrium states
B) is close to equilibrium states only at the beginning and end
C) might never be close to any equilibrium state
D) is close to equilibrium states throughout, except at the beginning and end
E) is none of the above

Question 11

One mole of an ideal gas expands reversibly and isothermally at temperature T until its volume is doubled. The change of entropy of this gas for this process is:

A) R ln 2
B) (ln 2)/T
C) 0
D) RT ln 2
E) 2R

Question 12

A hot object and a cold object are placed in thermal contact and the combination is isolated. They transfer energy until they reach a common temperature. The change $\Delta$ S_h in the entropy of the hot object, the change $\Delta$ S_c in the entropy of the cold object, and the change $\Delta$ S_total in the entropy of the combination are:

A) $\Delta$ S_h > 0, $\Delta$ S_c > 0, $\Delta$ S_total > 0
B) $\Delta$ S_h < 0, $\Delta$ S_c > 0, $\Delta$ S_total > 0
C) $\Delta$ S_h < 0, $\Delta$ S_c > 0, $\Delta$ S_total < 0
D) $\Delta$ S_h > 0, $\Delta$ S_c < 0, $\Delta$ S_total > 0
E) $\Delta$ S_h > 0, $\Delta$ S_c < 0, $\Delta$ S_total < 0

Question 13

An ideal gas is to taken reversibly from state i, at temperature T₁, to other states labeled I, II, III, IV and V on the p-V diagram below. All are at the same temperature T_2. Rank the five processes according to the change in entropy of the gas, least to greatest.

A) I, II, III, IV, V
B) V, IV, III, II, I
C) I, then II, III, IV, and V tied
D) I, II, III, and IV, tied, then V
E) I and V tied, then II, III, IV

Question 14

Which of the following processes leads to a change in entropy of zero for the system undergoing the process?

A) Non-cyclic isobaric (constant pressure)
B) Non-cyclic isochoric (constant volume)
C) Non-cyclic isothermal (constant temperature)
D) Any closed cycle
E) None of these

Question 15

An ideal gas, consisting of n moles, undergoes a reversible isothermal process during which the volume changes from V_i to V_f. The change in entropy of the thermal reservoir in contact with the gas is given by:

A) nR(V_f - V_i)
B) nR ln(V_f - V_i)
C) nR ln(V_i/V_f)
D) nR ln(V_f/V_i)
E) none of the above (entropy can't be calculated for the thermal reservoir)

Question 16

Which of the following is NOT a state variable?

A) Work
B) Internal energy
C) Entropy
D) Temperature
E) Pressure

Question 17

A slow (quasi-static) process is NOT reversible if:

A) the temperature changes
B) energy is absorbed or emitted as heat
C) work is done on the system
D) friction is present
E) the pressure changes

Question 18

For all reversible processes involving a system and its environment:

A) the entropy of the system does not change
B) the entropy of the system increases
C) the total entropy of the system and its environment does not change
D) the total entropy of the system and its environment increases
E) none of the above

Question 19

The change in entropy is zero for:

A) reversible adiabatic processes
B) reversible isothermal processes
C) reversible processes during which no work is done
D) reversible isobaric processes
E) all adiabatic processes

Question 20

The difference in entropy $\Delta$ S = S_B - S_A for two states A and B of a system can computed as the integral $\int$ dQ/T provided:

A) A and B are on the same adiabat
B) A and B have the same temperature
C) a reversible path is used for the integral
D) the change in internal energy is first computed
E) the energy absorbed as heat by the system is first computed

Question 21

A heat engine operates between a high temperature reservoir at T_H and a low temperature reservoir at T_L. Its efficiency is given by 1 - T_L/T_H:

A) only if the working substance is an ideal gas
B) only if the engine is reversible
C) only if the engine is quasi-static
D) only if the engine operates on a Stirling cycle
E) no matter what characteristics the engine has

Question 22

A heat engine absorbs energy of magnitude $\mid$ Q_H $\mid$ from a high temperature reservoir, does work of magnitude $\mid$ W $\mid$ , and transfers energy of magnitude $\mid$ Q_L $\mid$ as heat to a low temperature reservoir. Its efficiency is:

A) $\mid$ Q_H $\mid$ / $\mid$ W $\mid$
B) $\mid$ Q_L $\mid$ / $\mid$ W $\mid$
C) $\mid$ Q_H $\mid$ / $\mid$ Q_L $\mid$
D) $\mid$ W $\mid$ / $\mid$ Q_H $\mid$
E) $\mid$ W $\mid$ / $\mid$ Q_L $\mid$

Question 23

A heat engine in each cycle absorbs energy from a reservoir as heat and does an equivalent amount of work, with no other changes. This engine violates:

A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) the third law of thermodynamics
E) none of the above

Question 24

In a thermally insulated kitchen, an ordinary refrigerator is turned on and its door is left open. The temperature of the room:

A) remains constant according to the first law of thermodynamics
B) increases according to the first law of thermodynamics
C) decreases according to the first law of thermodynamics
D) remains constant according to the second law of thermodynamics
E) increases according to the second law of thermodynamics

Question 25

A Carnot engine operates between 200 $\degree$ C and 20 $\degree$ C. Its maximum possible efficiency is:

A) 90%
B) 100%
C) 38%
D) 72%
E) 24%

Question 26

A certain heat engine draws 500 cal/s from a water bath at 27 $\degree$ C and transfers 400 cal/s to a reservoir at a lower temperature. The efficiency of this engine is:

A) 80%
B) 75%
C) 55%
D) 25%
E) 20%

Question 27

A Carnot cycle heat engine operates between 400 K and 500 K. Its efficiency is:

A) 20%
B) 25%
C) 44%
D) 80%
E) 100%

Question 28

A Carnot heat engine operates between a hot reservoir at absolute temperature T_H and a cold reservoir at absolute temperature T_L. Its efficiency is:

A) T_H/ T_L
B) T_L /T_H
C) 1 - T_H/ T_L
D) 1 - T_L /T_H
E) 100%

Question 29

The temperature T_L of the cold reservoirs and the temperatures T_H of the hot reservoirs for four Carnot heat engines are Rank these engines according to their efficiencies, least to greatest

A) 3, 4, 1, 2
B) 1 and 2 tie, then 3 and 4 tie
C) 2, 1, 3, 4
D) 1, 2, 4, 3
E) 2, 1, 4, 3

Question 30

A heat engine that in each cycle does positive work and loses energy as heat, with no heat energy input, would violate:

A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) the third law of thermodynamics
E) Newton's second law

Question 31

A Carnot engine operates with a cold reservoir at a temperature of T_L = 400 K and a hot reservoir at a temperature of T_H = 500 K. What is the net entropy change as it goes through a complete cycle?

A) 0 J/K
B) 20 J/K
C) 80 J/K
D) 400 J/K
E) 500 J/K

Question 32

The maximum theoretical efficiency of a Carnot engine operating between reservoirs at the steam point and at room temperature is about:

A) 10%
B) 20%
C) 50%
D) 80%
E) 99%

Question 33

A heat engine:

A) converts heat input to an equivalent amount of work
B) converts work to an equivalent amount of heat
C) takes heat in, does work, and loses energy as heat
D) uses positive work done on the system to transfer heat from a low temperature reservoir to a high temperature reservoir
E) uses positive work done on the system to transfer heat from a high temperature reservoir to a low temperature reservoir

Question 34

A Carnot cycle:

A) is bounded by two isotherms and two adiabats on a p-V graph
B) consists of two isothermal and two constant volume processes
C) is any four sided process on a p-V graph
D) only exists for an ideal gas
E) has an efficiency equal to the enclosed area on a p-V diagram

Question 35

An inventor suggests that a house might be heated by using a refrigerator to draw energy as heat from the ground and reject energy as heat into the house. He claims that the energy supplied to the house can exceed the work required to run the refrigerator. This:

A) is impossible by first law
B) is impossible by second law
C) would only work if the ground and the house were at the same temperature
D) is impossible since heat flows from the (hot) house to the (cold) ground
E) is possible

Question 36

According to the second law of thermodynamics:

A) all heat engines have the same efficiency
B) all reversible heat engines have the same efficiency
C) the efficiency of any heat engine is independent of its working substance
D) the efficiency of a Carnot engine depends only on the temperatures of the two reservoirs
E) all Carnot engines theoretically have 100% efficiency

Question 37

A Carnot heat engine runs between a cold reservoir at temperature T_L and a hot reservoir at temperature T_H. You want to increase its efficiency. Of the following, which change results in the greatest increase in efficiency? The value of $\Delta$ T is the same for all changes.

A) Raise the temperature of the hot reservoir by $\Delta$ T
B) Raise the temperature of the cold reservoir by $\Delta$ T
C) Lower the temperature of the hot reservoir by $\Delta$ T
D) Lower the temperature of the cold reservoir by $\Delta$ T
E) Lower the temperature of the hot reservoir by (1/2) $\Delta$ T and raise the temperature of the cold reservoir by (1/2) $\Delta$ T

Question 38

For one complete cycle of a reversible heat engine, which of the following quantities is NOT zero?

A) the change in the entropy of the working gas
B) the change in the pressure of the working gas
C) the change in the internal energy of the working gas
D) the work done by the working gas
E) the change in the temperature of the working gas

Question 39

A force of 5 N stretches an elastic band at room temperature. The rate at which its entropy changes as it stretches is about:

A) -2 x 10^-2 J/K·m
B) 2 x 10^-2 J/K·m
C) 1500 J/K·m
D) -1500 J/K·m
E) cannot be calculated without knowing the heat capacity

Question 40

Let S_I denote the change in entropy of a sample for an irreversible process from state A to state B. Let S_R denote the change in entropy of the same sample for a reversible process from state A to state B. Then:

A) S_I > S_R
B) S_I = S_R
C) S_I < S_R
D) S_I = 0
E) S_R = 0

Question 41

For a system of molecules,

A) each configuration is equally probable.
B) microstates with more configurations are more probable than other microstates.
C) configurations with more microstates are more probable than other configurations.
D) microstates with more configurations are less probable than other microstates.
E) configurations with more microstates are less probable than other configurations.

Question 42

Let k be the Boltzmann constant. If the configuration of the molecules in a gas changes so that the multiplicity is reduced to one-third its previous value, the entropy of the gas changes by:

A) $\Delta$ S = 0
B) $\Delta$ S = 3k ln 2
C) $\Delta$ S = -3k ln 2
D) $\Delta$ S = k ln(1/3)
E) $\Delta$ S = -3 ln 3

Question 43

Consider the following processes: Which are never found to occur?

A) Only I
B) Only II
C) Only III
D) Only II and III
E) I, II and III

Question 44

Twenty-five identical molecules are in a box. Microstates are designated by identifying the molecules in the left and right halves of the box. The multiplicity of the configuration with 15 molecules in the right half and 10 molecules in the left half is:

A) 1.03 * 10²³
B) 3.27 *10⁶
C) 150
D) 25
E) 5

Question 45

A Carnot refrigerator runs between a cold reservoir at temperature T_L and a hot reservoir at temperature T_H. You want to increase its coefficient of performance. Of the following, which change results in the greatest increase in the coefficient? The value of $\Delta$ T is the same for all changes.

A) Raise the temperature of the hot reservoir by $\Delta$ T
B) Raise the temperature of the cold reservoir by $\Delta$ T
C) Lower the temperature of the hot reservoir by $\Delta$ T
D) Lower the temperature of the cold reservoir by $\Delta$ T
E) Lower the temperature of the hot reservoir by (1/2) $\Delta$ T and raise the temperature of the cold reservoir by (1/2) $\Delta$ T

Question 46

Is it possible to transfer energy from a low-temperature reservoir to a high-temperature reservoir?

A) No, this violates the conservation of energy.
B) No, this violates the second law of thermodynamics.
C) Yes, this is what a heat engine does, and it can happen without the engine doing work.
D) Yes, this is what a refrigerator does, and it can happen without the refrigerator doing work.
E) Yes, this is what a refrigerator does, and the refrigerator must do work to make this happen.

Question 47

A perfectly reversible heat pump with a coefficient of performance of 14 supplies energy to a building as heat to maintain its temperature at 27 $\degree$ C. If the pump motor does work at the rate of 1 kW, at what rate does the pump supply energy to the building?

A) 15 kW
B) 3.9 kW
C) 1.4 kW
D) 0.26 kW
E) 0.067 kW

Question 48

On a warm day a pool of water transfers energy to the air as heat and freezes. This is a direct violation of:

A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) the third law of thermodynamics
E) none of the above

Question 49

According to the second law of thermodynamics:

A) heat energy cannot be completely converted to work
B) work cannot be completely converted to heat energy
C) for all cyclic processes we have dQ/T < 0
D) the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable
E) all of the above are true

Question 50

For a system of molecules,

A) each configuration consists of a set of equivalent microstates.
B) each microstate consists of a set of equivalent configurations.
C) the number of configurations in a microstate is the multiplicity of the microstate.
D) the multiplicity of the configuration is the product of the number of molecules in each microstate.
E) each configuration is equally probable.

Question 51

Let k be the Boltzmann constant. If the configuration of molecules in a gas changes from one with a multiplicity of M₁ to one with a multiplicity of M₂, then entropy changes by:

A) $\Delta$ S = 0
B) $\Delta$ S = k(M₂ - M₁)
C) $\Delta$ S = kM₂/M₁
D) $\Delta$ S = k ln(M₂M₁)
E) $\Delta$ S = k ln(M₂/M₁)

Question 52

A heat engine operates between 200 K and 100 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) both the first and second laws of thermodynamics
B) the first law but not the second law of thermodynamics
C) the second law but not the first law of thermodynamics
D) neither the first law nor the second law of thermodynamics
E) cannot answer without knowing the mechanical equivalent of heat

Question 53

A Carnot heat engine and an irreversible heat engine both operate between the same high temperature and low temperature reservoirs. They absorb the same heat from the high temperature reservoir as heat. The irreversible engine:

A) does more work
B) rejects more energy to the low temperature reservoir as heat
C) has the greater efficiency
D) has the same efficiency as the reversible engine
E) cannot absorb the same energy from the high temperature reservoir as heat without violating the second law of thermodynamics

Question 54

The thermodynamic state of gas changes configuration from one with 3.8 * 10¹⁸ microstates to one with 7.9 *10¹⁹ microstates. The Boltzmann constant is 1.38 *10^-23 J/K. The change in entropy is:

A) $\Delta$ S = 0
B) $\Delta$ S = 1.05 * 10^-23 J/K
C) $\Delta$ S = -1.05 *10^-23 J/K
D) $\Delta$ S = 4.19*10^-23 J/K
E) $\Delta$ S = -4.19 *10^-23 J/K

Question 55

An inventor claims to have a heat engine that has efficiency of 40% when it operates between a high temperature reservoir of 150 $\degree$ C and a low temperature reservoir of 30 $\degree$ C. This engine:

A) must violate the zeroth law of thermodynamics
B) must violate the first law of thermodynamics
C) must violate the second law of thermodynamics
D) must violate the third law of thermodynamics
E) does not necessarily violate any of the laws of thermodynamics

Question 56

A cyclical process that transfers energy as heat from a high temperature reservoir to a low temperature reservoir with no other change would violate:

A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) the third law of thermodynamics
E) none of the above

Question 57

Twenty-five identical molecules are in a box. Microstates are designated by identifying the molecules in the left and right halves of the box. The Boltzmann constant is 1.38 *10^-23 J/K. The entropy associated with the configuration for which 15 molecules are in the left half and 10 molecules are in the right half is:

A) 2.07 *10^-22 J/K
B) 7.31*10^-22 J/K
C) 4.44 * 10^-23 J/K
D) 6.91 * 10^-23 J/K
E) 2.22 *10^-23 J/K

Question 58

A refrigerator absorbs energy of magnitude $\mid$ Q_L $\mid$ as heat from a low temperature reservoir and rejects energy of magnitude $\mid$ Q_H $\mid$ as heat to a high temperature reservoir. Work W is done on the working substance. The coefficient of performance is given by:

A) $\mid$ Q_L $\mid$ /W
B) $\mid$ Q_H $\mid$ /W
C) ( $\mid$ Q_L $\mid$ + $\mid$ Q_H $\mid$ )/W
D) W/ $\mid$ Q_L $\mid$
E) W/ $\mid$ Q_H $\mid$

Question 59

A reversible refrigerator operates between a low temperature reservoir at T_L and a high temperature reservoir at T_H. Its coefficient of performance is given by:

A) (T_H - T_L)/ T_L
B) T_L /(T_H - T_L)
C) (T_H - T_L)/T_H
D) T_H/(T_H - T_L)
E) T_H(T_H + T_L)

Question 60

A heat engine in each cycle absorbs energy of magnitude $\mid$ Q_H $\mid$ as heat from a high temperature reservoir, does work of magnitude $\mid$ W $\mid$ , and then absorbs energy of magnitude $\mid$ Q_L $\mid$ as heat from a low temperature reservoir. If $\mid$ W $\mid$ = $\mid$ Q_H $\mid$ + $\mid$ Q_L $\mid$ this engine violates:

A) the zeroth law of thermodynamics
B) the first law of thermodynamics
C) the second law of thermodynamics
D) the third law of thermodynamics
E) none of the above

Question 61

Let k be the Boltzmann constant. If the thermodynamic state of gas at temperature T changes isothermally and reversibly to a state with three times the number of microstates as initially, the energy input to gas as heat is:

A) Q = 0
B) Q = 3kT
C) Q = -3kT
D) Q = kT ln 3
E) Q = -kT ln 3