Question 1

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

Accepted Answer

A)  is zero for all 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 
A)  is zero for all 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 2

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:

Accepted Answer

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

Question 3

For all reversible processes involving a system and its environment:

Accepted Answer

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 
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 4

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

Accepted Answer

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 
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 5

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:

Accepted Answer

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) 
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 6

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:

Accepted Answer

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 
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 7

A Carnot refrigerater runs between a cold reservoir at temperature TC and a hot reservoir at temperature TH. 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.

Accepted Answer

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 
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 8

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

Accepted Answer

A)  nCp ln(Tf/Ti) 
B)  nCp ln(Ti/Tf) 
C)  nCp ln(Tf - Ti) 
D)  nCp ln(1 - Ti/Tf) 
E)  nCp (Tf - Ti) 
A)  nCp ln(Tf/Ti) 
B)  nCp ln(Ti/Tf) 
C)  nCp ln(Tf - Ti) 
D)  nCp ln(1 - Ti/Tf) 
E)  nCp (Tf - Ti)

Question 9

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:

Accepted Answer

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 
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 10

An ideal gas is to taken reversibly from state i, at temperature T1, to another states labeled I, II, III, IV and V on the p-V diargram below. All are at the same temperature T2. Rank the five processes according to the change in entropy of the gas, least to greatest.

Accepted Answer

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 
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 11

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

Accepted Answer

A)  (TH - T
C) /TC 
B)  TC/(TH - T
C)  
C)  (TH - T
C) /TH 
D)  TH/(TH - T
C)  
E)  TH(TH + T
C)  
A)  (TH - T
C) /TC 
B)  TC/(TH - T
C)  
C)  (TH - T
C) /TH 
D)  TH/(TH - T
C)  
E)  TH(TH + T
C)

Question 12

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

Accepted Answer

A)  1, 2, 3, 4 
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 
A)  1, 2, 3, 4 
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 13

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?

Accepted Answer

A)  15 kW 
B)  3.85 kW 
C)  1.35 kW 
D)  1.07 kW 
E)  1.02 kW 
A)  15 kW 
B)  3.85 kW 
C)  1.35 kW 
D)  1.07 kW 
E)  1.02 kW

Question 14

For all irreversible processes involving a system and its environment:

Accepted Answer

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 
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 15

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 Vi to Vf, the change in entropy is given by:

Accepted Answer

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

Question 16

A heat engine:

Accepted Answer

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 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 
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 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 17

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

Accepted Answer

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

Question 18

In a reversible process the system:

Accepted Answer

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 
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 19

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:

Accepted Answer

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 
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 20

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

Accepted Answer

A)  1, 2, 3, 4 
B)  5,4,3,2 
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 
A)  1, 2, 3, 4 
B)  5,4,3,2 
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

Exam 20: Entropy and the Second Law of Thermodynamics

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

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:

For all reversible processes involving a system and its environment:

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:

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:

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

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:

An ideal gas is to taken reversibly from state i, at temperature T1, to another states labeled I, II, III, IV and V on the p-V diargram below. All are at the same temperature T2. Rank the five processes according to the change in entropy of the gas, least to greatest.

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

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

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?

For all irreversible processes involving a system and its environment:

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 Vi to Vf, the change in entropy is given by:

A heat engine:

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

In a reversible process the system:

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:

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

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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:

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:

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:

An ideal gas is to taken reversibly from state i, at temperature T₁, to another states labeled I, II, III, IV and V on the p-V diargram 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 reversible refrigerator operates between a low temperature reservoir at T_C and a high temperature reservoir at T_H. Its coefficient of performance is given by:

The temperature T_C 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 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?

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: