Question 1

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

Accepted Answer

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 
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 B

Question 2

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 C

Question 3

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

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 E

Question 4

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 5

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:

Accepted Answer

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

Question 6

The change in entropy is zero for:

Accepted Answer

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 
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 7

The temperature TL 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)  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 
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 8

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

Accepted Answer

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 
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 9

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 10

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

Accepted Answer

A)  TH/ TL 
B)  TL /TH 
C)  1 - TH/ TL 
D)  1 - TL /TH 
E)  100% 
A)  TH/ TL 
B)  TL /TH 
C)  1 - TH/ TL 
D)  1 - TL /TH 
E)  100%

Question 11

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

Accepted Answer

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 
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 12

Possible units of entropy are:

Accepted Answer

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

Question 13

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:

Accepted Answer

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 
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 14

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 15

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

Accepted Answer

A)  $\mid$QH $\mid$/$\mid$W $\mid$ 
B)  $\mid$QL $\mid$/ $\mid$W $\mid$ 
C)  $\mid$QH $\mid$/ $\mid$QL $\mid$ 
D)  $\mid$W $\mid$/$\mid$QH $\mid$ 
E)  $\mid$W $\mid$/ $\mid$QL $\mid$ 
A)  $\mid$QH $\mid$/$\mid$W $\mid$ 
B)  $\mid$QL $\mid$/ $\mid$W $\mid$ 
C)  $\mid$QH $\mid$/ $\mid$QL $\mid$ 
D)  $\mid$W $\mid$/$\mid$QH $\mid$ 
E)  $\mid$W $\mid$/ $\mid$QL $\mid$

Question 16

A Carnot refrigerator runs between a cold reservoir at temperature TL 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 17

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 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 18

A Carnot cycle:

Accepted Answer

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 
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 19

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 $\Delta$Sh in the entropy of the hot object, the change $\Delta$Sc in the entropy of the cold object, and the change $\Delta$Stotal in the entropy of the combination are:

Accepted Answer

A) $\Delta$Sh > 0, $\Delta$Sc > 0, $\Delta$Stotal > 0 B) $\Delta$Sh c > 0, $\Delta$Stotal > 0 C) $\Delta$Sh c > 0, $\Delta$Stotal h > 0, $\Delta$Sc total > 0 E) $\Delta$Sh > 0, $\Delta$Sc total < 0 A) $\Delta$Sh > 0, $\Delta$Sc > 0, $\Delta$Stotal > 0 B) $\Delta$Sh c > 0, $\Delta$Stotal > 0 C) $\Delta$Sh c > 0, $\Delta$Stotal h > 0, $\Delta$Sc total > 0 E) $\Delta$Sh > 0, $\Delta$Sc total < 0

Question 20

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

Exam 20: Entropy and the Second Law of Thermodynamics

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

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 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:

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:

The change in entropy is zero for:

The temperature TL 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

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

For all reversible processes involving a system and its environment:

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

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

Possible units of entropy are:

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:

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

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 T2. Rank the five processes according to the change in entropy of the gas, least to greatest.

A Carnot cycle:

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:

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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:

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 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:

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 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:

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.