Question 1

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% B

Question 2

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 A

Question 3

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 A

Question 4

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 5

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:

Accepted Answer

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

Question 6

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 7

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

Accepted Answer

A)  $\Delta$S = 0 
B)  $\Delta$S = 1.04 *10-23 J/K 
C)  $\Delta$S = -1.04 *10-23 J/K 
D)  $\Delta$S = 4.19 * 10-23 J/K 
E)  $\Delta$S = -4.19 *10-23 J/K 
A)  $\Delta$S = 0 
B)  $\Delta$S = 1.04 *10-23 J/K 
C)  $\Delta$S = -1.04 *10-23 J/K 
D)  $\Delta$S = 4.19 * 10-23 J/K 
E)  $\Delta$S = -4.19 *10-23 J/K

Question 8

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 9

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

Accepted Answer

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

Question 10

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:

Accepted Answer

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

Question 11

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

Question 12

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 13

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

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 14

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 15

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 16

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 17

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:

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 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Exam 20: Entropy and the Second Law of Thermodynamics

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

A Carnot cycle:

The change in entropy is zero for:

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

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:

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:

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

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:

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

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

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

A heat engine:

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

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

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

For all reversible processes involving a system and its environment:

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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:

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

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 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 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:

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

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: