Question 1

When water of mass m and specific heat c is heated from absolute temperature T1 to absolute temperature T2,its change in entropy is

Accepted Answer

A)  cm ln(T2/T1) 
B)  cm (T2/T1) 
C)  cm (T2 − T1) /T1
D)  cm (T2 − T1) /T2
E)  cm (T2 − T1) /(T2 + T1)  A

Question 2

A vessel containing 5.0 kg of water at 10°C is put into a refrigerator.The 1/7 HP motor (1 HP = 746 W)runs for 5.0 minutes to cool the liquid to the refrigerator's low temperature,0°C.What is the κ of the refrigerator?

Accepted Answer

A)  5.7
B)  4.6
C)  6.5
D)  7.2
E)  3.6 C

Question 3

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Accepted Answer

8360 kJ/K

Question 4

A heat engine absorbs 2 500 J of heat from a hot reservoir and expels 1 000 J to a cold reservoir.When it is run in reverse,with the same reservoirs,the engine pumps 2 500 J of heat to the hot reservoir,requiring 1 500 J of work to do so.Find the ratio of the work done by the heat engine to the work done by the pump.Is the heat engine reversible?

Accepted Answer

A)  1.0 (no) 
B)  1.0 (yes) 
C)  1.5 (yes) 
D)  1.5 (no) 
E)  2.5 (no)

Question 5

Ten kilograms of water at 0°C is mixed with 10 kg of water at 100°C.The change in entropy (in cal/K)of the system is

Accepted Answer

A)  1 000
B)  480
C)  −720
D)  240
E)  −168

Question 6

Selena states that 
Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says 
,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Accepted Answer

A)  Only Selena,because entropy can depend only on macroscopic variables.
B)  Only Ron,because entropy can depend only on microscopic variables.
C)  Only Selena,because  in an adiabatic free expansion.
D)  Neither,because we cannot calculate changes in entropy in an adiabatic free expansion.
E)  Both,because entropy,which is macroscopic is a function of microscopic disorder.

Question 7

Determine the change in entropy (in J/K)when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm3 to a final volume of 20 cm3.

Accepted Answer

A)  −191
B)  −52
C)  −71
D)  −67
E)  −208

Question 8

An ideal gas is allowed to expand adiabatically.Assume the process is reversible.The change in entropy is

Accepted Answer

A)  0
B)  nR ln (V2/V1) 
C)  nR ln (T2/T1) 
D)  kn ln (V2/V1) 
E)  kn ln (T2/T1)

Question 9

A lawn mower has a 6-horsepower engine (1 HP = 750 W).If the engine has an efficiency of 20%,and the throttle is such that the engine cycles 10 times a second,the heat that is expelled in one cycle is

Accepted Answer

A)  1 800 J
B)  2 000 J
C)  2 200 J
D)  2 400 J
E)  2 250 J

Question 10

For a gas of N identical molecules of molecular volume Vm in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

Accepted Answer

A)   m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is 
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Question 11

The thermal efficiency of a heat engine is given by

Accepted Answer

A)    .
B)    .
C)    .
D)  all of the formulas above.
E)  only (a) or (b) above.

Question 12

A Carnot cycle,operating as a heat engine,consists,in the order given,of

Accepted Answer

A)  an isothermal expansion,an isothermal compression,an adiabatic expansion and an adiabatic compression.
B)  an adiabatic expansion,an adiabatic compression,an isothermal expansion and an isothermal compression.
C)  an isothermal expansion,an adiabatic compression,an isothermal compression and an adiabatic expansion.
D)  an adiabatic compression,an isothermal compression,an isothermal expansion and an adiabatic expansion.
E)  an isothermal expansion,an adiabatic expansion,an isothermal compression and an adiabatic compression.

Question 13

An engine is designed to obtain energy from the temperature gradient of the ocean.What is the thermodynamic efficiency of such an engine if the temperature of the surface of the water is 59°F (15°C)and the temperature well below the surface is 41°F (5°C)?

Accepted Answer

A)  3.5%
B)  67%
C)  31%
D)  17%
E)  96%

Question 14

Find the change in entropy (in J/K)when 5.00 moles of an ideal gas undergo a free expansion from an initial volume of 20 cm3 to a final volume of 100 cm3.

Accepted Answer

A)  71
B)  52
C)  67
D)  191
E)  208

Question 15

The change in entropy of 1.00 kg of water that is heated from 50°C to 100°C is (in cal/K)

Accepted Answer

A)  516
B)  312
C)  144
D)  946
E)  391

Question 16

The reason that we can calculate the change in entropy of a system is that

Accepted Answer

A)  entropy always decreases.
B)  entropy always increases.
C)  the entropy of the universe always remains constant.
D)  it depends only on the properties of the initial and final equilibrium states.
E)  systems always follow reversible paths.

Question 17

A gasoline engine absorbs 2 500 J of heat and performs 1 000 J of mechanical work in each cycle.The amount of heat expelled in each cycle is

Accepted Answer

A)  1 000 J
B)  1 500 J
C)  2 000 J
D)  500 J
E)  3 000 J

Question 18

On a cold day,a heat pump absorbs heat from the outside air at 14°F (−10°C)and transfers it into a home at a temperature of 86°F (30°C).Determine the maximum κ of the heat pump.

Accepted Answer

A)  0.2
B)  4.4
C)  0.5
D)  7.6
E)  6.7

Question 19

A new electric power plant has an efficiency of 42%.For every 100 barrels of oil needed to run the turbine,how many are essentially lost as waste heat (in barrels of oil)to the environment?

Accepted Answer

A)  21
B)  42
C)  58
D)  10
E)  79

Question 20

An adiabatic free expansion of a gas in a thermally isolated container is not reversible because

Accepted Answer

A)  work must be done on the gas to return it to its original volume.
B)  heat must be exchanged with the surroundings to return the gas to its original temperature.
C)  its internal energy has a greater value after the expanded gas is returned to its original volume and temperature.
D)  of all of the above.
E)  of (a) and (b) above only.

Exam 22: Heat Engines, entropy, and the Second Law of Thermodynamics

When water of mass m and specific heat c is heated from absolute temperature T₁ to absolute temperature T₂,its change in entropy is

A vessel containing 5.0 kg of water at 10°C is put into a refrigerator.The 1/7 HP motor (1 HP = 746 W) runs for 5.0 minutes to cool the liquid to the refrigerator's low temperature,0°C.What is the κ of the refrigerator?

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Ten kilograms of water at 0°C is mixed with 10 kg of water at 100°C.The change in entropy (in cal/K) of the system is

Selena states that Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says ,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm³ to a final volume of 20 cm³.

An ideal gas is allowed to expand adiabatically.Assume the process is reversible.The change in entropy is

A lawn mower has a 6-horsepower engine (1 HP = 750 W) .If the engine has an efficiency of 20%,and the throttle is such that the engine cycles 10 times a second,the heat that is expelled in one cycle is

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

The thermal efficiency of a heat engine is given by

A Carnot cycle,operating as a heat engine,consists,in the order given,of

An engine is designed to obtain energy from the temperature gradient of the ocean.What is the thermodynamic efficiency of such an engine if the temperature of the surface of the water is 59°F (15°C) and the temperature well below the surface is 41°F (5°C) ?

Find the change in entropy (in J/K) when 5.00 moles of an ideal gas undergo a free expansion from an initial volume of 20 cm³ to a final volume of 100 cm³.

The change in entropy of 1.00 kg of water that is heated from 50°C to 100°C is (in cal/K)

The reason that we can calculate the change in entropy of a system is that

A gasoline engine absorbs 2 500 J of heat and performs 1 000 J of mechanical work in each cycle.The amount of heat expelled in each cycle is

On a cold day,a heat pump absorbs heat from the outside air at 14°F (−10°C) and transfers it into a home at a temperature of 86°F (30°C) .Determine the maximum κ of the heat pump.

A new electric power plant has an efficiency of 42%.For every 100 barrels of oil needed to run the turbine,how many are essentially lost as waste heat (in barrels of oil) to the environment?

An adiabatic free expansion of a gas in a thermally isolated container is not reversible because

Exam 22: Heat Engines, entropy, and the Second Law of Thermodynamics

When water of mass m and specific heat c is heated from absolute temperature T1 to absolute temperature T2,its change in entropy is

A vessel containing 5.0 kg of water at 10°C is put into a refrigerator.The 1/7 HP motor (1 HP = 746 W) runs for 5.0 minutes to cool the liquid to the refrigerator's low temperature,0°C.What is the κ of the refrigerator?

Every second at Niagara Falls,some 5000 m3 of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Ten kilograms of water at 0°C is mixed with 10 kg of water at 100°C.The change in entropy (in cal/K) of the system is

Selena states that Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says ,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm3 to a final volume of 20 cm3.

An ideal gas is allowed to expand adiabatically.Assume the process is reversible.The change in entropy is

A lawn mower has a 6-horsepower engine (1 HP = 750 W) .If the engine has an efficiency of 20%,and the throttle is such that the engine cycles 10 times a second,the heat that is expelled in one cycle is

For a gas of N identical molecules of molecular volume Vm in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

The thermal efficiency of a heat engine is given by

A Carnot cycle,operating as a heat engine,consists,in the order given,of

An engine is designed to obtain energy from the temperature gradient of the ocean.What is the thermodynamic efficiency of such an engine if the temperature of the surface of the water is 59°F (15°C) and the temperature well below the surface is 41°F (5°C) ?

Find the change in entropy (in J/K) when 5.00 moles of an ideal gas undergo a free expansion from an initial volume of 20 cm3 to a final volume of 100 cm3.

The change in entropy of 1.00 kg of water that is heated from 50°C to 100°C is (in cal/K)

The reason that we can calculate the change in entropy of a system is that

A gasoline engine absorbs 2 500 J of heat and performs 1 000 J of mechanical work in each cycle.The amount of heat expelled in each cycle is

On a cold day,a heat pump absorbs heat from the outside air at 14°F (−10°C) and transfers it into a home at a temperature of 86°F (30°C) .Determine the maximum κ of the heat pump.

A new electric power plant has an efficiency of 42%.For every 100 barrels of oil needed to run the turbine,how many are essentially lost as waste heat (in barrels of oil) to the environment?

An adiabatic free expansion of a gas in a thermally isolated container is not reversible because

When water of mass m and specific heat c is heated from absolute temperature T₁ to absolute temperature T₂,its change in entropy is

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0°C are compressed isothermally from an initial volume of 100 cm³ to a final volume of 20 cm³.

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

Find the change in entropy (in J/K) when 5.00 moles of an ideal gas undergo a free expansion from an initial volume of 20 cm³ to a final volume of 100 cm³.