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

Question 1

A heat pump has a coefficient of performance of 4.If the heat pump absorbs 20 cal of heat from the cold outdoors in each cycle,the heat expelled (in cal)to the warm indoors is

A)34
B)27
C)36
D)40
E)80

Answer 1

27

Question 2

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

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

Answer 2

1 800 J

Question 3

A refrigerator has a coefficient of performance of 4.If the refrigerator absorbs 30 cal of heat from the cold reservoir in each cycle,the heat expelled (in cal)into the heat reservoir is

A)40.5
B)37.5
C)36.5
D)34.5
E)22.5

Answer 3

37.5

Question 4

An 800-MW electric power plant has an efficiency of 30%.It loses its waste heat in large cooling towers.Approximately how much waste heat (in MJ)is discharged to the atmosphere per second?

A)1 200
B)1 900
C)800
D)560
E)240

Question 5

Exactly 500 grams of ice are melted at a temperature of 32°F.(L_ice = 333 J/g. )The change in entropy (in J/K)is

A)321
B)146
C)512
D)610
E)5 230

Question 6

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?

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

Question 7

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?

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

Question 8

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

Question 9

A steam engine is operating at its theoretical maximum efficiency of 60%.If the waste heat has a temperature of 100°F (38°C),what is the temperature of the boiler?

A)350°C
B)94°C
C)225°C
D)504°C
E)775°C

Question 10

A company that produces pulsed gas heaters claims their efficiency is approximately 90%.If an engine operates between 250°C and 25°C,what is its maximum thermodynamic efficiency?

A)83%
B)65%
C)43%
D)90%
E)56%

Question 11

One kilogram of chilled water at 32°F (0°C)is placed in a freezer which is kept at 0°F (−18°C).Approximately how much electric energy (in kilocalories)is needed to operate the compressor to cool this water to 0°F if the room temperature is maintained at 75°F (24°C)? (L_ice = 3.33 × 10⁵ J/kg;c_ice = 2.09 × 10³ J/kg⋅°C)

A)13
B)1.5
C)15
D)16
E)33

Question 12

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

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

Question 13

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?

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

Question 14

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

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

Question 15

An automobile engine operates with an overall efficiency of 12%.How much energy is delivered as waste heat (in gallons of gasoline)for each 10 gallons of fuel burned?

A)1.2
B)8.8
C)6.5
D)4.7
E)7.5

Question 16

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

A)80%
B)40%
C)60%
D)20%
E)50%

Question 17

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)?

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

Question 18

One kilogram of chilled water (0°C)is placed in a freezer which is kept at 0°F (−18°C).Approximately how much electric energy (in kilocalories)is needed just to freeze the water if the room temperature is maintained at 75°F (24°C)? (L_ice = 333 J/g;c_ice = 209 J/g⋅°C. )

A)11
B)15
C)16
D)13
E)33

Question 19

A homeowner has a new oil furnace which has an efficiency of 60%.For every 100 barrels of oil needed to heat his house,how much (in barrels of oil)goes up the chimney as waste heat?

A)20
B)60
C)40
D)80
E)10

Question 20

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

Question 21

Which of the following is an almost reversible process?

A)The explosion of hydrogen and oxygen to form water.
B)Heat transfer through thick insulation.
C)The adiabatic free expansion of a gas.
D)A slow isothermal compression of a gas.
E)A slow leakage of gas into an empty chamber through a small hole in a membrane.

Question 22

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

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 23

A gasoline engine absorbs 2 500 J of heat at 250°C and expels 2 000 J at a temperature of 50°C.The magnitude of the change in entropy (in J/K)for the system is

A)6.2
B)4.7
C)1.4
D)10.9
E)3.2

Question 24

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

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

Question 25

An ideal heat engine can have an efficiency of 1 if the temperature of the low temperature reservoir is

A)0 K.
B)0°C.
C)0°F.
D)0°R.
E)the same as the temperature of the heat source.

Question 26

A vessel containing 10 kg of water is left out where it evaporates.If the temperature remains constant at 20°C,what is the change in entropy (in kcal/K)? (The latent heat of vaporization at 20°C is 585 cal/g. )

A)30
B)10
C)20
D)40
E)290

Question 27

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

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.

Question 28

The change in entropy of a mass m of a solid substance which has a latent heat of fusion L and melts at a temperature T is

A)LT/m
B)mL ln(T)
C)mLT
D)mL/T
E)L/mT

Question 29

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

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 30

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.

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

Question 31

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.

A)−191
B)−52
C)−71
D)−67
E)−208

Question 32

All real engines are less efficient than the Carnot engine because

A)they do not operate through the Otto cycle.
B)they do not operate through a reversible cycle.
C)the working substance does not maintain a constant volume through the cycle.
D)the working substance does not maintain a constant pressure through the cycle.
E)the working substance does not maintain a constant temperature through the cycle.

Question 33

An ideal gas is allowed to undergo a free expansion.If its initial volume is V₁ and its final volume is V₂,the change in entropy is

A)nR ln (V₂/V₁)
B)nRT ln (V₂/V₁)
C)nk ln (V₂/V₁)
D)0
E)nR V₂/V₁

Question 34

Since L_ice = 333 J/g,the change in entropy (in cal/K)when 1.00 kg of ice melts is

A)144
B)291
C)312
D)516
E)80

Question 35

If n moles of an ideal gas are compressed isothermally from an initial volume V₁ to a final volume V₂,the change in entropy is

A)nR ln (V₂/V₁)
B)nRT ln (V₂/V₁)
C)nk_B ln (V₂/V₁)
D)
E)n C_v/T

Question 36

100 grams of molten lead (600°C)is used to make musket balls.If the lead shot is allowed to cool to room temperature (21°C),what is the change in entropy (in J/K)of the lead? (For the specific heat of molten and solid lead use 1.29 J/g⋅°C;the latent heat of fusion and the melting point of lead are 2.45 × 10⁴ J/kg and 327°C. )

A)−145
B)−252
C)−302
D)−429
E)−100

Question 37

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

A)1 000
B)480
C)−720
D)240
E)−168

Question 38

The change in entropy when 1 kg of ice melts at 0°C is (in J/K).(L_ice = 333 J/g. )

A)335.
B)603.
C)1 220.
D)1 310.
E)2 160.

Question 39

Find the change in entropy (in J/K)when 5.00 moles of an ideal monatomic gas are allowed to expand isobarically from an initial volume of 20 cm³ to a final volume of 100 cm³.

A)167
B)100
C)67
D)52
E)152

Question 40

By operating a reversible heat engine with an ideal gas as the working substance in a Carnot cycle and measuring the ratio Q_c/Q_h,we can calculate

A)n,the number of moles of the ideal gas.
B)the ratio V_c/V_h of the volumes of the ideal gas.
C)the ratio P_c/P_h of the pressures of the ideal gas.
D)the ratio P_cV_c/P_hV_h of the products of volumes and pressures of the ideal gas.
E)the value of Avogadro's number.

Question 41

A 4.00-liter container is divided into two equal parts,one part containing 0.0100 mole of neon,and the other part containing 0.0100 mole of helium.The divider is removed and the gases mix.What is the change in entropy (in J/K)of this system?

A)0.057 6
B)0.115
C)0.173
D)0.086 4
E)0.144

Question 42

One end of a copper rod is in thermal contact with a hot reservoir at T = 500 K and the other end is in thermal contact with a cooler reservoir at T = 300 K.Find the entropy change of each reservoir,and the total entropy change,when 8 000 J of heat energy are conducted from one end of the rod to the other with no change in the temperature distribution in the rod.

Question 43

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

A) .
B) .
C) .
D) .
E) .

Question 44

A violation of the second law of thermodynamics would occur if

A)a ball lying on the ground started to bounce.
B)transfer of energy by heat moved energy from an object at low temperature to an object at a higher temperature.
C)a motion picture was run backwards through the projector.
D)any of the above occurred.
E)(a)or (b)occurred,but not (c).

Question 45

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?

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 46

In a nuclear power plant,the reactor produces 500°C steam that is used to power the steam turbines which generate 1 500 MW of electrical power.The cooling tower eliminates the waste heat at 50°C.If the efficiency of the plant were that of a Carnot engine,at what rate would waste heat be vented to the atmosphere?

Question 47

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).

Question 48

A violation of the second law of thermodynamics would occur if

A)a ball lying on the ground started to bounce.
B)transfer of energy by heat moved energy from an object at low temperature to an object at a higher temperature.
C)a refrigerator heated the air in the room in which the refrigerator is located.
D)any of the above occurred.
E)(a)or (b)occurred,but not (c).

Question 49

For the same temperature increase in a system,the change in entropy,ΔS,is largest in a reversible

A)constant volume process.
B)constant pressure process.
C)adiabatic process.
D)process in which no heat is transferred.
E)process in which no work is performed.

Question 50

Suppose there are 3 molecules in a container.If each molecule has a 1-in-2 chance of being in the left half of the container,what is the probability that there are exactly 2 molecules in the left half of the container?

A)1/2
B)1/3
C)1/8
D)3/8
E)3/5

Question 51

For a pair of dice,how many microstates are there that result in the macrostate of rolling a 7?

A)1
B)5
C)6
D)7
E)36

Question 52

In an engine operating in the Otto cycle,the final volume of the fuel-air mixture is one sixth the initial volume.Assume γ = 1.4.The maximum theoretical efficiency of this cycle,in per cent,is

A)17.
B)49.
C)51.
D)56.
E)83.

Question 53

What is the probability of rolling either a 7 or 11 on a single roll of a pair of dice?

A)1/6
B)2/9
C)3/8
D)1/3
E)1/2

Question 54

Which answer below is not a statement of the second law of thermodynamics?

A)Real processes proceed in a preferred direction.
B)Energy does not flow spontaneously by heat from a cold to a hot reservoir.
C)The entropy of the universe increases in all natural processes.
D)In theory,heat engines working in a cycle employ reversible processes.
E)You cannot construct a heat engine,operating in a cycle that does nothing but take heat from a reservoir and perform an equal amount of work.

Question 55

The thermal efficiency of a heat engine is given by

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