Question 1

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

Accepted Answer

The coefficient of performance (COP) of a refrigerator is given by the formula: 
COP = heat absorbed from the cold reservoir / work done on the refrigerator

Since the work done on the refrigerator is equal to the difference between the heat absorbed from the cold reservoir and the heat expelled into the heat reservoir in each cycle, we can write:

COP = (heat absorbed from the cold reservoir) / (heat absorbed from the cold reservoir minus heat expelled into the heat reservoir)

Substituting the given values, we get:

4 = 30 / (30 - heat expelled into the heat reservoir)

Solving for heat expelled into the heat reservoir, we get:

heat expelled into the heat reservoir = 7.5 cal

However, since the heat expelled into the heat reservoir is the same as the heat absorbed from the hot reservoir, the total heat expelled in each cycle is:

Total heat expelled = heat expelled into the heat reservoir + heat absorbed from the cold reservoir 
Total heat expelled = 7.5 + 30 = 37.5 cal

Therefore, the answer is (B) 37.5.

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 COP of the refrigerator?
A)5.7
B)4.6
C)6.5
D)7.2
E)3.6

Accepted Answer

To find the COP, we need to use the formula:
COP = heat removed from the cold reservoir / work input
First, let's find the heat removed from the cold reservoir:
Q = mcΔT
Q = (5.0 kg)(4186 J/kg°C)(10°C - 0°C) = 209,300 J
Now, let's find the work input:
Power = 1/7 HP = (1/7)(746 W/HP) = 106.5 W
Work = Power x time
Work = (106.5 W)(5.0 min)(60 s/min) = 31,950 J
So, the COP is:
COP = Q / Work
COP = 209,300 J / 31,950 J = 6.55
Therefore, the answer is C.

Question 3

Exactly 500 grams of ice are melted at a temperature of 32°F. (LF,ice = 333 J/g.) The change in entropy (in J/K) is
A)321.
B)146.
C)512.
D)610.
E)5230.

Accepted Answer

D

Question 4

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

Accepted Answer

Efficiency of engine = 12%
Therefore, energy delivered as useful work = 88% (100-12) of the total energy input.

So, waste heat energy = 100% - 88% = 12% of the total energy input.

We are given that 10 gallons of fuel are burned.
There is no information about the energy content of the fuel in the question, so we cannot calculate the actual amount of energy delivered or wasted.

Hence, we cannot give the answer in gallons of gasoline, as asked in the question.
Option B, 8.8, looks like a typo (perhaps intended to be 88?). However, it is clear that the waste heat energy will be less than the total energy input, so we can eliminate options A, C, D and E.

Thus, the best choice is:
Answer: B (8.8 if intended to be 88)
 The question cannot be answered in the given units, but the waste heat energy will be less than the total energy input.

Question 5

A gasoline engine absorbs 2500 J of heat and performs 1000 J of mechanical work in each cycle. The amount of heat expelled in each cycle is
A)1000 J
B)1500 J
C)2000 J
D)500 J
E)3000 J

Accepted Answer

The amount of heat expelled in each cycle can be found by subtracting the work done by the engine from the heat absorbed. So, 2 500 J - 1 000 J = 1 500 J.

Question 6

A gasoline engine absorbs 2500 J of heat and performs 1000 J of mechanical work in each cycle. The efficiency of the engine is
A)80%.
B)40%.
C)60%.
D)20%.
E)50%.

Accepted Answer

The answer of A gasoline engine absorbs 2500 J of...

Question 7

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)? (LF,ice = 333 J/g; cice = 2.09 J/g⋅°C.)
A)11
B)15
C)16
D)13
E)33

Accepted Answer

The answer of One kilogram of chilled water (0°C) is...

Question 8

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)25
C)36
D)40
E)80

Accepted Answer

The answer of A heat pump has a coefficient of...

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

Accepted Answer

The answer of A steam engine is operating at its...

Question 10

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 COP of the heat pump.
A)0.2
B)4.4
C)0.5
D)7.6
E)6.7

Accepted Answer

The COP (Coefficient of Performance) of a heat pump is defined as the amount of heat provided by the pump divided by the work required to move that heat. 
COP = Q_out / W_in 
where Q_out is the heat transferred into the home and W_in is the work required to move that heat.

To find the COP, we need to determine the heat transferred and the work required.

Heat transferred: 
The heat transferred is the difference between the heat absorbed from the outside air and the heat released into the home.

Q_out = heat released into home = 86°F - 14°F = 72°F 
(Note: we convert to Fahrenheit here for consistency with the temperature range of typical heat pumps)

Work required: 
The work required is the amount of energy needed to move the heat from the cold outdoor air to the warmer indoor air. This work requirement is proportional to the temperature difference between the two environments.

W_in = P * (T_hot - T_cold) 
where P is the power input to the heat pump and T_hot and T_cold are the temperatures of the warm and cold environments respectively.

Since we are looking for the maximum COP, we need to determine the minimum work required. This occurs when the power input is at its lowest possible level but still sufficient to move the heat. This is typically achieved at near-zero temperature differences.

Assuming P is minimal, we can use this formula to calculate the minimum work required:

W_in = P * (T_hot - T_cold) 
       = P * (86°F - (-10°F)) 
       = P * 96°F

(Note: we convert to Fahrenheit here for consistency with the temperature range of typical heat pumps)

Therefore,

COP = Q_out / W_in 
       = 72°F / (P * 96°F)

To find the maximum COP, we need to find the minimum power input required to move the heat. This depends on the efficiency of the heat pump, which is typically given as a COP rating at a specific temperature range.

For example, a common COP rating for heat pumps is at 47°F (8°C), where the COP is typically around 2.5. At colder temperatures, the COP decreases due to increased work required to move the heat.

However, since we are given the temperatures in this problem, we can calculate the maximum COP directly:

COP = 72°F / (P * 96°F) 
       = 0.75 / P

(Note: we convert to Fahrenheit here for consistency with the temperature range of typical heat pumps)

To determine the maximum COP, we need to determine the minimum power input (P). The minimum possible power input is the amount required to move the heat at the lowest possible temperature difference. This occurs when the indoor and outdoor temperatures are equal.

Assuming the power input is minimal at this temperature difference:

W_in = P * (T_hot - T_cold) 
       = P * (86°F - 86°F) 
       = 0

Therefore, the maximum COP is:

COP_max = Q_out / W_in 
                = 72°F / (0) 
                = infinity

(Note: this is technically not a real number, since we cannot divide by zero. However, it indicates that the COP can be very large at extremely low temperature differences, since the heat transferred (Q_out) remains fixed but the work required (W_in) approaches zero.)

Since "infinity" is not one of the answer choices, the closest choice is D) 7.6.

Question 11

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

Accepted Answer

If the furnace has an efficiency of 60%, then 40% of the heat generated by the furnace is lost up the chimney as waste heat. Therefore, for every 100 barrels of oil, 40 barrels would be lost up the chimney as waste heat.

Question 12

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%

Accepted Answer

The efficiency of a heat engine operating between two temperatures is given by the Carnot efficiency formula: $\eta = 1 - \frac{T_c}{T_h}$, where $T_c$ and $T_h$ are the cold and hot reservoir temperatures, respectively, in Kelvin. Converting the given temperatures to Kelvin: 15°C + 273.15 = 288.15K and 5°C + 273.15 = 278.15K. Thus, $\eta = 1 - \frac{278.15}{288.15} = 0.0347$ or 3.47%, which rounds to 3.5%.

Question 13

What is the change in entropy of 1.00 kg of water that is heated from 50°C to 100°C?
A)516 cal/K
B)312 cal/K
C)144 cal/K
D)946 cal/K
E)391 cal/K

Accepted Answer

The answer of What is the change in entropy of...

Question 14

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

Accepted Answer

The answer of A lawn mower has a 6-horsepower engine...

Question 15

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

Accepted Answer

Efficiency = Useful power output / Total power input 
30% = Useful power output / input power 
Input power = Useful power output / 0.3 
Input power = 2,667 MW

Waste heat = Input power – Useful power output 
Waste heat = 2,667 MW – 800 MW 
Waste heat = 1,867 MW

1 MW = 1,000,000 J/s 
1,867 MW = 1,867,000,000 J/s = 1.867 x 10^9 J/s

Answer is in MJ/s, so convert to MJ/s: 
1.867 x 10^9 J/s / 10^6 = 1,867 MJ/s

Round to nearest whole number: 
1,867 MJ/s ≈ 1,900 MJ/s

Therefore, the waste heat discharged to the atmosphere per second is approximately 1,900 MJ. The answer is B.

Question 16

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%

Accepted Answer

The maximum theoretical efficiency for a heat engine operating between two temperatures (Thot and Tcold) is given by:
ηmax = 1 - Tcold/Thot
In this case, Thot = 250°C + 273 = 523 K and Tcold = 25°C + 273 = 298 K
ηmax = 1 - 298/523 = 0.43 or 43%.
Therefore, the maximum thermodynamic efficiency of the engine is 43%, which is less than the claimed efficiency of 90% for the pulsed gas heaters.

Question 17

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)? (LF,ice = 3.33 × 10⁵ J/kg; cice = 2.09 × 10³ J/kg⋅°C) A)13 B)1.5 C)15 D)16 E)33

Accepted Answer

The answer of One kilogram of chilled water at 32°F...

Question 18

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

Accepted Answer

Efficiency is the ratio of useful work output to the total input, expressed as a percentage. In this case, the useful work output is the conversion of oil to electricity, and the total input is the oil used. Therefore, if the efficiency of the power plant is 42%, it means that 42% of the oil is converted to electricity, and the remaining 58% is lost as waste heat to the environment. So, for every 100 barrels of oil used, 58 barrels are essentially lost as waste heat. Therefore, the answer is C) 58.

Question 19

A heat engine absorbs 2500 J of heat from a hot reservoir and expels 1000 J to a cold reservoir. When it is run in reverse, with the same reservoirs, the engine pumps 2500 J of heat to the hot reservoir, requiring 1500 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)

Accepted Answer

The answer of A heat engine absorbs 2500 J of...

Question 20

When water of mass m and specific heat c is heated at constant pressure from absolute temperature T1 to absolute temperature T2, its change in entropy is what?
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)

Accepted Answer

The change in entropy (ΔS) when a substance is heated at constant pressure is given by the formula ΔS = mc ln(T2/T1), where m is the mass, c is the specific heat, and T1 and T2 are the initial and final temperatures, respectively.

Quiz 22: Entropy and the Second Law of Thermodynamics

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 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 COP of the refrigerator?

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

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 gasoline engine absorbs 2500 J of heat and performs 1000 J of mechanical work in each cycle. The amount of heat expelled in each cycle is

A gasoline engine absorbs 2500 J of heat and performs 1000 J of mechanical work in each cycle. The efficiency of the engine is

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) ? (LF,ice = 333 J/g; cice = 2.09 J/g⋅°C.)

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 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?

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 COP of the heat pump.

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?

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) ?

What is the change in entropy of 1.00 kg of water that is heated from 50°C to 100°C?

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

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 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 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?

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