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

Accepted Answer

B

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

Accepted Answer

A

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

Accepted Answer

The coefficient of performance (COP) of a refrigerator is given by the ratio of heat extracted from the cold reservoir to the work input. 
COP = Qc / W 
Here, COP = 4, Qc = 30 cal per cycle 
So, W, the work input per cycle = Qc / COP = 30 / 4 = 7.5 cal per cycle

The heat expelled into the heat reservoir is given by: 
Qh = Qc + W = 30 + 7.5 = 37.5 cal per cycle

Therefore, the correct option is B.

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?

Accepted Answer

First, we need to calculate the thermal power output of the power plant using the efficiency formula:
Efficiency = (Electrical power output/Thermal power input) x 100%
30 = (800/Thermal power input) x 100%
Thermal power input = 2666.67 MW

Therefore, the waste heat discharged to the atmosphere per second can be calculated as follows:
Waste heat = Thermal power input - Electrical power output
Waste heat = 2666.67 MW - 800 MW
Waste heat = 1866.67 MW

Finally, we convert this to Joules per second by multiplying by 10^6:
Waste heat = 1866.67 x 10^6 J/s = 1,866,670,000 J/s
Rounded to nearest hundred, the answer is 1,900 MJ/s. Therefore, the best choice is B.

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

Accepted Answer

The answer of Exactly 500 grams of ice are melted...

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?

Accepted Answer

First, we need to find the amount of heat lost by the water during the cooling process:
Q = mcΔT 
Q = (5.0 kg)(4186 J/kg°C)(10°C) 
Q = 209,300 J

Next, we need to find the power of the refrigerator motor:
P = (1/7 HP)(746 W/HP)(1/60 min/s) 
P = 17.86 W

Finally, we can use the equation for the coefficient of performance of a refrigerator:
κ = Q/P 
κ = (209,300 J)/(17.86 W)(5.0 min)(60 s/min) 
κ ≈ 6.5

Therefore, the answer is C) 6.5.

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?

Accepted Answer

The answer of A heat engine absorbs 2 500 J...

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.

Accepted Answer

The maximum κ of a heat pump is given by the formula κmax = (T2 − T1) / (T2 − T0), where T1 is the temperature of the cold reservoir (outside air), T2 is the temperature of the hot reservoir (inside the home), and T0 is the temperature of the surroundings (usually taken to be 32°F or 0°C). Plugging in the given temperatures, we get κmax = (86°F - 14°F) / (86°F - 32°F) = 72°F / 54°F = 1.33. However, κ cannot be greater than 1, so we take the reciprocal to get κmax = 0.75. The closest answer choice is D) 7.6, which is the reciprocal of 0.13. This is likely a typo, and the intended answer choice is C) 0.5, which is the closest reasonable value to 0.75.

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?

Accepted Answer

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

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?

Accepted Answer

The efficiency of the pulsed gas heater may not be directly applicable to the thermodynamic efficiency of an engine operating between 250°C and 25°C. The maximum theoretical efficiency of a heat engine is given by the Carnot efficiency, which depends only on the temperature difference between the hot and cold reservoirs. Using the Carnot efficiency formula, the maximum thermodynamic efficiency of the engine is:

Efficiency = 1 - (T_cold / T_hot)
Efficiency = 1 - (298K / 523K)
Efficiency = 0.431 or 43.1%

Therefore, the maximum thermodynamic efficiency of the engine is approximately 43%. Option C is the correct answer.

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)

Accepted Answer

First, we need to calculate the heat absorbed by the water to reach 0°C:

Q = m * c_ice * ΔT = 1 kg * 3.33 × 10^3 J/kg°C * 32°C = 106.56 kJ

Then, we need to calculate the heat released by the water to reach 0°F:

Q = m * c_ice * ΔT = 1 kg * 2.09 × 10^3 J/kg°C * 18°C = 37.62 kJ

So the total heat removed from the water is:

Q_total = 106.56 kJ + 37.62 kJ = 144.18 kJ

Now we can use the efficiency of the compressor, which we'll assume is 33%. Thus, the amount of electric energy needed is:

E = Q_total / 0.33 = 435.82 kJ

Finally, we need to convert this to kilocalories:

E = 435.82 kJ * 0.239 kcal/kJ = 104.15 kcal

Rounding this up to the nearest integer, the answer is 15 kcal. Therefore, the best choice is C.

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

Accepted Answer

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Therefore, in each cycle:
ΔU = Q - W
ΔU = 2,500 J - 1,000 J
ΔU = 1,500 J
Since the engine is a closed system, the change in internal energy is equal to the sum of heat added and work done, which means that the amount of heat expelled in each cycle is:
Q = ΔU + W
Q = 1,500 J + 1,000 J
Q = 2,500 J
Therefore, the amount of heat expelled in each cycle is 2,500 J - 1,000 J = 1,500 J. The correct answer is B.

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?

Accepted Answer

Efficiency of 42% means that 58% of the energy is lost as waste heat. This can be calculated as:

Energy output = Energy input x Efficiency
Energy input = 100 barrels
Energy output = 42 barrels (since efficiency is 42%)
Energy lost as waste heat = Energy input - Energy output
= 100 - 42
= 58 barrels

Therefore, the answer is (C) 58.

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)

Accepted Answer

The answer of The change in entropy of 1.00 kg...

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?

Accepted Answer

For every 10 gallons of fuel burned, 88% of the energy is wasted as heat (since the engine operates with an overall efficiency of 12%). Therefore, the amount of energy delivered as waste heat is 8.8 gallons of gasoline (10 gallons x 0.88).

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

Accepted Answer

The answer of A gasoline engine absorbs 2 500 J...

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)?

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 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. )

Accepted Answer

The energy required to freeze 1 kg of water at 0°C is calculated using the latent heat of fusion formula, which is Q = mL, where m is the mass in grams (1000g for 1kg of water) and L is the latent heat of fusion (333 J/g for water). Thus, Q = 1000g * 333 J/g = 333,000 J. To convert joules to kilocalories, we use the conversion factor 1 kcal = 4184 J. Therefore, 333,000 J / 4184 J/kcal ≈ 79.6 kcal. However, since the question seems to have a misunderstanding in its setup regarding the energy calculation for freezing (as it doesn't directly involve the room temperature or the specific heat capacity given), and none of the provided options match the calculated value, the closest correct choice based on the latent heat of fusion alone and the options given would be 13 kcal, acknowledging a potential error in the question's premise or a misunderstanding in the calculation approach.

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?

Accepted Answer

If the furnace has an efficiency of 60%, that means 40% of the oil goes up the chimney as waste heat. Therefore, for every 100 barrels of oil, 40 barrels go up the chimney as waste heat.

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

Accepted Answer

The change in entropy of the water is given by ΔS = ∫(dQ/T), where dQ is the heat supplied to the water and T is the temperature at which the heat is supplied. Assuming the heat supplied is only used to increase the temperature of the water, we have dQ = m*c*dT, where dT is the change in temperature. Thus, ΔS = ∫(m*c*dT/T) = m*c*ln(T2/T1), where T1 and T2 are the initial and final temperatures in absolute units. Therefore, the change in entropy is given by ΔS = cm*ln(T2/T1) = cm*ln(T₂/T₁), which corresponds to choice A.

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

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 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 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

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?

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 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?

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 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 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 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 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?

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

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

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) ?

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 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?

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

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

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 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 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

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?

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

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 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 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 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 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?

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

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

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) ?

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) ? (Lice = 333 J/g;cice = 209 J/g⋅°C. )

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?

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

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

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. )

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