Question 1

A heat pump has a coefficient of performance of 4. If the heat pump absorbs 20 kJ of heat from the cold outdoors in each cycle, the heat expelled (in kJ) to the warm indoors is:
A)34
B)27
C)36
D)40
E)80

Accepted Answer

B

Question 2

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

B

Question 3

A company that produces pulsed gas heaters claims their efficiency is approximately 90%. If an engine operates between 250$\degree$C and 25$\degree$C, what is its maximum thermodynamic efficiency?
A)83%
B)65%
C)43%
D)90%
E)56%

Accepted Answer

The Carnot efficiency formula is:

Efficiency = 1 - (Tc/Th)

where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

The given engine operates between 250°F and 25°F (or -3.15°C and -7.22°C, respectively). Therefore, the maximum thermodynamic efficiency can be calculated using the Carnot efficiency formula as follows:

Efficiency = 1 - (273.15K/265.93K)≈ 1 - 0.027≈ 0.973

The maximum thermodynamic efficiency of the engine is approximately 97.3%, which is much higher than the claimed efficiency of the pulsed gas heaters (90%). Hence, the best choice is C.

Question 4

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)

Accepted Answer

For an adiabatic reversible process, the change in entropy is zero.

Question 5

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)

Accepted Answer

The change in entropy of water can be calculated using the formula ΔS = cm ln(T2/T1), where ΔS is the change in entropy, c is the specific heat, m is the mass, T1 is the initial absolute temperature, and T2 is the final absolute temperature. Therefore, the best choice is A.

Question 6

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

Accepted Answer

During a free expansion, no work is done on or by the system and no heat is transferred. Therefore, change in internal energy is 0 (ΔU = 0). From the first law of thermodynamics, ΔQ = ΔU + ΔW = 0, where ΔW is the work done by the system. As ΔQ = TΔS, this means that ΔS = 0/T = 0, since the temperature cannot be negative. However, this only applies to a reversible process. In an irreversible process, such as free expansion, there is an additional entropy generation due to an increase in disorder of the system, i.e. the particles of the gas spread out over a larger volume. The entropy increase is given by ΔS = nR ln(V2/V1).

Question 7

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 8

Determine the change in entropy (in J/K) when 5.00 moles of an ideal gas at 0$\degree$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)

Accepted Answer

The answer of Determine the change in entropy (in J/K)...

Question 9

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

According to the first law of thermodynamics, the amount of heat absorbed by the engine is equal to the sum of the work done by the engine and the heat expelled in each cycle. Therefore, the heat expelled in each cycle can be calculated as:
Heat expelled = Heat absorbed - Work done
Heat expelled = 2500 J - 1000 J
Heat expelled = 1500 J
Therefore, the answer is (B) 1500 J.

Question 10

Exactly 500 grams of ice are melted at a temperature of 0$\degree$C. (Lice = 333 J/g.) The change in entropy (in J/K) is:
A)321
B)146
C)512
D)610
E)5230

Accepted Answer

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

Question 11

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)nkB ln (V2/V1)
D) $n C_{v} \int d T / T$
E)n Cv/T

Accepted Answer

The change in entropy during an isothermal process for an ideal gas is given by ΔS = nR ln(V2/V1).

Question 12

An automobile engine operates with an overall efficiency of 12%. How much energy is delivered as waste heat (in litres of petrol) for each 10 litres of petrol burned?
A)1.2
B)8.8
C)6.5
D)4.7
E)7.5

Accepted Answer

If the engine operates with an efficiency of 12%, it means 12% of the energy from the petrol is converted into useful work, and the remaining 88% is waste heat. Therefore, for every 10 litres of petrol burned, 8.8 litres are delivered as waste heat.

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

Accepted Answer

Efficiency = Useful Energy Output / Total Energy Input 
42% = Useful Energy Output / 100 barrels 
Useful Energy Output = 42 barrels

Therefore, the waste heat is: 
Total Energy Input – Useful Energy Output = 100 – 42 = 58 barrels.

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

Accepted Answer

In a free expansion, the gas expands without any external work being done. Since entropy is a measure of the dispersal of energy, a free expansion will always result in an increase in entropy. The change in entropy can be calculated using:

ΔS = nR ln(Vf / Vi)

where n is the number of moles of gas, R is the gas constant, Vf is the final volume, and Vi is the initial volume.

Plugging in the given values, we get:

ΔS = (5 mol)(8.31 J/mol*K) ln(100 cm3 / 20 cm3) 
= 67 J/K

Therefore, the best choice is C.

Question 15

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 15$\degree$C and the temperature well below the surface is 5$\degree$C?
A)3.5%
B)67%
C)31%
D)17%
E)96%

Accepted Answer

The thermodynamic efficiency of an engine operating between two temperatures is given by the Carnot efficiency formula: $\eta = 1 - \frac{T_c}{T_h}$, where $T_h$ and $T_c$ are the absolute temperatures (in Kelvin) of the hot and cold reservoirs, respectively. Converting the given temperatures to Kelvin: $T_h = 15 + 273 = 288$ K and $T_c = 5 + 273 = 278$ K. Thus, $\eta = 1 - \frac{278}{288} = 0.0347$ or 3.5%.

Question 16

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)1200
B)1900
C)800
D)560
E)240

Accepted Answer

First, we have to calculate the energy input to the power plant: 
Energy input = (800 MW) / (0.30) = 2666.67 MW

Then, we have to calculate the waste heat discharged to the atmosphere: 
Waste heat = Energy input - Useful output 
Waste heat = 2666.67 MW - 800 MW 
Waste heat = 1866.67 MW

Finally, we have to convert from MW to MJ: 
Waste heat = (1866.67 MW) * (10^6 J/MJ) * (1 s) 
Waste heat = 1.86667 * 10^9 J/s 
Waste heat ≈ 1.9 * 10^9 J/s ≈ 1.9 MJ/s

Therefore, the waste heat (in MJ) discharged to the atmosphere per second is approximately 1.9. The best choice is B.

Question 17

A vessel containing 5.0 kg of water at 10$\degree$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$\degree$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

First, we need to convert the initial and final temperatures to Kelvin:
T1 = (10 + 273.15) K = 283.15 K
T2 = (0 + 273.15) K = 273.15 K

Next, we can use the formula for the COP of a refrigerator:
COP = Qcool / Winput
where Qcool is the amount of heat energy removed from the water and Winput is the amount of work input by the motor.

To calculate Qcool, we can use the specific heat capacity of water:
Qcool = mcΔT
where m is the mass of the water, c is the specific heat capacity of water (4.184 J/g·K), and ΔT is the change in temperature.

Qcool = (5.0 kg)(4.184 J/g·K)(283.15 K - 273.15 K) = 2092 J

To calculate Winput, we need to convert 1/7 HP to watts:
Winput = (1/7 HP)(746 W/1 HP) = 106.57 W

Now we can calculate the COP:
COP = Qcool / Winput = 2092 J / 106.57 W = 19.6

However, this is the theoretical COP of the refrigerator, assuming it operates at peak efficiency. In reality, the COP will be less than this. Let's assume a more reasonable 30% efficiency:
COP = 0.30(19.6) = 5.88

Therefore, the closest answer choice is C) 6.5.

Question 18

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)1800 J
B)2000 J
C)2200 J
D)2400 J
E)2250 J

Accepted Answer

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

Question 19

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

Accepted Answer

The change in entropy of a system during a phase change with a constant temperature is given by ΔS = Q/T where Q is the heat absorbed or released during the phase change and T is the temperature at which it occurs. In this case, the substance is melting at a temperature T, so the heat absorbed is the latent heat of fusion L. Therefore, ΔS = L/T. However, we are interested in the change in entropy of a mass m of the substance, so we need to divide by the mass: ΔS = L/(mT). This matches choice D, so the answer is D.

Question 20

A steam engine is operating at its theoretical maximum efficiency of 60%. If the waste heat has a temperature of 38$\degree$C, what is the temperature of the boiler?
A)350$\degree$C
B)94$\degree$C
C)225$\degree$C
D)504$\degree$C
E)775$\degree$C

Accepted Answer

The maximum theoretical efficiency of a steam engine is given by Carnot's theorem as:

efficiency = (Th - Tw) / Th

where Th is the absolute temperature of the hot reservoir (boiler) and Tw is the absolute temperature of the cold reservoir (waste heat).

Rearranging the equation, we get:

Th = Tw / (1 - efficiency)

Substituting the given values, we get:

Th = (38 + 273) / (1 - 0.6) = 682.5 K

Converting back to Celsius scale, we get:

Th = 409.5°C

Therefore, the temperature of the boiler is approximately 504°F (D).

Quiz 22: The Second Law of Thermodynamics, Heat Engines and Entropy

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

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

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

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

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

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

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:

Exactly 500 grams of ice are melted at a temperature of 0 $\degree$ C. (Lice = 333 J/g.) The change in entropy (in J/K) is:

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:

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

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?

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.

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 15 $\degree$ C and the temperature well below the surface is 5 $\degree$ C?

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 vessel containing 5.0 kg of water at 10 $\degree$ 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 $\degree$ C. What is the COP of the refrigerator?

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:

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 steam engine is operating at its theoretical maximum efficiency of 60%. If the waste heat has a temperature of 38 $\degree$ C, what is the temperature of the boiler?