Question 1

A heat engine having the maximum possible efficiency has an efficiency of 35.0% when operating between two heat reservoirs. If the temperature of the hot reservoir is 700 K, what is the temperature of the cold reservoir?
A)200 K
B)245 K
C)350 K
D)455 K
E)600 K

Accepted Answer

The answer of A heat engine having the maximum possible...

Question 2

The ocean thermal energy conversion project uses the surface water near tropical islands with a temperature of 20°C as the hot temperature reservoir, and the water at some depth, with a temperature of 5.0°C, as the cold temperature reservoir for a heat engine. What is the maximum possible efficiency of an engine running between those two temperatures?
A)4.7%
B)5.1%
C)7.9%
D)15%
E)30%

Accepted Answer

The answer of The ocean thermal energy conversion project uses...

Question 3

For a certain ideal Carnot engine, the hot reservoir is 35 C° higher than the cold reservoir. If this engine is to have an efficiency of 20%, what must be the temperature of the hot reservoir?
A)70.0 K
B)140 K
C)175 K
D)210 K
E)245 K

Accepted Answer

The answer of For a certain ideal Carnot engine, the...

Question 4

An ideal Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is 284°C. If the efficiency of this ideal engine is 24.0%, find the temperature of the cold reservoir in degrees Celsius.

Accepted Answer

The answer of An ideal Carnot engine is operated between...

Question 5

An ideal Carnot engine has an efficiency of 83.0% and performs 4500 J of work every cycle. How much energy is discharged to the lower temperature reservoir every cycle?
A)920 J
B)830 J
C)740 J
D)3700 J
E)5400 J

Accepted Answer

The answer of An ideal Carnot engine has an efficiency...

Question 6

A heat engine absorbs 85.6 kJ of heat each cycle and exhausts 61.8 kJ.
(a)What is the efficiency of the engine?
(b)How much work does it do each cycle?

Accepted Answer

The answer of A heat engine absorbs 85.6 kJ of...

Question 7

During each cycle, a heat engine takes in 4.0 J of heat, does 1.0 J of work, and expels 3.0 J of heat. What is its efficiency?

Accepted Answer

The answer of During each cycle, a heat engine takes...

Question 8

An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of $294.0 \mathrm {~K}$ and a hot reservoir, what is the temperature of the hot reservoir?
A)735 K
B)490 K
C)470 K
D)784 K

Accepted Answer

The efficiency of a Carnot engine is given by $ \eta = 1 - \frac{T_C}{T_H} $. Given $\eta = 0.600$ and $T_C = 294.0 \, \text{K}$, solve for $T_H$: $0.600 = 1 - \frac{294.0}{T_H}$, which gives $T_H = 735 \, \text{K}$.

Question 9

A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 10⁶ kg of coal each day, and the heat of combustion of coal is 3.3 × 10⁷ J/kg. The steam that drives the turbines is at a temperature of 300°C, and the exhaust water is at 37°C. (a)What is the overall efficiency of the plant for generating electric power? (b)How much thermal energy is exhausted each day? (c)Using the same heat reservoirs, what is the maximum possible efficiency for a heat engine?

Accepted Answer

The answer of A coal-fired plant generates 600 MW of...

Question 10

A nuclear power plant has an actual efficiency of 33%. If $0.19 \mathrm { MW }$ of energy are released from fission, how much electric power does the power plant produce?
A)0.063 MW
B)6.3 MW
C)25 MW
D)0.25 MW

Accepted Answer

The electric power produced is calculated by multiplying the energy released by the efficiency: $0.19 \, \text{MW} \times 0.33 = 0.0627 \, \text{MW}$, which rounds to 0.063 MW.

Question 11

An ideal Carnot heat engine operates between $285 \mathrm {~K}$ and $460 \mathrm {~K}$ What is its efficiency?
A)0.38
B)0.62
C)0.61
D)1.61

Accepted Answer

The efficiency of a Carnot engine is given by $1 - \frac{T_c}{T_h}$, where $T_c$ is the cold reservoir temperature and $T_h$ is the hot reservoir temperature. Substituting the given values: $1 - \frac{285}{460} = 0.3804$, which is approximately 0.38.

Question 12

A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle.
(a)How much work does it perform in each cycle?
(b)How much heat does it exhaust in each cycle?

Accepted Answer

The answer of A heat engine has an efficiency of...

Question 13

One of the most efficient engines built so far has the following characteristics: The combustion chamber temperature is 1900°C, the exhaust temperature = 430°C, 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour. (1 cal = 4.186 J) (a)What is the actual efficiency of this engine? (b)What is the power output of this engine? (c)What would be the maximum possible efficiency for an engine using the same temperature extremes?

Accepted Answer

The answer of One of the most efficient engines built...

Question 14

A gas follows the pV trajectory shown in Figure 16.2. How much work is done per cycle by the gas if The gas in a heat engine follows the cycle shown in the pV diagram. How much work does this engine do each cycle if p₀ = $$5.4 \mathrm {~atm} ?$$ A)220 J B)440 J C)870 J D)1100 J

Accepted Answer

The answer of A gas follows the pV trajectory shown...

Question 15

Two ideal Carnot heat engines have the same efficiency. One operates between 5.0 × 10² K and 3.0 × 10² K, and the other between 4.0 × 10² K and some lower temperature. What is the lower temperature? A)200 K B)220 K C)240 K D)260 K E)280 K

Accepted Answer

Efficiency of a Carnot engine is given by:
η = (T1 - T2)/T1
where η is the efficiency, T1 is the hot reservoir temperature, and T2 is the cold reservoir temperature.

Since both engines have the same efficiency,
(T1 - T2)/T1 = (T3 - T2)/T3

where T3 is the temperature of the cold reservoir for the second engine.

Simplifying and solving for T3, we get:
T3 = 2T2 - T1

Substituting the given values for T1 and T2, we get:
T3 = 2(4.0 × 10^3) - 5.0 × 10^3
T3 = 3.0 × 10^2 K

Therefore, the lower temperature is 240 K.

Question 16

The figure shows a pV diagram for a cycle of a heat engine for which Q_H = 59 J. What is the thermal efficiency of the engine? A)17% B)34% C)8.5% D)14%

Accepted Answer

The answer of The figure shows a pV diagram for...

Question 17

A heat engine having the maximum possible efficiency has an efficiency of 25% when operating between two heat reservoirs. If the temperature of the cold reservoir is 300 K, what is the temperature of the hot reservoir?
A)350 K
B)375 K
C)400 K
D)450 K
E)500 K

Accepted Answer

The maximum efficiency of a heat engine operating between two heat reservoirs is given by:
Efficiency = 1 - (Tc/Th)
where Tc and Th are the temperatures of the cold and hot reservoirs, respectively. We are given that the efficiency is 25%, or 0.25, and the temperature of the cold reservoir is 300 K. Solving for Th, we get:
0.25 = 1 - (300/Th)
0.75 = 300/Th
Th = 400 K
Therefore, the temperature of the hot reservoir is 400 K, which is answer choice C.

Question 18

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects $225 \mathrm {~J}$ of heat to a low-temperature reservoir during the same cycle. What is the efficiency of the engine?
A)0.57
B)1.35
C)2.35
D)0.7

Accepted Answer

The efficiency of a Carnot engine is given by the formula: $\eta = 1 - \frac{Q_C}{Q_H}$, where $Q_H$ is the heat absorbed from the high-temperature reservoir and $Q_C$ is the heat rejected to the low-temperature reservoir. Substituting the given values, $\eta = 1 - \frac{225}{529} = 0.57$.

Question 19

An ideal Carnot heat engine operates between reservoirs at 1740 K and $150 \mathrm {~K} .$ In each cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much mechanical work W is performed by the engine?

Accepted Answer

The answer of An ideal Carnot heat engine operates between...

Question 20

A certain automobile engine takes in 4.00 kJ of heat and performs 1.10 kJ of mechanical work in each cycle.
(a)Calculate the engine's efficiency.
(b)How much heat is "wasted" in each cycle?

Accepted Answer

The answer of A certain automobile engine takes in 4.00...

Quiz 11: Using Energy

A heat engine having the maximum possible efficiency has an efficiency of 35.0% when operating between two heat reservoirs. If the temperature of the hot reservoir is 700 K, what is the temperature of the cold reservoir?

For a certain ideal Carnot engine, the hot reservoir is 35 C° higher than the cold reservoir. If this engine is to have an efficiency of 20%, what must be the temperature of the hot reservoir?

An ideal Carnot engine is operated between a hot and a cold reservoir. The temperature difference between the two reservoirs is 284°C. If the efficiency of this ideal engine is 24.0%, find the temperature of the cold reservoir in degrees Celsius.

An ideal Carnot engine has an efficiency of 83.0% and performs 4500 J of work every cycle. How much energy is discharged to the lower temperature reservoir every cycle?

A heat engine absorbs 85.6 kJ of heat each cycle and exhausts 61.8 kJ. (a)What is the efficiency of the engine? (b)How much work does it do each cycle?

During each cycle, a heat engine takes in 4.0 J of heat, does 1.0 J of work, and expels 3.0 J of heat. What is its efficiency?

An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of 294.0 K294.0 \mathrm {~K}294.0 K and a hot reservoir, what is the temperature of the hot reservoir?

A nuclear power plant has an actual efficiency of 33%. If 0.19MW0.19 \mathrm { MW }0.19MW of energy are released from fission, how much electric power does the power plant produce?

An ideal Carnot heat engine operates between 285 K285 \mathrm {~K}285 K and 460 K460 \mathrm {~K}460 K What is its efficiency?

A heat engine has an efficiency of 31.4% and receives 8.72 kJ of heat per cycle. (a)How much work does it perform in each cycle? (b)How much heat does it exhaust in each cycle?

A gas follows the pV trajectory shown in Figure 16.2. How much work is done per cycle by the gas if The gas in a heat engine follows the cycle shown in the pV diagram. How much work does this engine do each cycle if p0 = 5.4 atm?5.4 \mathrm {~atm} ?5.4 atm?

Two ideal Carnot heat engines have the same efficiency. One operates between 5.0 × 102 K and 3.0 × 102 K, and the other between 4.0 × 102 K and some lower temperature. What is the lower temperature?

The figure shows a pV diagram for a cycle of a heat engine for which QH = 59 J. What is the thermal efficiency of the engine?

A heat engine having the maximum possible efficiency has an efficiency of 25% when operating between two heat reservoirs. If the temperature of the cold reservoir is 300 K, what is the temperature of the hot reservoir?

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects 225 J225 \mathrm {~J}225 J of heat to a low-temperature reservoir during the same cycle. What is the efficiency of the engine?

An ideal Carnot heat engine operates between reservoirs at 1740 K and 150 K.150 \mathrm {~K} .150 K. In each cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much mechanical work W is performed by the engine?

A certain automobile engine takes in 4.00 kJ of heat and performs 1.10 kJ of mechanical work in each cycle. (a)Calculate the engine's efficiency. (b)How much heat is "wasted" in each cycle?

An ideal Carnot heat engine has an efficiency of 0.600. If it operates between a deep lake with a constant temperature of $294.0 \mathrm {~K}$ and a hot reservoir, what is the temperature of the hot reservoir?

A nuclear power plant has an actual efficiency of 33%. If $0.19 \mathrm { MW }$ of energy are released from fission, how much electric power does the power plant produce?

An ideal Carnot heat engine operates between $285 \mathrm {~K}$ and $460 \mathrm {~K}$ What is its efficiency?

Two ideal Carnot heat engines have the same efficiency. One operates between 5.0 × 10² K and 3.0 × 10² K, and the other between 4.0 × 10² K and some lower temperature. What is the lower temperature?

The figure shows a pV diagram for a cycle of a heat engine for which Q_H = 59 J. What is the thermal efficiency of the engine?

An ideal Carnot engine extracts 529 J of heat from a high-temperature reservoir during each cycle, and rejects $225 \mathrm {~J}$ of heat to a low-temperature reservoir during the same cycle. What is the efficiency of the engine?

An ideal Carnot heat engine operates between reservoirs at 1740 K and $150 \mathrm {~K} .$ In each cycle, 260 J of heat energy is rejected to the low temperature reservoir. In each cycle, how much mechanical work W is performed by the engine?