Heat Engines and Refrigerators

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JEE Main 2019

LEVELJEE Main

Two Carnot engines $A$ and $B$ are operated in series. The first one, $A$ receives heat at $T_{1} (= 600 K)$ and rejects to a reservoir at temperature $T_{2}$ . The second engine $B$ receives heat rejected by the first engine and in turn rejects to a heat reservoir at $T_{3} (= 400 K)$ . Calculate the temperature $T_{2}$ if the work outputs of the two engines are equal.

A Carnot engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62°C, its efficiency is doubled. The temperatures of the source and the sink are respectively,

A heat engine operates between a cold reservoir at temperature $T_{2} = 400 K$ and a hot reservoir at temperature $T_{1}$ . It takes $300 J$ of heat from the hot reservoir and delivers $240 J$ of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be ............ K.

JEE Main 2021

LEVELJEE Main

A refrigerator consumes an average $35 W$ power to operate between temperature $- 1 0^{\circ} C$ to $2 5^{\circ} C$ . If there is no loss of energy, then how much average heat per second does it transfer ?

(A)

263 J/s

(B)

298 J/s

(C)

350 J/s

(D)

35 J/s

LEVELJEE Main

Even Carnot engine cannot give $100%$ efficiency, because we cannot

reach absolute zero temperature

For an ideal heat engine, the temperature of the source is $12 7^{\circ} C$ . In order to have $60%$ efficiency the temperature of the sink should be ...... $^{\circ} C$ . (Round off to the nearest integer)

LEVELJEE Main

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

(A)

efficiency of Carnot engine cannot be made larger than 50%

A heat engine is involved with exchange of heat of $1915 J$ , $- 40 J$ , $+ 125 J$ and $- Q J$ , during one cycle achieving an efficiency of $50.0%$ . The value of $Q$ is

(A)

640 J

(B)

40 J

(C)

980 J

(D)

400 J

JEE Main 2021

LEVELJEE Main

A Carnot's engine working between $400 K$ and $800 K$ has a work output of $1200 J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is

(A)

3200 J

(B)

1800 J

(C)

1600 J

(D)

2400 J

JEE Main 2019

LEVELJEE Advanced

Three Carnot engines operate in series between a heat source at a temperature $T_{1}$ and a heat sink at temperature $T_{4}$ (see figure). There are two other reservoirs at temperatures $T_{2}$ and $T_{3}$ , as shown with $T_{1} > T_{2} > T_{3} > T_{4}$ . The three engines are equally efficient if

(A)

T_{2} = (T_{1}^{3} T_{4})^{1/4}; T_{3} = (T_{1} T_{4}^{3})^{1/4}

(B)

T_{2} = (T_{1}^{2} T_{4})^{1/3}; T_{3} = (T_{1} T_{4}^{2})^{1/3}

(C)

T_{2} = (T_{1} T_{4})^{1/2}; T_{3} = (T_{1}^{2} T_{4})^{1/3}

(D)

T_{2} = (T_{1} T_{4}^{2})^{1/3}; T_{3} = (T_{1}^{2} T_{4})^{1/3}

LEVELJEE Main

A Carnot engine operating between temperatures $T_{1}$ and $T_{2}$ has efficiency $\frac{1}{6}$ . When $T_{2}$ is lowered by $62 K$ , its efficiency increases to $1/3$ . Then, $T_{1}$ and $T_{2}$ are respectively

(A)

372 K

and

330 K

(B)

330 K

and

268 K

(C)

310 K

and

248 K

(D)

372 K

and

310 K

JEE Main 2021

LEVELJEE Advanced

Two Carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat at $T_{1}$ and rejects heat to a sink at temperature $T$ . engine $B$ absorbs half of the heat rejected by engine $A$ and rejects heat to the sink at $T_{3}$ . When work done in both the cases is equal, then the value of $T$ is

(A)

\frac{2}{3} T_{1} + \frac{3}{2} T_{3}

(B)

\frac{1}{3} T_{1} + \frac{2}{3} T_{3}

(C)

\frac{3}{2} T_{1} + \frac{1}{3} T_{3}

(D)

\frac{2}{3} T_{1} + \frac{1}{3} T_{3}

JEE Main 2003

LEVELJEE Main

A Carnot engine takes $3 \times 1 0^{6}$ cal of heat from a reservoir at $62 7^{\circ} C$ and gives it to a sink at $2 7^{\circ} C$ . The work done by the engine is

(A)

4.2 \times 1 0^{6}

(B)

8.4 \times 1 0^{6}

(C)

16.8 \times 1 0^{6}

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir in a cycle, is ......... .

JEE Main 2012

LEVELJEE Advanced

Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas)

A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 J$ , then the amount of heat absorbed from the reservoir at lower temperature is:

(A)

99 J

(B)

100 J

(C)

90 J

(D)

1 J

JEE Main 2020

LEVELJEE Main

If minimum possible work is done by a refrigerator in converting $100 g$ of water at $0^{\circ} C$ to ice, how much heat (in cal) is released to the surroundings at temperature $2 7^{\circ} C$ to the nearest integer …… ? (Take, latent heat of ice $= 80 cal/g$ )

LEVELBoard

Which statement is incorrect?

(A)

All reversible cycles have same efficiency

(B)

Reversible cycle has more efficiency than an irreversible one

(C)

Carnot cycle is a reversible one

(D)

Carnot cycle has the maximum efficiency in all cycles

JEE Main 2021

LEVELJEE Main

A reversible engine has an efficiency of $1/4$ . If the temperature of the sink is reduced by $5 8^{\circ} C$ , its efficiency becomes double. Calculate the temperature of the sink.

(A)

17 4^{\circ} C

(B)

28 0^{\circ} C

(C)

180. 4^{\circ} C

(D)

38 2^{\circ} C

LEVELJEE Main

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4. It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10. The hot reservoir of the heat pump is at a temperature of 300 K. Which of the following statements is/are correct:

* Multiple Correct Options

(A)

Work extracted from the Carnot engine in one cycle is 60 J.

(B)

Temperature of the cold reservoir of the Carnot engine is 600 K.

(C)

Temperature of the cold reservoir of the heat pump is 270 K.

(D)

Heat supplied to the hot reservoir of the heat pump in one cycle is 540 J.

JEE Advanced 2026

LEVELJEE Advanced

As shown in the figure, five Carnot engines, each with efficiency $η$ and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider $Q_{0}$ to be the amount of heat absorbed per cycle by the first engine and $W$ as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be $η_{net} = \frac{W}{Q _{0}} = \frac{211}{243}$ . The value of $η$ is:

A Carnot engine has an efficiency of 1/6. When the temperature of the sink is reduced by 62°C, its efficiency is doubled. The temperatures of the source and the sink are respectively,

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Even Carnot engine cannot give 100% efficiency, because we cannot

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A heat engine is involved with exchange of heat of 1915 J, −40 J, +125 J and −Q J, during one cycle achieving an efficiency of 50.0%. The value of Q is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The amount of heat energy supplied to the engine from the source in each cycle is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A Carnot engine takes 3×106 cal of heat from a reservoir at 627∘C and gives it to a sink at 27∘C. The work done by the engine is

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir in a cycle, is ......... .

Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas)

Which statement is incorrect?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A reversible engine has an efficiency of 1/4. If the temperature of the sink is reduced by 58∘C, its efficiency becomes double. Calculate the temperature of the sink.

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

Even Carnot engine cannot give $100%$ efficiency, because we cannot

A heat engine is involved with exchange of heat of $1915 J$ , $- 40 J$ , $+ 125 J$ and $- Q J$ , during one cycle achieving an efficiency of $50.0%$ . The value of $Q$ is

A Carnot's engine working between $400 K$ and $800 K$ has a work output of $1200 J$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is

A Carnot engine takes $3 \times 1 0^{6}$ cal of heat from a reservoir at $62 7^{\circ} C$ and gives it to a sink at $2 7^{\circ} C$ . The work done by the engine is

A reversible engine has an efficiency of $1/4$ . If the temperature of the sink is reduced by $5 8^{\circ} C$ , its efficiency becomes double. Calculate the temperature of the sink.