The thermal efficiency of a reversible heat engine operating between two given thermal reservoirs is 0.4. The device is used either as a refrigerator or as a heat pump between the same reservoirs. Then the coefficient of performance as a refrigerator (COP)<sub>R</sub> and the co-efficient of performance as a heat pump (COP)<sub>HP</sub> are

Consider the following statements: 1. The entropy of a pure crystalline substance at absolute zero temperature is zero. 2. the efficiency of a reversible heat engine is independent of the nature of the working substance and depends only on the temperature of the reservoirs between which it operates. 3. Carnot’s theorem states that of all heat engines operating between a given constant temperature source and a given constant temperature sink, none has a higher efficiency than a reversible engine Which of the above statements are correct?

A

1 and 2 only

B

1 and 3 only

C

2 and 3 only

D

1, 2 and 3

The efficiency η of any heat engine and efficiency ηR of a reversible heat engine operating between common heat source and heat sink are related as

A

η > η_R

B

η < η_R

C

η ≥ η_R

D

η ≤ η_R

Consider the following statement: a) In a refrigerator the heat is taken out from the system. b) In a refrigerator the heat is given to the system. c) In a heat pump the heat is taken out from the system. d) In a heat pump the heat is given to the system. Which of the above statements are correct?

A

Both a and c are correct

B

Both a and d are correct

C

Both b and c are correct

D

Both b and d are correct

One reversible heat engine operates between 1600 K and T2 K and another reversible heat engine operates between T2 K and 400 K. If both the engines have the same heat input and output, then temperature T2 is equal to

A

800 K

B

1000 K

C

1200 K

D

1400 K

If the Coefficient of performance of a heat pump is 5, then what is the value of the Coefficient of performance of the refrigerator operating under the same conditions?

A

0.2

B

3

C

4

D

6

If the coefficient of performance of the refrigerator is 4.67, then what is the value of the coefficient of performance of the heat pump operating under the same conditions?

A

3.67

B

5.67

C

0.214

D

9.34

A Carnot heat engine receives heat at 750 K and rejects the waste heat to the environment at 300 K. The net work output of the heat engine is used to drive a Carnot refrigerator, whose COP is 6.14. If the heat removal rate from the refrigerated space is 6.6 kW, determine the rate of heat supply to the heat engine?

A

2.79 kW

B

1.79 kW

C

4.79 kW

D

7.79 kW

The efficiency of a Carnot heat engine operating between absolute temperatures T₁ and T₂ (when, T₁ > T₂) is given by (T₁ - T₂)/T₁. The co-efficient of performance (CO.P.) of a Carnot heat pump operating between T₁ and T₂ is given by

A

T₁/(T₁-T₂)

B

T₂/(T₁-T₂)

C

T₁/T₂

D

T₂/T₁

The efficiency of a Carnot heat engine operating between absolute temperatures T₁ and T₂ (when, T₁ > T₂) is given by (T₁ - T₂)/T₁. The co-efficient of performance (C.O.P.) of a Carnot heat pump operating between T₁ and T₂ is given by

A

T₁/(T₁-T₂)

B

T₂/(T₁-T₂)

C

T₁/T₂

D

T₂/R1

The efficiency of a Carnot heat engine operating between absolute temperatures T₁ and T₂ (when, T₁ > T₂) is given by $$\frac{{{{\text{T}}_1} - {{\text{T}}_2}}}{{{{\text{T}}_1}}}.$$ The co-efficient of performance (C.O.P.) of a Carnot heat pump operating between T₁ and T₂ is given by

A

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_1} - {{\text{T}}_2}}}$$

B

$$\frac{{{{\text{T}}_2}}}{{{{\text{T}}_1} - {{\text{T}}_2}}}$$

C

$$\frac{{{{\text{T}}_1}}}{{{{\text{T}}_2}}}$$

D

$$\frac{{{{\text{T}}_2}}}{{{{\text{T}}_1}}}$$

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