In a mechanical refrigerator, the low temperature coils are at a temperature of -23° C and the compressed gas in the condenser has a temperature of 27° C . The theoretical coefficient of performance is

Question

In a mechanical refrigerator, the low temperature coils are at a temperature of -23° C and the compressed gas in the condenser has a temperature of 27° C . The theoretical coefficient of performance is (A) 5 (B) 8 (C) 6 (D) 10

Tardigrade Admin · Accepted Answer

Coefficient of performance of the refrigerator is

β = \frac{Q _{2}}{W} = \frac{Q _{2}}{Q _{1} - Q _{2}} = \frac{Q _{2} / Q _{1}}{1 - Q _{2} / Q _{1}}

= \frac{T _{2} / T _{1}}{1 - T _{1} / T _{2}} = \frac{T _{2}}{T _{1} - T _{2}}

where,

T_{1}

is temperature of source,

T_{2}

of sink.
Given,

T_{1} = 273 + 27 = 300 K

T_{2} = 273 + (- 23) = 250 K

∴ β = \frac{250}{300 - 250} = \frac{250}{50} = 5

Coefficient of performance of refrigerator increases when

T_{1}

is small.

Q. In a mechanical refrigerator, the low temperature coils are at a temperature of −23∘C and the compressed gas in the condenser has a temperature of 27∘C . The theoretical coefficient of performance is

5

8

6

10

Q. In a mechanical refrigerator, the low temperature coils are at a temperature of $- 23^{\circ} C$ and the compressed gas in the condenser has a temperature of $27^{\circ} C$ . The theoretical coefficient of performance is