Question

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

• A. 5
• B. 8
• C. 6
• D. 10

Answer 1

Answer: (A)

Coefficient of performance of the refrigerator is
$\beta=\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 $
$\therefore \beta =\frac{250}{300-250}=\frac{250}{50}=5$
Coefficient of performance of refrigerator increases when $T_{1}$ is small.