First slide

Refrigerator

Question

Efficiency of a carnot engine operating between a source at temperature $T_{1}$ and a sink at temperature $T_{2}$ is 60%. If a carnot refrigerator operates between the same temperature limits, its coefficient of performance will be

Moderate

A

2.450
B

1.252
C

0.823
D

0.666

Solution

For the engine, $η = 1 - \frac{T_{2}}{T_{1}} \Rightarrow \frac{T_{2}}{T_{1}} = (1 - η)$
For the refrigerator, $C O P = \frac{T_{2}}{T_{1} - T_{2}}$
$∴ C O P = \frac{T_{2} / T_{1}}{(1 - \frac{T_{2}}{T_{1}})} = \frac{(1 - η)}{1 - (1 - η)} = (\frac{1}{η} - 1) = (\frac{1}{0.6} - 1) = 0.666$

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