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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

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Solution

Given,

Temperature of cold body, $T_{2} = - 23^{\circ} C$

$\Rightarrow T_{2} = (273 - 23) K$

Temperature of compressed gas, $T_{1} = 27^{\circ} C$

$\Rightarrow T_{1} = (273 + 27) K$

Coefficient of performance, $β = \frac{T_{2}}{T_{1} - T_{2}}$

$\Rightarrow β = \frac{273 - 23}{(273 + 27) - (273 - 23)}$

$\Rightarrow β = \frac{250}{300 - 250}$

$\Rightarrow β = \frac{250}{50}$

Final answer: $5$

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