The coefficient of performance of a refrigerator is $5$ . If the temperature inside freezer is $- 20^{o} C$ , the temperature of the surroundings to which it rejects heat is :

21^{o} C

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31^{o} C

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41^{o} C

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11^{o} C

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Solution

The correct option is A $31^{o} C$
coefficient of performance : $C O P = \frac{Q_{1}}{W} = \frac{Q_{1}}{Q_{1} - Q_{2}} = \frac{T_{2}}{T_{1} - T_{2}}$ where where $T_{1}$ is temp of heat bath and $T_{2}$ is temp of cold bath.
$\Rightarrow 5 = \frac{T_{2}}{T_{1} - (- 20)}$
$\Rightarrow 6 T_{2} = 5 T_{1}$
$\Rightarrow 6 \times (- 20 + 273) = 5 T_{1}$
$\Rightarrow T_{1} = 31^{o} C$

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