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  4. A refrigerator is to maintain eatables at 9° C . If room temperature is 36° C, then the coefficient of performance is

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Q. A refrigerator is to maintain eatables at $9^{\circ} C .$ If room temperature is $36^{\circ} C$, then the coefficient of performance is

Thermodynamics

Solution:

$\alpha=\frac{O_{2}}{Q_{1}-Q_{2}}$
Assuming the refrigerator to be a Carnot refrigerator, where
$\frac{Q_{1}}{T_{1}}=\frac{Q_{2}}{T_{2}}$
$\alpha=\frac{T_{2}}{T_{1}-T_{2}}$
$=\frac{(9+273) K }{(36+273) K -(9+273) K }=\frac{282 K }{27 K }=10.4$.