Question

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

• A. $11^{\circ }C$
• B. $21^{\circ }C$
• C. $31^{\circ }C$
• D. $41^{\circ }C$

Answer 1

Answer: (C)

The coefficient of performance of a refrigerator is where $T_{1}$ and $T_{2}$ are the temperatures of hot and cold reservoirs (in kelvin) respectively.
Here, $\alpha=5, T_{2}=-20^{\circ} C=-20+273 K=253 K$
$T_{1}=? $
$\therefore 5=\frac{253 K}{T_{1}-253 K} $
$5 T_{1}-5(253 K)=253 K $
$5 T_{1}=253 K+5(253 K)=6(253 K) $
$T_{1}=\frac{6}{5}(253 K)=303.6 K=303.6-273 $
$=30.6^{\circ} C \approx 31^{\circ} C$