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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
$21^\circ C$
B
$31^\circ C$
C
$41^\circ C$
D
$11^\circ C$
Detailed Solution
$COP = \frac{T_L}{T_H - T_L}$, with $T_L = 253$ K
$5 = \frac{253}{T_H - 253} \Rightarrow T_H = \frac{6}{5}\times 253 = 303.6$ K
$T_H \approx 31^\circ C$
$5 = \frac{253}{T_H - 253} \Rightarrow T_H = \frac{6}{5}\times 253 = 303.6$ K
$T_H \approx 31^\circ C$