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

The Correct Option is 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=? $
$\therefore \, \, \, 5=\frac {253\,K}{T_1 -253\,K }$
$5T_1-5(253\,K)=253\,K $
$5T_1=253\,K+5(253\,K)=6(253\,K)$
$T_1= \frac {6}{5}(253 \,K)=303.6 \, K=303.6-273 $
$ =30.6^{\circ}C \approx 31^{\circ}C $