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Question

Physics Question on work done thermodynamics

The coefficient of performance of a refrigerator is 55. If the temperature inside freezer is −20∘C,-20^{\circ }C, the temperature of the surroundings to which it rejects heat is

A

11∘C11^{\circ }C

B

21∘C21^{\circ }C

C

31∘C31^{\circ }C

D

41∘C41^{\circ }C

Answer

31∘C31^{\circ }C

Explanation

Solution

The coefficient of performance of a refrigerator is
where T1T_1 and T2T_2 are the temperatures of hot and cold reservoirs (in kelvin) respectively.
Here, α=5, T2=−20∘C=−20+273 K=253 K\alpha =5 , \, T_2=-20^{\circ}C=-20+273\,K=253\, K
     T1=?\, \, \, \, \, T_1=?
∴   5=253 KT1−253 K\therefore \, \, \, 5=\frac {253\,K}{T_1 -253\,K }
5T1−5(253 K)=253 K5T_1-5(253\,K)=253\,K
5T1=253 K+5(253 K)=6(253 K)5T_1=253\,K+5(253\,K)=6(253\,K)
T1=65(253 K)=303.6 K=303.6−273T_1= \frac {6}{5}(253 \,K)=303.6 \, K=303.6-273
=30.6∘C≈31∘C=30.6^{\circ}C \approx 31^{\circ}C