Thermodynamics - Result Question 39

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

[2015 RS]

(a) $41^{\circ} C$

(b) $11^{\circ} C$

(c) $21^{\circ} C$

(d) $31^{\circ} C$

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Answer:

Correct Answer: 41. (d)

Solution:

  1. (d) Coefficient of performance,

Cop $=\frac{T_2}{T_1-T_2}$

$5=\frac{273-20}{T_1-(273-20)}=\frac{253}{T_1-253}$

$5 T_1-(5 \times 253)=253$

$5 T_1=253+(5 \times 253)=1518$

$\therefore T_1=\frac{1518}{5}=303.6$

or, $T_1=303.6-273=30.6 \cong 31^{\circ} C$