The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is -20° C, the temperature of the surroundings to which it rejects heat is

Question

The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is -20° C, the temperature of the surroundings to which it rejects heat is (A) 11° C (B) 21° C (C) 31° C (D) 41° C

Tardigrade Admin · Accepted Answer

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,

α = 5, T_{2} = - 2 0^{\circ} C = - 20 + 273 K = 253 K

T_{1} = ?

∴ 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 3 1^{\circ} C

Q. The coefficient of performance of a refrigerator is $5$ . If the temperature inside freezer is $- 2 0^{\circ} C,$ the temperature of the surroundings to which it rejects heat is

$1 1^{\circ} C$

$2 1^{\circ} C$

$3 1^{\circ} C$

$4 1^{\circ} C$

Q. The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is −20∘C, the temperature of the surroundings to which it rejects heat is

11∘C

21∘C

31∘C

41∘C

Q. The coefficient of performance of a refrigerator is $5$ . If the temperature inside freezer is $- 2 0^{\circ} C,$ the temperature of the surroundings to which it rejects heat is

$1 1^{\circ} C$

$2 1^{\circ} C$

$3 1^{\circ} C$

$4 1^{\circ} C$