First slide

Refrigerator

Question

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

Moderate

A

11°C
B

21°C
C

31°C
D

41°C

Solution

The coefficient of performance of a refrigerator is
$α = \frac{T_{2}}{T_{1} - T_{2}}$
$where T_{1} and T_{2} are the temperatures of hot and cold$
reservoirs (in kelvin) respectively.
$Here, α = 5, T_{2} = - 20 ° C = - 20 + 273 K = 253 K$
$T_{1} = ?$
$∴ 5 = \frac{253 K}{T_{1} - 253 K}$
$\begin{array}{l} 5 T_{1} - 5 (253 K) = 253 K \\ 5 T_{1} = 253 K + 5 (253 K) = 6 (253 K) \end{array}$
$T_{1} = \frac{6}{5} (253 K) = 303.6 K = 303.6 - 273$
$= 30.6 ° C \approx 31 ° C$

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