The coefficient of performance of a refrigera | vedclass

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(B) The coefficient of performance $(COP)$ of a refrigerator is given by the formula:$\alpha = \frac{T_2}{T_1 - T_2}$where $T_1$ is the temperature of

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$31$

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(B) The coefficient of performance $(COP)$ of a refrigerator is given by the formula:$\alpha = \frac{T_2}{T_1 - T_2}$where $T_1$ is the temperature of the hot reservoir (surroundings) and $T_2$ is the temperature of the cold reservoir (freezer) in Kelvin.Given: $\alpha = 5$,$T_2 = -20^{\circ}C = (-20 + 273) K = 253 K$.Substituting the values into the formula:$5 = \frac{253}{T_1 - 253}$$5(T_1 - 253) = 253$$5T_1 - 1265 = 253$$5T_1 = 1518$$T_1 = \frac{1518}{5} = 303.6 K$Converting back to Celsius:$T_1 = 303.6 - 273 = 30.6^{\circ}C \approx 31^{\circ}C$.

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

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