An ideal refrigerator has a freezer at a temperature of -13...

An ideal refrigerator has a freezer at a temperature of $-13$ C, The coefficient of performance of the engine is 5 . The temperature of the air to which heat is rejected will be.
(A) $325^{\circ} \mathrm{C}$
(B) $39^{\circ} \mathrm{C}$
(C) $325 \mathrm{~K}$
(D) $320^{\circ} \mathrm{C}$

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Key Concepts

Coefficient of Performance

The coefficient of performance (COP) is a measure of the efficiency of a refrigeration cycle. It is defined as the ratio of heat removed from the cold reservoir to the work input required for the process. In reversible cycles, the COP relates directly to the temperatures of the refrigerated space and the heat rejection reservoir, which helps in determining operational temperatures when one of the temperatures and the COP are known.

Carnot Refrigerator

A Carnot refrigerator is an idealized model that operates on a reversible Carnot cycle. It establishes the maximum possible coefficient of performance for a given temperature difference between the cold and hot reservoirs. The relationship, expressed as COP = T_cold / (T_hot - T_cold) (with temperatures measured in Kelvin), is fundamental when calculating one temperature knowing the other and the COP.

Temperature Conversion

Temperature conversion, specifically converting between Celsius and Kelvin scales, is crucial in thermodynamics since the equations governing idealized cycles require absolute temperature values. To convert from Celsius to Kelvin, one adds 273.15 to the Celsius temperature. This conversion ensures that the thermodynamic formulas yield accurate results.

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