The coefficient of performance of a Carnot re | vedclass

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(C) The coefficient of performance $(COP)$ of a refrigerator is given by $\alpha = \frac{Q_2}{Q_1 - Q_2}$.For a Carnot refrigerator,the ratio of heat

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) The coefficient of performance $(COP)$ of a refrigerator is given by $\alpha = \frac{Q_2}{Q_1 - Q_2}$.For a Carnot refrigerator,the ratio of heat exchanged is proportional to the absolute temperatures: $\frac{Q_1}{Q_2} = \frac{T_1}{T_2}$.This implies $\frac{Q_1 - Q_2}{Q_2} = \frac{T_1 - T_2}{T_2}$.Therefore,the $COP$ is $\alpha = \frac{T_2}{T_1 - T_2}$.Given temperatures are $T_1 = 30 + 273 = 303 \, 	ext{K}$ and $T_2 = 0 + 273 = 273 \, 	ext{K}$.Substituting these values: $\alpha = \frac{273}{303 - 273} = \frac{273}{30} = 9.1$.Rounding to the nearest integer provided in the options,we get $9$.

The coefficient of performance of a Carnot refrigerator working between temperatures $30 \, ^\circ\text{C}$ and $0 \, ^\circ\text{C}$ is:

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