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(C) The coefficient of performance $\alpha$ of a refrigerator is defined as the ratio of heat extracted from the cold reservoir $(Q_2)$ to the work do

Vedclass · Accepted Answer

$\frac{\alpha Q_1}{1+\alpha}$

Vedclass · Answer

(C) The coefficient of performance $\alpha$ of a refrigerator is defined as the ratio of heat extracted from the cold reservoir $(Q_2)$ to the work done $(W)$ on the system: $\alpha = \frac{Q_2}{W}$.Since $W = Q_1 - Q_2$,where $Q_1$ is the heat released to the hot reservoir,we have $\alpha = \frac{Q_2}{Q_1 - Q_2}$.Cross-multiplying gives: $\alpha(Q_1 - Q_2) = Q_2$.Expanding the equation: $\alpha Q_1 - \alpha Q_2 = Q_2$.Rearranging to solve for $Q_2$: $\alpha Q_1 = Q_2 + \alpha Q_2 = Q_2(1 + \alpha)$.Therefore,$Q_2 = \frac{\alpha Q_1}{1 + \alpha}$.

If $\alpha$ is the coefficient of performance of a refrigerator and $Q_1$ is the heat released to the hot reservoir,then the heat extracted from the cold reservoir $Q_2$ is

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