Which of the following can be the coefficient | vedclass

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(D) The coefficient of performance $(\beta)$ of a refrigerator is defined as the ratio of the heat extracted from the cold reservoir $(Q_2)$ to the wo

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All of these

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(D) The coefficient of performance $(\beta)$ of a refrigerator is defined as the ratio of the heat extracted from the cold reservoir $(Q_2)$ to the work done on the system $(W)$: $\beta = \frac{Q_2}{W}$.Since $W = Q_1 - Q_2$, we have $\beta = \frac{Q_2}{Q_1 - Q_2}$.Dividing numerator and denominator by $Q_1$, we get $\beta = \frac{Q_2/Q_1}{1 - Q_2/Q_1}$.Using the efficiency of a Carnot engine $\eta = 1 - \frac{Q_2}{Q_1}$, we can write $\frac{Q_2}{Q_1} = 1 - \eta$.Substituting this into the expression for $\beta$: $\beta = \frac{1 - \eta}{\eta} = \frac{1}{\eta} - 1$.Since the efficiency $\eta$ of any heat engine is always less than $1$, the term $\frac{1}{\eta}$ is always greater than $1$.Therefore, $\beta = \frac{1}{\eta} - 1$ can take any positive value greater than $0$.Since $1$, $0.5$, and $9$ are all positive values, all of these can be the coefficient of performance of a refrigerator.

Which of the following can be the coefficient of performance of a refrigerator?

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