Define and write the formula for the coefficient of performance of a refrigerator.

(N/A) The coefficient of performance ($\beta$ or $COP$) of a refrigerator is defined as the ratio of the amount of heat extracted from the cold reservoir $(Q_2)$ to the work done $(W)$ by the external agent on the system to extract that heat.
Mathematically, it is expressed as:
$\beta = \frac{Q_2}{W}$
Since $W = Q_1 - Q_2$, where $Q_1$ is the heat rejected to the hot reservoir, the formula can also be written as:
$\beta = \frac{Q_2}{Q_1 - Q_2}$
In terms of temperatures of the cold reservoir $(T_2)$ and the hot reservoir $(T_1)$, for an ideal refrigerator, it is given by:
$\beta = \frac{T_2}{T_1 - T_2}$