The freezing compartment of a refrigerator is at $0^{\circ} C$ and the room temperature is $27.3^{\circ} C$. Calculate the work done by the refrigerator to freeze $1 \ g$ of water at $0^{\circ} C$. (Given: $L_{\text{ice}} = 80 \ cal \ g^{-1}$) (in $J$)

In a refrigerator,one removes heat from a lower temperature and deposits it to the surroundings at a higher temperature. In this process,mechanical work has to be done,which is provided by an electric motor. If the motor is of $1\,kW$ power and heat is transferred from $-3\,^{\circ}C$ to $27\,^{\circ}C$,find the heat taken out of the refrigerator per second,assuming its efficiency is $50\%$ of a perfect engine.

In a cold storage,ice melts at the rate of $2 \ kg$ per hour when the external temperature is $20^{\circ} C$. The minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting is (latent heat of fusion of ice $= 80 \ cal \ g^{-1}$) (in $W$)

$A$ refrigerator with a coefficient of performance $0.25$ releases $250 \, J$ of heat to a hot reservoir. The work done on the working substance is

$A$ Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 \; J,$ the amount of heat absorbed from the reservoir at lower temperature is .............. $J$.

Explain the working of refrigerators/heat pumps and their coefficient of performance.