An ideal heat engine has an efficiency $\eta$. The coefficient of performance of the engine when driven backward will be

$A$ Carnot engine,having an efficiency of $\eta = 1/10$ as a heat engine,is used as a refrigerator. If the work done on the system is $10 \ J$,the amount of energy absorbed from the reservoir at a lower temperature is ....... $J$.

Obtain the formula for the coefficient of performance of a Carnot refrigerator.

In a refrigerator,heat is removed from a low-temperature reservoir and deposited at a high-temperature reservoir. This requires mechanical work,which is provided by an electric motor. If the motor power is $1 \ kW$ and heat is transferred from $-3^{\circ} C$ to $27^{\circ} C$,calculate the heat removed from the refrigerator per second,assuming the efficiency is $50\%$ of the ideal Carnot refrigerator. (in $kJ/s$)

$A$ refrigerator works between $4^{\circ}C$ and $30^{\circ}C$. It is required to remove $600 \, cal$ of heat every second in order to keep the temperature of the refrigerated space constant. The power required is ....... $W$ (Take $1 \, cal = 4.2 \, J$)

An electrical refrigerator with $\beta=5$ extracts $5000 \,J$ from the contents of the refrigerator. During this process, find the electrical energy utilised by its motor. (in $\,kJ$)