Why can the coefficient of performance of a refrigerator never be infinite?

$A$ Carnot freezer takes heat from water at $0\,^{\circ}C$ inside it and rejects it to the room at a temperature of $27\,^{\circ}C$. The latent heat of ice is $336 \times 10^3\, J\,kg^{-1}$. If $5\, kg$ of water at $0\,^{\circ}C$ is converted into ice at $0\,^{\circ}C$ by the freezer,then the energy consumed by the freezer is close to

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 $\,kJ$)

The coefficient of performance of a refrigerator is $5$. If the temperature inside the freezer is $-20^{\circ}C$,the temperature of the surroundings to which it rejects heat is ........ $^{\circ}C$.

Write the formula for the coefficient of performance of a heat pump.

$A$ Carnot engine having an efficiency of $1/5$ as a heat engine is used as a refrigerator. If the work done on the system is $50 \ J$,then the amount of energy absorbed from the reservoir at the lower temperature is (in $J$)