Is the coefficient of performance of a refrigerator constant?

If minimum possible work is done by a refrigerator in converting $100 \; g$ of water at $0^{\circ} C$ to ice,how much heat (in calories) is released to the surrounding at temperature $27^{\circ} C$ (Latent heat of ice $= 80 \; cal/g$)? Round to the nearest integer.

For a refrigerator,heat absorbed from the cold reservoir (sink) is $500\, J$ and heat rejected to the hot reservoir (source) is $800\, J$. The coefficient of performance is:

$A$ 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 ....... $J$.

The specific heat capacity of a metal at low temperature $T$ is given as $C_p = 32 \left( \frac{T}{400} \right)^3 \text{ kJ K}^{-1} \text{ kg}^{-1}$. $A$ $100 \text{ g}$ vessel of this metal is to be cooled from $20 \text{ K}$ to $4 \text{ K}$ by a special refrigerator operating at room temperature $27^\circ \text{C}$. The amount of work required to cool the vessel is

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 $W$)