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

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.

$A$ refrigerator is to maintain eatables kept inside at $9^{\circ} C$. If room temperature is $36^{\circ} C$,calculate the coefficient of performance.

$A$ household refrigerator with a coefficient of performance $1.2$ removes heat from the refrigerated space at the rate of $60 \ kJ/min$. What would be the cost of running this fridge for one month $(30 \ days)$, assuming it is used for $4 \ hours$ each day and the cost of one electrical unit is $6 \ Rs.$?

The temperatures inside and outside a refrigerator are $273 \, K$ and $300 \, K$ respectively. Assuming that the refrigerator cycle is reversible,for every joule of work done,the heat delivered to the surrounding will be nearly ........ $J$.

What is the coefficient of performance of a refrigerator operating between $30^{\circ}C$ and $0^{\circ}C$?