The coefficient of performance of a Carnot refrigerator working between $30^oC$ and $0^oC$ is

$A$ refrigerator of coefficient of performance $5$ that extracts heat from the cooling compartment at the rate of $250 \ J$ per cycle is placed in a room. The heat released per cycle to the room by the refrigerator is (in $J$)

$A$ 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 $1 \, cal = 4.2 \, J$)

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

If the door of a refrigerator is kept open in an insulated room,the temperature of the air in the room will . . . . . .

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