The fundamental limitation to the coefficient of performance of a refrigerator is given by

If the ratio of specific heats of a gas at constant pressure and at constant volume is $\gamma$, then the number of degrees of freedom of the rigid molecules of the gas is

If a gas of volume 400 cc at an initial pressure $p$ is suddenly compressed to 100 cc , then its final pressure is

(The ratio of the specific heat capacities of the gas at constant pressure and constant volume is 1.5 )

A Carnot engine having efficiency $60 \%$ receives heat from a source at a temperature 600 K . For the same sink temperature, to increase its efficiency to $80 \%$, then the temperature of the source is