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

A gaseous mixture consists of 2 moles of oxygen and 4 moles of argon at an absolute temperature $T$. Neglecting all vibrational modes, the total internal energy of the mixture of the gases is