A Carnot heat engine absorbs 600 J of heat from a source at a temperature of $127^{\circ} \mathrm{C}$ and rejects 400 J of heat to a sink in each cycle. The temperature of the sink is

During adiabatic expansion, if the temperature of 3 moles of a diatomic gas decreases by $50^{\circ} \mathrm{C}$, then the work done by the gas is

( $R=$ Universal gas constant)

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