A gas has $$n$$ degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of $$40 \mathrm{~K}$$ at constant pressure. The increase in the internal energy of the gas in this process is :

(Given $$\mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ )

A monoatomic gas at pressure $$\mathrm{P}$$ and volume $$\mathrm{V}$$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $$\sqrt2$$ times the speed of sound, then the value of n will be :