Assertion: Consider a system of gas having N molecules; Instantaneous K.E. of few molecules can be greater than average K.E. of the molecules of the given gas.

Reason: Number of molecules having most probable speed is greater than number of molecules having average speed.

Assertion: The root mean square velocity of molecules of a gas having Maxwellian distribution of velocities is higher than their most probable velocity at any temperature.

Reason: A very small number of molecules of a gas possessing very large velocities increases the root mean square velocity without affecting the most probable velocity.

For a rigid diatomic molecule, universal gas constant $R=n{C}_P$ whare $C_P$ is the molar specific heat at constant pressure and $n$ is a number. Hence $n$ is equal to

A cylinder of fixed capacity $67.2$ $\mathrm{L}$ contains helium gas at $\mathrm{S}.\mathrm{T}.\mathrm{P}.$ . The amount of heat needed to raise the temperature of the gas in the cylinder by $20 °\mathrm{C}$ is $\left(R=8.31 \mathrm{J} {\mathrm{mol}}^{-1 }{\mathrm{K}}^{-1}\right)$

A gaseous mixture consists of $16 \mathrm{g}$ of helium and $16 \mathrm{g}$ of oxygen. The ratio $\frac{C_{\mathrm{P}}}{C_{\mathrm{V}}}$ of the mixture is 

Assuming the expression for the pressure exerted by the gas on the walls of the container, it can be shown that the pressure is