$A$ gas at temperature $T$ consists of only rigid diatomic molecules. If the moment of inertia of a molecule is $I$,what is the root mean square angular velocity of the rotating molecule? ($k$ = Boltzmann constant)

Supposing the distance between the atoms of a diatomic gas to be constant,its specific heat at constant volume per mole (gram mole) is

The average thermal energy for a mono-atomic gas is: ($k_{B}$ is Boltzmann constant and $T$ is absolute temperature)

The number of vibrational degrees of freedom of a diatomic molecule is

The ratio of specific heat at constant pressure to specific heat at constant volume $(\gamma)$ for a gas is given by $\gamma = 1 + \frac{2}{f}$,where $f$ is the number of degrees of freedom of a molecule of the gas. What is the ratio of $\gamma_{d}$ for a rigid diatomic gas to $\gamma_{m}$ for a monoatomic gas?

If the kinetic energy of a monoatomic gas molecule is $\frac{3}{2}PV$,then the kinetic energy of a diatomic gas molecule is: