The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule at temperature $T$ is

$A$ 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)

At standard temperature and pressure $(STP)$,the density of a gas is $1.3 \ kg/m^3$ and the speed of sound in the gas is $330 \ m/s$. The degree of freedom of the gas is:

Internal energy of $n_1$ moles of hydrogen at temperature $T$ is equal to the internal energy of $n_2$ moles of helium at temperature $2T$. Then the ratio $n_1:n_2$ is: [Degree of freedom of $He = 3$,Degree of freedom of $H_2 = 5$]

For a gas having $X$ degrees of freedom,what is the value of $\gamma$ (where $\gamma$ is the ratio of specific heats,$\gamma = C_{P} / C_{V}$)?

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is