If the internal energy of $3$ moles of a gas at a temperature of $27^{\circ} C$ is $2250 R$,then the number of degrees of freedom of the gas is (where $R$ is the universal gas constant).

$A$ container holds $1 \, \text{mole}$ of oxygen and $2 \, \text{moles}$ of nitrogen at a temperature of $300 \, K$. What is the ratio of the average rotational kinetic energy of $O_2$ to that of $N_2$?

$A$ diatomic gas consisting of rigid molecules is at a temperature of $87^{\circ} C$. If the moment of inertia of the rotating diatomic rigid molecule is $2.76 \times 10^{-39} \text{ g cm}^2$,then the rms angular speed of the molecule is (Boltzmann constant $= 1.38 \times 10^{-23} \text{ J K}^{-1}$).

The degrees of freedom of a triatomic gas 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)

The mean kinetic energy per degree of freedom of gas molecules is: