The internal energy $(U)$,pressure $(P)$,and volume $(V)$ of an ideal gas are related as $U = 3PV + 4$. The gas is:

The mean rotational kinetic energy of a diatomic molecule at temperature $T$ is

How many degrees of freedom does a diatomic gas have due to its translational motion?

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

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature $T$ is $......RT$.

Under standard conditions,the density of a gas is $\frac{1400}{1089} \ kg \ m^{-3}$ and the speed of sound propagation in it is $330 \ ms^{-1}$. The number of degrees of freedom of the gas molecules is: