Write the degree of freedom for a polyatomic gas.

An ideal gas has molecules with $5$ degrees of freedom. The ratio of specific heats at constant pressure $(C_p)$ and at constant volume $(C_v)$ is

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

$\gamma_{A}$ is the specific heat ratio of a monoatomic gas $A$ having $3$ translational degrees of freedom. $\gamma_{B}$ is the specific heat ratio of a polyatomic gas $B$ having $3$ translational,$3$ rotational degrees of freedom,and $1$ vibrational mode. If $\frac{\gamma_{A}}{\gamma_{B}} = (1 + \frac{1}{n})$,then the value of $n$ is . . . . . . .

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:

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