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

Calculate the degree of freedom of a diatomic gas.

Calculate the total number of degrees of freedom of molecules of hydrogen in $1$ $cc$ of hydrogen gas at $NTP$.

$\gamma_{A}$ 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 . . . . . . .

$A$ polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $K$ is Boltzmann's constant):

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_p/C_v$ of the gas is $8/7$, then the value of $f$ is: