The mean kinetic energy of $1 \, mole$ of gas per degree of freedom (on the basis of kinetic theory of gases) 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 . . . . . . .

For polyatomic gases,the ratio of molar specific heat at constant pressure to constant volume is $(f=$ degrees of freedom $)$

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

Calculate the degree of freedom of a diatomic gas.

Supposing the distance between the atoms of a diatomic gas to be constant,its specific heat at constant volume per mole (gram mole) is