Degree of freedom of a gas depends on which factors?

According to the law of equipartition of energy, the molar specific heat of a non-rigid diatomic gas at constant volume is

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

For a gas having $X$ degrees of freedom,what is the value of $\gamma$ (where $\gamma$ is the ratio of specific heats,$\gamma = C_{P} / C_{V}$)?

Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is

For a gas, $\frac{R}{C_v} = 0.4$, where $R$ is the universal gas constant and $C_v$ is the molar specific heat at constant volume. The gas is made up of molecules which are