A poly atomic molecule has $3$ translational, $3$ rotational degrees of freedom and $2$ vibrational modes. The ratio of specific heats $\frac{C_P}{C_V}$ is

Match the $\frac{{\text{C}}_{\text{p}}}{{\text{C}}_{\text{v}}}$ ratio for ideal gases with different type of molecules:

Given below are two statements:

Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.

Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

In the light of the above statements, choose the correct answer from the options given below:

Using equipartition of energy, the specific heat (in $\mathrm{J}\mathrm{ }{\mathrm{kg}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium $=27$)

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:

Which statements are correct about degrees of freedom?

A. A molecule with $n$ degrees of freedom has $n^2$ different ways of storing energy.

B. Each degree of freedom is associated with $\frac{1}{2}RT$ average energy per mole.

C. A monoatomic gas molecule has $1$ rotational degree of freedom where as diatomic molecule has $2$ rotational degrees of freedom

D. ${\mathrm{CH}}_4$ has a total to $6$ degrees of freedom.

Choose the correct answer from the option given below: