For an ideal gas,$R = \frac{2}{3} C_v$. This suggests that the gas consists of molecules which are: $[R = \text{universal gas constant}]$

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:

State the law of equipartition of energy.

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:

$500 \text{ g}$ of a diatomic gas is enclosed at a pressure of $10^5 \text{ N m}^{-2}$. The density of the gas is $5 \text{ kg m}^{-3}$. The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator].

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