The number of rotational degrees of freedom of a monatomic molecule is

What is the degree of freedom?

The value of $\gamma \left( = \frac{C_{p}}{C_{v}} \right)$ for hydrogen,helium,and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode) are respectively equal to:

If the internal energy of $n_1$ moles of $He$ at temperature $10T$ is equal to the internal energy of $n_2$ moles of hydrogen $(H_2)$ at temperature $6T$,find the ratio $\frac{n_1}{n_2}$.

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 $......RT$.

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is