The total kinetic energy of $1$ mole of oxygen at $27^{\circ} C$ is:
[Use universal gas constant $(R) = 8.31 \ J/mol \cdot K$] (in $J$)

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

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 $......RT$.

Energy of $10$ non-rigid diatomic molecules at temperature $T$ 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 two different gases $X$ and $Y,$ having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{v_1}$ and $C_{v_2}$ respectively, for an adiabatic process, the $\ln P$ versus $\ln V$ graph is plotted as shown: