When $x$ amount of heat is given to a gas at constant pressure,it performs $x/3$ amount of work. The average number of degrees of freedom per molecule is

The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule 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 whereas a diatomic molecule has $2$ rotational degrees of freedom.
$D.$ $CH_{4}$ has a total of $6$ degrees of freedom.
Choose the correct answer from the options given below:

The ratio of specific heats of a gas is $\frac{9}{7}$. The number of degrees of freedom of the gas molecules for translational motion is:

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

$A$ gas at temperature $T$ consists of only rigid diatomic molecules. If the moment of inertia of a molecule is $I$,what is the root mean square angular velocity of the rotating molecule? ($k$ = Boltzmann constant)