$\gamma_{A}$ 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 . . . . . . .

The number of vibrational degrees of freedom of a diatomic molecule 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:

At a certain temperature,the degrees of freedom per molecule for a gas is $8$. The gas performs $150 \; J$ of work when it expands under constant pressure. The amount of heat absorbed by the gas will be $..... \; J$.

Ratio of translational degrees of freedom to rotational degrees of freedom of a polyatomic linear gas molecule is

$A$ container holds $1 \, \text{mole}$ of oxygen and $2 \, \text{moles}$ of nitrogen at a temperature of $300 \, K$. What is the ratio of the average rotational kinetic energy of $O_2$ to that of $N_2$?