The gases carbon monoxide $(CO)$ and nitrogen $(N_{2})$ at the same temperature have kinetic energies $E_{1}$ and $E_{2}$ respectively. Then

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of $T$. The total internal energy,$U$ of a mole of this gas,and the value of $\gamma \left( = \frac{C_P}{C_V} \right)$ are given,respectively,by:

$A$ monoatomic gas molecule has

$A$ 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 $N_2$?

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(A)$ $3$ Translational degrees of freedom	$(I)$ Monoatomic gases
$(B)$ $3$ Translational,$2$ rotational degrees of freedom	$(III)$ Rigid diatomic gases
$(C)$ $3$ Translational,$2$ rotational and $1$ vibrational degrees of freedom	$(IV)$ Non-rigid diatomic gases
$(D)$ $3$ Translational,$3$ rotational and more than one vibrational degrees of freedom	$(II)$ Polyatomic gases

Choose the correct answer from the options given below:

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