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

For a diatomic gas,let $\gamma_1 = \frac{C_p}{C_v}$ for rigid molecules and $\gamma_2 = \frac{C_p}{C_v}$ for diatomic molecules that also have a vibrational mode. Which of the following options is correct? ($C_p$ and $C_v$ are the specific heats of the gas at constant pressure and volume,respectively.)

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 $..... \; J$.

For a triatomic gas molecule,if the degrees of freedom for translation,rotation,and vibration are considered,then $C_P/C_V = ?$

$A$ diatomic gas consisting of rigid molecules is at a temperature of $87^{\circ} C$. If the moment of inertia of the rotating diatomic rigid molecule is $2.76 \times 10^{-46} kg \cdot m^2$,then the rms angular speed of the molecule is (Boltzmann constant $= 1.38 \times 10^{-23} J \cdot K^{-1}$)

At standard temperature and pressure $(STP)$,the density of a gas is $1.3 \ kg/m^3$ and the speed of sound in the gas is $330 \ m/s$. The degree of freedom of the gas is: