An ideal gas has molecules with $5$ degrees of freedom. The ratio of specific heats at constant pressure $(C_p)$ and at constant volume $(C_v)$ is

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 $J$)

$A$ polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $K$ is Boltzmann's constant):

Under standard conditions,the density of a gas is $\frac{1400}{1089} \ kg \ m^{-3}$ and the speed of sound propagation in it is $330 \ ms^{-1}$. The number of degrees of freedom of the gas molecules is:

The total number of degrees of freedom in $1 \ cm^3$ of $H_2$ gas at $NTP$ is ....

If one mole of a polyatomic gas has two vibrational modes and $\beta$ is the ratio of molar specific heats for the polyatomic gas $\left(\beta=\frac{C_{P}}{C_{V}}\right)$,then the value of $\beta$ is: