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:

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 $J$)

Internal energy of $n_1$ moles of hydrogen at temperature $T$ is equal to the internal energy of $n_2$ moles of helium at temperature $2T$. Then the ratio $n_1:n_2$ is: [Degree of freedom of $He = 3$,Degree of freedom of $H_2 = 5$]

$A$ 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 $2.76 \times 10^{-39} \text{ g cm}^2$,then the rms angular speed of the molecule is (Boltzmann constant $= 1.38 \times 10^{-23} \text{ J K}^{-1}$).

Write the degree of freedom for a diatomic rigid rotator.