The average thermal energy for a mono-atomic gas is: ($k_{B}$ is Boltzmann constant and $T$ is absolute temperature)

The internal energy $(U)$,pressure $(P)$,and volume $(V)$ of an ideal gas are related as $U = 3PV + 4$. The gas is:

The degrees of freedom of a triatomic gas is

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and $f$ number of vibrational modes. If the ratio of heat capacities $C_p/C_v$ of the gas is $8/7$, then the value of $f$ is:

$A$ 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 $= 1.38 \times 10^{-23} \text{ J K}^{-1}$).

Define degree of freedom.