If the degrees of freedom of a gas molecule is $6$,then the total internal energy of the gas molecule at a temperature of $47^{\circ} C$ (in $eV$) is (Boltzmann constant $= 1.38 \times 10^{-23} \ J \ K^{-1}$)

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 $H_2 = 5$]

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 $..... \; J$.

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

Calculate the degree of freedom of a diatomic gas.

The ratio of specific heats at constant pressure and at constant volume is $\gamma$. To find out the degree of freedom,the expression is