If the internal energy of $n_1$ moles of $He$ at temperature $10T$ is equal to the internal energy of $n_2$ moles of hydrogen $(H_2)$ at temperature $6T$,find the ratio $\frac{n_1}{n_2}$.

For two different gases $X$ and $Y,$ having degrees of freedom $f_1$ and $f_2$ and molar heat capacities at constant volume $C_{v_1}$ and $C_{v_2}$ respectively, for an adiabatic process, the $\ln P$ versus $\ln V$ graph is plotted as shown:

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is

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:

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature $T$ is $......RT$.

Calculate the total number of degrees of freedom of molecules of hydrogen in $1$ $cc$ of hydrogen gas at $NTP$.