Sound travels in a mixture of $2$ moles of helium and $n$ moles of hydrogen. If the root-mean-square (rms) speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound,then the value of $n$ will be:

The ratio of specific heat of a mixture of one mole of helium and one mole of hydrogen gas will be

One mole of a gas with $\gamma = 7/5$ is mixed with one mole of a gas with $\gamma = 4/3$. What will be the $\gamma$ of the mixture?

$A$ closed container contains a homogeneous mixture of two moles of an ideal monatomic gas $(\gamma=5/3)$ and one mole of an ideal diatomic gas $(\gamma=7/5)$. Here,$\gamma$ is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of $66 \ J$ when heated at constant pressure. The change in its internal energy is . . . . . . $J$.

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then:

If a mixture of $28 \, g$ of Nitrogen $(N_2)$,$4 \, g$ of Hydrogen $(H_2)$,and $8 \, g$ of Helium $(He)$ is contained in a vessel at temperature $400 \, K$ and pressure $8.3 \times 10^5 \, Pa$,the density of the mixture will be: