The ratio of the mean kinetic energy of hydrogen and nitrogen at temperatures $300 \, K$ and $450 \, K$ respectively is:

The total momentum of the molecules of $1 \,gm$ $mol$ of a gas in a container at rest at $300 \,K$ is

$A$ balloon has $5.0$ $g$ mole of helium at $7^{\circ} C$. Calculate
$(a)$ the number of atoms of helium in the balloon,
$(b)$ the total internal energy of the system.

For a gas at a particular temperature on an average,the quantity which remains same for all molecules is

$A$ cylinder of capacity $200 \ L$ is filled with $H_2$ gas. The total average translational kinetic energy of the molecules is $1.52 \times 10^5 \ J$. Calculate the pressure of $H_2$ in the cylinder in $N \ m^{-2}$.

On the basis of the kinetic theory of gases,the gas exerts pressure because its molecules: