The value closest to the thermal velocity of a Helium atom at room temperature $(300\,K)$ in $m/s$ is $[k_B = 1.4 \times 10^{-23}\,J/K; m_{He} = 7 \times 10^{-27}\,kg]$.

At what temperature $(K)$ will the $r.m.s.$ velocity of hydrogen gas be equal to the escape velocity from the Earth?

The density of hydrogen gas at standard atmospheric pressure $(P = 1.01 \times 10^{5} \ Pa)$ is $0.09 \ kg/m^{3}$. Find the root mean square velocity $(v_{rms})$ and the average kinetic energy of $1 \ mole$ of the gas.

The rms speed of oxygen at room temperature is about $500 \,m/s$. The rms speed of hydrogen at the same temperature is about (in $\,m/s$)

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

The temperature of a gas is doubled $(i)$ on the absolute scale and $(ii)$ on the centigrade scale. The increase in the root mean square velocity of the gas will be: