The $v_{rms}$ of gas molecules in a container is $400 \ ms^{-1}$. If half of the gas leaks out of the container at a constant temperature,the $v_{rms}$ of the remaining gas molecules will be . . . . . . $ms^{-1}$.

The $N_2$ molecule is $14$ times heavier than the $H_2$ molecule. At what temperature will the $rms$ speed of $H_2$ molecules be equal to the $rms$ speed of $N_2$ molecules at $27^{\circ}C$?

For which gas is the $rms$ velocity maximum?

The temperature at which the root mean square velocity of hydrogen molecules equals their escape velocity from the Earth is closest to: [Boltzmann constant $k_B = 1.38 \times 10^{-23} \, J/K$,Avogadro number $N_A = 6.02 \times 10^{23} \, mol^{-1}$,Molar mass of $H_2 = 2 \times 10^{-3} \, kg/mol$,Radius of Earth $R_e = 6.4 \times 10^6 \, m$,Gravitational acceleration $g = 10 \, m/s^2$]

For an ideal gas with constant pressure,the root mean square velocity $v_{rms}$ is proportional to . . . . . . .

The number of molecules in a closed container is doubled. What will be the effect on $v_{rms}$?