In thermal equilibrium,the average velocity of gas molecules is

At what temperature will the root mean square $(rms)$ speed of oxygen molecules be sufficient to escape from the Earth's atmosphere? (Mass of an oxygen molecule $m = 2.76 \times 10^{-26} \, kg$,Boltzmann constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$,Escape velocity of Earth $v_e = 11.2 \, km/s$)

Uranium has two isotopes of masses $235$ and $238$ units. If both are present in Uranium hexafluoride $(UF_6)$ gas,which would have the larger average speed? If the atomic mass of fluorine is $19$ units,estimate the percentage difference in speeds at any temperature.

At a given temperature,the $r.m.s.$ velocity of molecules of a gas is

In Maxwell's speed distribution curve,for $N_2$ gas,the average relative velocity (in $m/s$) between two molecules at $300 \, K$ is:

The temperature of a gas is $-80^{\circ} C$. To what temperature should the gas be heated so that the r.m.s. speed is increased by $2$ times (in $^{\circ} C$)?