If the oxygen $(O_2)$ has a root mean square velocity of $C \ m/s$,then the root mean square velocity of hydrogen $(H_2)$ at the same temperature will be:

The atmosphere on a planet is possible only if [where $v_{rms}$ is the root mean square speed of gas molecules on the planet and $v_e$ is the escape speed on its surface]

The $rms$ velocity of molecules of a given mass of gas at $27^{\circ}C$ and $1.0 \times 10^5 \, Nm^{-2}$ pressure is $200 \, m \, s^{-1}$. What will be the $rms$ velocity if the temperature and pressure are $127^{\circ}C$ and $0.5 \times 10^5 \, Nm^{-2}$ respectively?

The curve between absolute temperature $T$ and $v_{rms}^2$ 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 molecules of a given mass of a gas have $r.m.s.$ velocity of $200 \,m s^{-1}$ at $27^o C$ and $1.0 \times 10^5 \,N m^{-2}$ pressure. When the temperature and pressure of the gas are respectively $127^o C$ and $0.05 \times 10^5 \,N m^{-2},$ the $r.m.s.$ velocity of its molecules in $m s^{-1}$ is