The curve between absolute temperature $T$ and ${v^2}_{rms}$ is

$A$ tube is divided into two parts,containing two different ideal gases,$L$ and $R$. If the $rms$ velocity of the gas on the left side is equal to the average velocity of the gas on the right side,what is the ratio of the masses of the molecules in $L$ and $R$?

At a certain temperature,the $r.m.s.$ velocity for ${O_2}$ is $400\, m/sec.$ At the same temperature,the $r.m.s.$ velocity for ${H_2}$ molecules will be ....... $m/sec$.

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 $v_e = 11.2 \, km/s$)

At what temperature is the $rms$ speed of air molecules doubled compared to its value at $NTP$?

The gas having average speed four times as that of $SO_{2}$ (molecular mass $64$) is