The temperature of an ideal gas is increased from $120 \ K$ to $480 \ K.$ If at $120 \ K,$ the root mean square velocity of the gas molecules is $v,$ at $480 \ K$ it becomes

At what temperature is the $rms$ speed of hydrogen molecules equal to the $rms$ speed of oxygen molecules at $47^{\circ}C$ (in $K$)?

At what temperature in $K$ will the $r.m.s.$ speed of a hydrogen molecule be equal to the escape velocity from the Earth?

The relation between root mean square speed $(v_{rms})$ and most probable speed $(v_{p})$ for the molar mass $M$ of oxygen gas molecule at the temperature of $300\, K$ 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 $v_e = 11.2 \, km/s$)

The root mean square velocity of molecules of a gas is $200 \,m/s$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?