At what temperature $(^oC)$ is the average speed of hydrogen molecules equal to the average speed of oxygen molecules at $31^oC$?

What is $rms$ value? What is $v_{rms}$? Derive the equation of $v_{rms}$ in terms of pressure.

At what temperature will the $rms$ speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere $?$ (Given: Mass of oxygen molecule $(m) = 2.76 \times 10^{-26} \, kg$,Boltzmann's constant $k_B = 1.38 \times 10^{-23} \, JK^{-1}$)

At what temperature does an oxygen molecule have the same r.m.s. velocity as a hydrogen molecule at $20 \ K$ (in $K$)?

Consider an ideal gas in a closed container at $300 \ K$. The container is then heated so that the average velocity of particles of the gas increases by a factor of $4$. What would be the final temperature (in $^{\circ} C$)?

The $rms$ speed of an ideal diatomic gas at temperature $T$ is $v$. When the gas dissociates into atoms,its new $rms$ speed becomes double. At what temperature does the dissociation of the gas occur?