The r.m.s. velocity of a gas at a certain temperature is $\sqrt{2}$ times that of the oxygen molecules at the same temperature. The gas can be:

The $r.m.s.$ speed of a certain gas is $v$ at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times,will be ...... $K$.

Two gases $A$ and $B$ are contained in two separate, but otherwise identical containers. Gas $A$ consists of monatomic molecules, each with atomic mass of $4 \ u$, whereas Gas $B$ consists of rigid diatomic molecules, each with atomic mass of $20 \ u$. If gas $A$ is kept at $27^{\circ} C$, at what temperature should gas $B$ be kept so that both have the same rms speed (in $^{\circ} C$)?

The r.m.s. speed of the molecules of a gas at $100^{\circ} C$ is $v$. The temperature at which the r.m.s. speed will be $\sqrt{3} v$ is: (in $^{\circ} C$)

The $N_2$ molecule is $14$ times heavier than the $H_2$ molecule. At what temperature will the $rms$ speed of $H_2$ molecules be equal to the $rms$ speed of $N_2$ molecules at $27^{\circ}C$?

Out of hydrogen and air,which will have a higher root mean square speed $(v_{\text{rms}})$?