To what temperature should the hydrogen at room temperature $(27^{\circ}C)$ be heated at constant pressure so that the $R.M.S.$ velocity of its molecules becomes double of its previous value?

How does the $rms$ velocity of an ideal gas vary with density at constant pressure?

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the r.m.s. velocity of its molecules at $100 \ K$,then at $400 \ K$,the r.m.s. velocity becomes:

$N$ molecules of gas $A$,each having mass $m$,and $2N$ molecules of gas $B$,each of mass $2m$,are contained in the same vessel at a constant temperature $T$. The mean square velocity of $B$ is $V^2$ and the mean square of the $x$-component of $A$ is $\omega^2$. The value of $\frac{\omega^2}{V^2}$ is

Three vessels $A$,$B$,and $C$ contain gases at the same temperature. Vessel $A$ contains $O_2$ gas,vessel $B$ contains $N_2$ gas,and vessel $C$ contains a mixture of $O_2$ and $N_2$ gases. If the average velocity of $O_2$ in vessel $A$ is $V_1$ and the average velocity of $N_2$ in vessel $B$ is $V_2$,what is the average velocity of $O_2$ in vessel $C$?

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 $27^{\circ}C$?