The temperature of a gas is $-73^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed of the molecules is doubled (in $^{\circ}C$)?

Two molecules of a gas have speeds of $9 \times 10^{6} \ m/s$ and $1 \times 10^{6} \ m/s$ respectively. What is the root mean square speed of these molecules?

The temperature at which oxygen molecules will have the same r.m.s. speed as helium molecules at $57^{\circ} C$ is (molecular masses of oxygen and helium are $32$ and $4$ respectively.) (in $K$)

An $HCl$ molecule has rotational,translational,and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar{v}$,$m$ is its mass,and $k_B$ is the Boltzmann constant,then its temperature will be:

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 $27^{\circ}C$?

The r.m.s. speed of hydrogen at $S.T.P.$ is $u \text{ m/s}$. If the gas is heated at constant pressure till its volume becomes three times, the final temperature of the gas and the r.m.s. speed are respectively: