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 $^{\circ}C$)?

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:

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:

At a pressure of $24 \times 10^5 \, \text{dyne/cm}^2$,the volume of $O_2$ is $10 \, \text{litre}$ and its mass is $20 \, \text{gm}$. The $r.m.s.$ velocity will be ....... $m/s$.

The speed of an oxygen molecule in a gas is $u$. If the temperature is doubled and the molecule dissociates into two atoms,the speed will be:

At what temperature $T$ (in $K$) will the $rms$ speed of $H_2$ be equal to the $rms$ speed of $O_2$ at $47^{\circ}C$?