The $r.m.s.$ speed of the molecules of a gas at a pressure $10^5 \ Pa$ and temperature $0^\circ C$ is $0.5 \ km \ sec^{-1}.$ If the pressure is kept constant but temperature is raised to $819^\circ C,$ the velocity will become ........ $km \ sec^{-1}.$

At what $^\circ C$ temperature will the molecules of nitrogen have the same $rms$ velocity as the molecules of oxygen at $127^\circ C$?

At room temperature,the $rms$ speed of a gas is $V_1$. If the pressure of the gas is doubled at the same room temperature,the $rms$ speed becomes $V_2$. Then:

$A$ cubical box with porous walls containing an equal number of ${O_2}$ and ${H_2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of the ${v_{rms}}$ of ${O_2}$ molecules to that of the ${v_{rms}}$ of ${H_2}$ molecules,found in the chamber outside the box after a short interval,is:

At a temperature of $300 \ K$,the kinetic energy of $O_2$ is $6.21 \times 10^{-21} \ J$ and its $rms$ speed is $484 \ m/s$. What will be the kinetic energy and $rms$ speed at $600 \ K$?

The temperature at which the rms speed of oxygen molecules is $75 \%$ of the rms speed of nitrogen molecules at a temperature of $287^{\circ} C$ is: (in $^{\circ} C$)