The temperature of a gas is $-68^{\circ} C$. To what temperature should it be heated,so that the r.m.s. velocity of the molecules be doubled (in $^{\circ} C$)?

At what temperature $(^oC)$ is the average speed of hydrogen molecules equal to the average speed of oxygen molecules at $31^oC$?

Four molecules of a gas have speeds $1, 2, 3$ and $4 \ km/s$. The value of root mean square speed of the gas molecules is

Equal volumes of two gases are kept in different containers having densities in the ratio $1:16$. They exert equal pressures on the walls of their respective containers. Then the ratio of their r.m.s. velocities is

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 ........ $km \ sec^{-1}.$

Let $\bar{v}$,$v_{rms}$ and $v_p$ respectively denote the mean speed,root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of the molecule is $m$. Then: