For an ideal gas with constant pressure,the root mean square velocity $v_{rms}$ is proportional to . . . . . . .

If the oxygen $(O_2)$ has a root mean square velocity of $C \ m/s$,then the root mean square velocity of hydrogen $(H_2)$ at the same temperature will be:

$A$ container is divided into two equal parts $L$ and $R$. If the root mean square (rms) speed of the molecules in part $L$ is equal to the average speed of the molecules in part $R$,find the ratio of the mass of a molecule in part $L$ to the mass of a molecule in part $R$.

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

The temperature at which the root mean square velocity of a molecule will be doubled than its value at $100^{\circ}C$ is:

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $27^{\circ} C$, then the final temperature of the ideal gas is : (in $^{\circ} C$)