At a certain temperature,the $r.m.s.$ velocity for ${O_2}$ is $400\, m/sec.$ At the same temperature,the $r.m.s.$ velocity for ${H_2}$ molecules will be ....... $m/sec$.

The rms speed of an oxygen molecule in a vessel at a particular temperature is $\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v$,where $v$ is the average speed of the molecule. The value of $x$ will be: (Take $\pi=\frac{22}{7}$)

When the temperature of a gas is raised from $27^{\circ} C$ to $90^{\circ} C$,the increase in the rms velocity of the gas molecules is: (in $\%$)

If $c$ is the $rms$ speed of molecules in a gas and $v$ is the speed of sound waves in the gas,show that $\frac{c}{v}$ is constant and independent of temperature for all diatomic gases.

At constant temperature,the vapour density of two gases are in the ratio of $6 : 9$. Compare their $v_{rms}$.

At what temperature is the $R$.$M$.$S$. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $K$)? (Molecular weight of hydrogen $= 2$,molecular weight of oxygen $= 32$)