At a given temperature,the ratio of $r.m.s.$ velocities of a hydrogen molecule and a helium atom will be:

The $r.m.s.$ velocity of nitrogen molecules at $NTP$ is ...... $m/s$.

The root mean square speed of molecules of a given mass of a gas at $27^{\circ} C$ and $1$ atmosphere pressure is $200\, ms^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}\, ms^{-1}$. The value of $x$ will be ......$ms^{-1}$.

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.

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

The respective speeds of the five molecules are $1, 2, 3, 4$ and $5 \ km/s$. The ratio of their root mean square (rms) velocity to their average velocity is: