The r.m.s. speed of oxygen molecules at $47^{\circ} C$ is equal to that of the hydrogen molecules kept at . . . . . . ${ }^{\circ} C$. (Mass of oxygen molecule/mass of hydrogen molecule $= 32 / 2$)

To what temperature should the hydrogen at room temperature $(27^{\circ}C)$ be heated at constant pressure so that the $R.M.S.$ velocity of its molecules becomes double of its previous value?

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

The $v_{rms}$ of gas molecules in a container is $400 \ ms^{-1}$. If half of the gas leaks out of the container at a constant temperature,the $v_{rms}$ of the remaining gas molecules will be . . . . . . $ms^{-1}$.

Uranium has two isotopes of masses $235$ and $238$ units. If both are present in Uranium hexafluoride $(UF_6)$ gas,which would have the larger average speed? If the atomic mass of fluorine is $19$ units,estimate the percentage difference in speeds at any temperature.

The molecular masses of helium and oxygen are $4$ and $32$ respectively. The ratio of r.m.s speed of helium at $327^{\circ} C$ to r.m.s speed of oxygen at $27^{\circ} C$ will be