At what temperature $T$ (in $K$) will the $rms$ speed of $H_2$ be equal to the $rms$ speed of $O_2$ at $47^{\circ}C$?

The temperature at which the $r.m.s.$ speed of hydrogen molecules is equal to the escape velocity on the Earth's surface will be ...... $K$.

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.

$A$ gas $A$ has $N$ molecules at temperature $T$ with mass $m$. Another gas $B$ has $2N$ molecules at the same temperature $T$ with mass $2m$. Both are contained in a vessel. If the $rms$ velocity of molecules of gas $B$ is $v$,and the $x$-component of the mean square velocity of molecules of gas $A$ is $w^2$,find the ratio $w^2/v^2$.

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

The temperature of an ideal gas is increased from $100 \ K$ to $400 \ K$. If '$x$' is the root mean square velocity of its molecules at $100 \ K$,what is the new root mean square velocity?