The temperature of the hydrogen at which the average speed of its molecules is equal to that of oxygen molecules at a temperature of $31\,^oC$ is ........ $^oC$.

To increase the rms speed of gas molecules by $25 \%$,the percentage increase in absolute temperature of the gas is to be

The $rms$ speed of oxygen at $27^{\circ}C$ will be .... $ms^{-1}$.

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 $^{\circ} C$)

$N$ molecules of gas $A$,each having mass $m$,and $2N$ molecules of gas $B$,each of mass $2m$,are contained in the same vessel at a constant temperature $T$. The mean square velocity of $B$ is $V^2$ and the mean square of the $x$-component of $A$ is $\omega^2$. The value of $\frac{\omega^2}{V^2}$ is

The temperature at which the r.m.s. velocity of hydrogen molecules is $4.5$ times that of an oxygen molecule at $47^{\circ}C$ is (molecular weights of hydrogen and oxygen are $2$ and $32$ respectively). (in $^{\circ}C$)