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 $rms$ speed of gas molecules in a container is $400 \, ms^{-1}$. If half of the gas is removed at a constant temperature,the new $rms$ speed will be .... $ms^{-1}$.

$A$ cubical box with porous walls containing an equal number of ${O_2}$ and ${H_2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T$. The ratio of the ${v_{rms}}$ of ${O_2}$ molecules to that of the ${v_{rms}}$ of ${H_2}$ molecules,found in the chamber outside the box after a short interval,is:

If the absolute temperature of a gas is increased $5$ times,the r.m.s. velocity of the gas molecules will be

$A$ certain amount of an ideal gas is taken from its initial state $1$ to final state $4$ through the path $1 \rightarrow 2 \rightarrow 3 \rightarrow 4$ as shown in the figure. $AB, CD, EF$ are all isotherms. If $v_p$ is the most probable speed of the molecules, then:

The ratio of $r.m.s.$ velocities of oxygen and hydrogen at a given temperature is: