$A$ perfect gas of volume $10 \ L$ is compressed isothermally to a volume of $1 \ L$. The $rms$ speed of the molecules will

Two vessels having equal volume contain molecular hydrogen at $1 \text{ atm}$ and helium at $2 \text{ atm}$ respectively. If both samples are at the same temperature,the mean velocity of hydrogen molecules is

$N$ 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

How does the $rms$ velocity of an ideal gas vary with density at constant pressure?

If the root mean square (rms) speed of nitrogen molecules at room temperature is $100 \ m \ s^{-1}$, then the rms speed of Helium molecules at the same temperature is

The temperature of a gas is $-50^{\circ}C$. To what temperature should the gas be heated so that the $rms$ speed is increased by $3$ times?