At what temperature $K$ will the $rms$ speed of $SO_2$ gas be equal to the $rms$ speed of $O_2$ gas at $303 \ K$?

Explain the following terms:
$(i) u_{mp}$
$(ii) u_{av}$
$(iii) \overline{u}^2$
$(iv) u_{rms}$

$A$ $50 \, L$ container holds $0.5 \, mol$ of $O_2$ gas at $27 \, ^oC$ and $2 \, atm$ pressure. If half of the $O_2$ molecules are removed from the container,what happens to the $rms$ speed of the $O_2$ molecules?

The ratio between the root mean square velocity of $H_2$ at $50 \ K$ and that of $O_2$ at $800 \ K$ is

The ratio of most probable velocity $(u_{mp})$,average velocity $(u_{av})$,and root mean square velocity $(u_{rms})$ is:

The temperature at which $RMS$ velocity of $SO_2$ molecules is half that of $He$ molecules at $300 \ K$ is ............... $K$.