At $400 \ K$,the root mean square $(rms)$ speed of a gas $X$ (molecular weight $= 40$) is equal to the most probable speed of gas $Y$ at $60 \ K$. The molecular weight of the gas $Y$ is:

At what temperature will the $rms$ speed of $N_2$ gas at $1 \, atm$ pressure be equal to the $rms$ speed of $CO_2$ at $STP$?

At $133.33 \ K$,the $RMS$ velocity of an ideal gas is $(M = 0.083 \ kg \ mol^{-1}; R = 8.3 \ J \ mol^{-1} \ K^{-1})$ (in $m \ s^{-1}$)

At a temperature of $27\,^{\circ}C$,$0.5 \, mol$ of $O_2$ gas is filled in a $50 \, L$ container at a pressure of $2 \, atm$. If half of the $O_2$ molecules are removed from the container,the $rms$ speed of the $O_2$ molecules will........

Which of the following pairs will diffuse at the same rate through a porous plug?

Give the formulas for the following:
$(i)$ Average speed of molecules $(u_{av})$
$(ii)$ Most probable speed $(u_{mp})$
$(iii)$ Root mean square speed $(u_{rms})$