At what temperature in $^oC$ will the $rms$ speed of $CO_2$ be equal to the $rms$ speed of $CO$ at $STP$?

If the kinetic energy and $RMS$ speed of a gas at a certain temperature are $4.0 \ kJ \ mol^{-1}$ and $5.0 \times 10^4 \ cm \ s^{-1}$,respectively,the molecular weight of the gas 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 $STP$?

Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed)

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

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:

If $C_1, C_2, C_3, ......$ represent the speeds of $n_1, n_2, n_3, ......$ molecules,then the root mean square speed is