At what temperature will the root mean square speed of ozone $(O_3)$ be equal to the root mean square speed of oxygen $(O_2)$ at $27\,^oC$?

At what temperature (in $K$) is the $rms$ velocity of $SO_2$ molecules equal to the $rms$ velocity of $O_2$ molecules at $27^{\circ} C$?

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 $m \ s^{-1}$)

Which of the following statement$(s)$ is (are) correct regarding the root mean square speed $(U_{rms})$ and average translational kinetic energy $(\varepsilon_{av})$ of a molecule in a gas at equilibrium?
$(1)$ $U_{rms}$ is doubled when its temperature is increased four times
$(2)$ $\varepsilon_{av}$ at a given temperature does not depend on its molecular mass
$(3)$ $U_{rms}$ is inversely proportional to the square root of its molecular mass
$(4)$ $\varepsilon_{av}$ is doubled when its temperature is increased four times

The $RMS$ speed of $SO_2$ is the same as that of $O_2$ at $303 \, K$. This speed will be achieved at a temperature of .......... $K$.

At what temperature $T$ will the average speed of $CO_2$ gas be $9.0 \times 10^4 \ cm \ s^{-1}$ (in $K$)?