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 $STP$?

What is the relationship between the most probable speed $(\alpha)$,average speed $(v)$,and root mean square speed $(u)$?

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin), the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

If the mass of a gas at $3 \, atm$ pressure and $14.8 \, L$ volume is $15 \, g$,calculate the root mean square speed $(u_{rms})$ of the gas molecules. (Assume $T = 300 \, K$)

What is the relationship between the average velocity $(v)$,root mean square velocity $(u)$,and most probable velocity $(\alpha)$?

Select the correct relationship among the following. The symbols have their usual meanings.