The rms velocity of oxygen molecules at $27^{\circ} C$ is around $800 \ m/s$. The rms velocity of methane molecules at $600 \ K$ temperature is around ...... (in $m/s$)

Molecular velocities of two gases at the same temperature $(T)$ are $u_{1}$ and $u_{2}$. Their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions is correct at temperature $T$?

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 temperature $T \ K$,the $rms$ speed of $CO_2$ is $x \ cm/s$. At what temperature (in $K$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

The volumes of ozone and chlorine gas diffusing in the same time are $35 \ mL$ and $29 \ mL$ respectively. If the molar mass of chlorine is $71$,calculate the molar mass of ozone. (in $.7$)

$\alpha, v$ and $u$ represent the most probable velocity, average velocity, and root mean square velocity, respectively, of a gas at a particular temperature. The correct order among the following is: