At what temperature is the $R$.$M$.$S$. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ} C$ (in $K$)? (Molecular weight of hydrogen $= 2$,molecular weight of oxygen $= 32$)

At a given temperature,which gas has a higher speed: light or heavy?

At a given temperature,if $V_{rms}$ is the root mean square velocity of the molecules of a gas and $V_s$ is the velocity of sound in it,then these are related as $\left( \gamma = \frac{C_P}{C_v} \right)$:

At what temperature will the root mean square speed $(\nu_{rms})$ of oxygen gas molecules be equal to the $\nu_{rms}$ of hydrogen gas molecules at $27 \, ^\circ C$? $(M_{O_2} = 32 \, g \, mol^{-1}, M_{H_2} = 2 \, g \, mol^{-1})$

When the temperature of a gas is increased to $3$ times,what will be the change in $v_{rms}$?

The velocities of $4$ gas molecules are given by $1 \ km/s, 3 \ km/s, 5 \ km/s$ and $7 \ km/s$. Calculate the difference between the average velocity and the root mean square $(RMS)$ velocity. (in $km/s$)