If the $r.m.s.$ velocity values for hydrogen,nitrogen,and oxygen are $V_H, V_N$,and $V_O$ respectively at a given temperature,then:

If a gas is compressed isothermally,then the r.m.s. velocity of its molecules

The average speed $\bar{v}$ and $r.m.s.$ speed $v_{rms}$ of the molecules are related as

At $T$ $K$ temperature,the average speed of $O_2$ will be $\left( \frac{7}{4} \right)$ of the $rms$ speed of $N_2$ at $47\,^oC$. Find the value of $T$.

The $rms$ speed of air molecules in a vessel is $90 \times 10^2 \ m/s$. If half of the gas leaks out at constant temperature,the $rms$ speed of the remaining air molecules will be

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 $= 32$)