When the temperature of a gas is raised from $27^o C$ to $90^o C$,the percentage increase in the $r.m.s.$ velocity of the molecules will be ..... $\%$

In Maxwell's speed distribution curve,for $N_2$ gas,the average relative velocity (in $m/s$) between two molecules at $300 \, K$ is:

At a certain temperature,the $r.m.s.$ velocity for ${O_2}$ is $400\, m/sec.$ At the same temperature,the $r.m.s.$ velocity for ${H_2}$ molecules will be ....... $m/sec$.

The $rms$ speed of hydrogen molecules at room temperature $(300 \ K)$ will be:

Let $\bar{v}$,${v_{rms}}$ and ${v_p}$ respectively denote the mean speed,root mean square speed,and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T$. The mass of a molecule is $m$. Then

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