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

If the r.m.s. speed of a chlorine molecule is $490\,m/s$ at $27^{\circ}C$,the r.m.s. speed of argon molecules at the same temperature will be $......\,m/s$ (Atomic mass of argon $= 39.9\,u$,molecular mass of chlorine $= 70.9\,u$). (in $.7$)

The temperature at which the rms speed of oxygen molecules is $75 \%$ of the rms speed of nitrogen molecules at a temperature of $287^{\circ} C$ is: (in $^{\circ} C$)

The molecules of a given mass of a gas have a $r.m.s.$ velocity of $200 \, m/s$ at $27^{\circ}C$ and $1.0 \times 10^5 \, N/m^2$ pressure. When the temperature is $127^{\circ}C$ and pressure is $0.5 \times 10^5 \, N/m^2$,the $r.m.s.$ velocity in $m/s$ will be

The r.m.s. speed of oxygen molecules at $47^{\circ} C$ is equal to that of the hydrogen molecules kept at . . . . . . ${ }^{\circ} C$. (Mass of oxygen molecule/mass of hydrogen molecule $= 32 / 2$)

The root mean square speed of the molecules of a gas is