By what factor will the $r.m.s.$ velocity change if the temperature is raised from $27^\circ C$ to $327^\circ C$?

At what $^\circ C$ temperature will the molecules of nitrogen have the same $rms$ velocity as the molecules of oxygen at $127^\circ C$?

An ideal gas of molar mass $M_0$ has r.m.s. velocity $V$ at temperature $T$. Then

At what temperature $(^oC)$ will the $rms$ speed of hydrogen be double its value at $S.T.P.$? The pressure remains constant.

At what temperature (in $K$) is the $rms$ velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^o \ C$?

The root mean square speed of molecules of a given mass of a gas at $27^{\circ} C$ and $1$ atmosphere pressure is $200\, ms^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} C$ and $2$ atmosphere pressure is $\frac{x}{\sqrt{3}}\, ms^{-1}$. The value of $x$ will be ......$ms^{-1}$.