For an ideal gas with constant pressure,the root mean square velocity $v_{rms}$ is proportional to . . . . . . .

What is the order of the speed of gas molecules?

What is $v_{rms}$? Write the equation of $v_{rms}$ in terms of: $(1)$ density,$(2)$ mass of a molecule,$(3)$ molar mass.

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

Find the $v_{rms}$ of nitrogen gas at $300 \ K$.

$N$ molecules each of mass $m$ of gas $A$ and $2N$ molecules each of mass $2m$ of gas $B$ are contained in a vessel which is maintained at temperature $T$. The mean square velocity of the molecules of gas $B$ is denoted by $V_2^2$ and the mean square of the $X$-component velocity of the molecules of gas $A$ is denoted by $V_1^2$,then $\frac{V_1}{V_2}$ is