Root mean square velocity is defined as the square root of the average of the squares of the individual velocities of the gas molecules i.e.,
\(v_{rms}=\sqrt{\frac{v_1^2+v_2^2+v_3^2+.....+v_n^2}{n}}\)
= \(\sqrt{\bar v^2}\)
Where, v1, v2, v3,… … . , vn are individual velocities.
\(v_{rms}=\sqrt\frac{3P}{ρ}=\sqrt\frac{3RT}{M}=\sqrt\frac{3RT}{m}\)
i.e., \(v_{rms}∝\sqrt{T}\)
