\(\bar{v}=\sqrt{\frac{8 R T}{\pi m}}=\sqrt{\frac{2.5 R T}{m}}\)

and \(v_{p}=\sqrt{\frac{2 R T}{m}}\)

From these expressions, we can see that

\(v_{p}<\bar{v}\)

Again, \(v_{r m s}=v_{p} \frac{\sqrt{3}}{2}\)

and average kinetic energy of a gas molecule

\(E_{k}=\frac{1}{2} m v_{rm s}^{2}\)

\(E_{k}=\frac{1}{2} m\left(\sqrt{\frac{3}{2}} v_{y}\right)^{2}=\frac{1}{2} m \times \frac{3}{2} v_{p}^{2}=\frac{3}{4} m v_{p}^{2}\)