Derive the relation between average velocity, root mean square and mos

1.	Derive the relation between average velocity, root mean square and most probable velocity.
Answer» The relationship among velocities are : C_mp\(:\)C_av\(:\)C_rms\(:\) = \(\sqrt{\frac{2RT}{M}}\): \(\sqrt{\frac{8RT}{\pi M}}\) = \(\sqrt{\frac{3RT}{M}}\) \(\sqrt2:\sqrt{\frac{8}{\pi}}:\sqrt3\) = 1∙414 \(:\) 1∙596 \(:\) 1∙732 C_mp\(:\)C_av\(:\)C_rms = 1 ∶ 1∙128 ∶ 1∙224.

Derive the relation between average velocity, root mean square and most probable velocity.

Answer»

The relationship among velocities are :

C_mp\(:\)C_av\(:\)C_rms\(:\) = \(\sqrt{\frac{2RT}{M}}\): \(\sqrt{\frac{8RT}{\pi M}}\) = \(\sqrt{\frac{3RT}{M}}\)

\(\sqrt2:\sqrt{\frac{8}{\pi}}:\sqrt3\)

= 1∙414 \(:\) 1∙596 \(:\) 1∙732

C_mp\(:\)C_av\(:\)C_rms = 1 ∶ 1∙128 ∶ 1∙224.