Question

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

Answer 1

The relationship among velocities are

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

c_rms,c_ave, c_m  = Root Mean Square, Average Velocity & Most Probable Velocity of gas molecules ;

M = Molecular Weight ; T = Temperature ; R = Universal Gas Constant ; 

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

= \(1.414:1.596:1.732\)

C_m: C_av : C_rms = \(1 : 1.128 : 1.224\)