Average Velocity, r.m.s. Velocity and Most Probable Velocity: Equations - QS Study
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Average Velocity, r.m.s. Velocity and Most Probable Velocity

The distribution equation [dn/n = 4π (M/2πRT)3/2 x e– (mc2/2RT) x c2dc]; may be used 10 obtain the average velocity, c , of the molecules.

This is given by the relation:

c = √(8RT/πM)

If we compare the average velocity with r.m.s. velocity it may be seen that values are not the same,

Average velocity: C = √(8/3π) x r.m.s. velocity = 0.9213 x r.m.s. velocity

Most probable velocity is the velocity possessed by the largest number of molecules in gas. Maxwell showed that the most probable velocity is given by the expression.

Cmpv = √(2RT/M)

A value of the most probable velocity may be calculated from the values of R, T and M. A relation between the r.m s. velocity and the most probable velocity can he established as follows:

Cmpv/Cr.m.s. = [√(2RT/M)/√3RT/M] = √2/3 = 0.8165

Hence, Cmpv = 0.8165 x Cr.m.s