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2.2.4 Mean velocity, free path and size of molecules

From the Maxwell–Boltzmann distribution law for molecular velocities, the mean square and mean velocities are

From the kinetic theory of gases, assuming that molecules interact like hard spheres, it follows that:

           η  =  (5/16σ²)(mkT/π)^½     τ  =  l/ = 4η/5p

            l = m/(πρσ²√2)

where k = Boltzmann's constant          σ = molecular diameter

         T = absolute temperature          m = mass of molecule

          p = pressure                           l = mean free path

         ρ = density                             τ = mean time between collisions.

         η = viscosity

A more exact theory uses the Lennard–Jones intermolecular potential. (See Hirschfelder, Curtiss and Bird (1954).

Equations are obtained for viscosity and second virial coefficient, B (i.e. first order departure from the perfect gas law) from which the molecular diameter, σ, can be estimated more accurately than from the simple equation for viscosity given above.

Reference

Hirschfelder, Curtiss and Bird (1954) Molecular Theory of Gases and Liquids, Wiley, New York.

J.T.R.Watson

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