大学物理（热学） Mean Free Path Diffusion, Thermal conductivity, and Viscosity 2006-10-12

Equilibrium distribution ni  the number of molecules of dn is the number of molecules vy vy + dvy in near v

Meaning of dn/N among N molecules, how many are near v probability that one molecule is near v proportional to dvx ...

The probability should be normalized Isotropic assumption The solution is The probability should be normalized Normalization is not necessary but conventional.

each normalized a a 12

Known while

For unit volume Maxwell velocity distribution

Maxwell speed distribution Most probable speed For one molecule, what speed is most possible? Among N molecules, what is the speed most molecules have in unit interval?

Maxwellian can be written as

The average speed

In an interval of Dt, number of collisions is

Then mean free path is

where the mean relative speed is

optional Reference L. E. Reichl, A Mordern Course in Statistical Physics. University of Texas Press, Austin 1980 pp458

Then mean free path is Only a factor different from dimension analysis result.

Transport phenomena Heat transfer : conduction convection thermal radiation diffusion viscosity thermal conductivity Conduction Fourier’s law

Diffusion Fick’s law Viscosity 6

Microscopic theory of transport coefficients

For mass transport, In general:

Similarly

Hydrogen under STP r = 1.12×10−10m

Experimental results: