1. 大学物理（热学） Mean Free Path Diffusion, Thermal conductivity, and Viscosity

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

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

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

5. each normalized a a 12

6. Known
while

7. For unit volume
Maxwell velocity distribution

8. 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?

9. Maxwellian can be written as

10. The average speed

16. In an interval of Dt, number of collisions is

17. Then mean free path is

18. where the mean relative speed is

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

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

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

22. Diffusion
Fick’s law
Viscosity 6

23. Microscopic theory of transport coefficients

24. For mass transport,
In general:

25. Similarly

26. Hydrogen under STP
r = 1.12×10−10m

27. Experimental results: