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College Physics (Thermodynamics): Mean Free Path, Diffusion, Thermal Conductivity, and Viscosity

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

  2. ni the number of moleculesof in vy vy + dvy Equilibrium distribution dn isthe number of molecules nearv

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

  4. Isotropic assumption The solution is The probability should be normalized

  5. a each normalized 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

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

  12. Then mean free path is

  13. where the mean relative speed is

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

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

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

  17. Diffusion Fick’s law Viscosity 6

  18. Microscopic theory of transport coefficients

  19. For mass transport, In general:

  20. Similarly

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

  22. Experimental results:

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