Thermodynamics and Statistical Mechanics

1. Thermodynamics and Statistical Mechanics Kinetic Theory of Gases Thermo & Stat Mech - Spring 2006 Class 14

2. Mixing of Two Ideal Gases Change of Gibbs Function An expression is needed for the specific Gibbs function. Thermo & Stat Mech - Spring 2006 Class 14

3. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

4. Specific Entropy Thermo & Stat Mech - Spring 2006 Class 14

5. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

6. Specific Gibbs Function Thermo & Stat Mech - Spring 2006 Class 14

7. Mixing of Two Ideal Gases Thermo & Stat Mech - Spring 2006 Class 14

8. For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14

9. For the Same Pressure Thermo & Stat Mech - Spring 2006 Class 14

10. For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14

11. For the Same Volume Thermo & Stat Mech - Spring 2006 Class 14

12. Basic Assumptions • 1. A macroscopic volume contains a large number of molecules. • 2. The separation of molecules is large compared to molecular dimensions. • 3. No forces exist between molecules except those associated with collisions • 4. The collisions are elastic. Thermo & Stat Mech - Spring 2006 Class 14

13. Basic Assumptions • When no external forces are applied: • 5. The molecules are uniformly distributed within a container. • 6. The directions of the velocities of the molecules are uniformly distributed. • The fraction of molecules with speeds in the range v to v + dv is: f (v) dv Thermo & Stat Mech - Spring 2006 Class 14

14. Molecular Speeds • f (v) is the probability density. Thermo & Stat Mech - Spring 2006 Class 14

15. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

16. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

17. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

18. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

19. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

20. Molecular Flux Thermo & Stat Mech - Spring 2006 Class 14

21. Gas Pressure Thermo & Stat Mech - Spring 2006 Class 14

22. Ideal Gas Law Thermo & Stat Mech - Spring 2006 Class 14

23. Molecular Kinetic Energy Thermo & Stat Mech - Spring 2006 Class 14

24. Equipartition of Energy Thermo & Stat Mech - Spring 2006 Class 14

25. Internal Energy Thermo & Stat Mech - Spring 2006 Class 14

26. Heat Capacities Thermo & Stat Mech - Spring 2006 Class 14

27. Maxwell Velocity Distribution • Consider a gas at equilibrium. The number of molecules in any range of velocity does not change. Collisions cause individual molecules to change velocity, but the distribution does not change. For every collision that changes the distribution, there must be one that changes it back. Thermo & Stat Mech - Spring 2006 Class 14

28. Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14

29. Molecular Collisions Thermo & Stat Mech - Spring 2006 Class 14

30. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

31. Evaluation of Constants Thermo & Stat Mech - Spring 2006 Class 14

32. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

33. Maxwell Distribution Thermo & Stat Mech - Spring 2006 Class 14

34. Some Molecular Speeds Thermo & Stat Mech - Spring 2006 Class 14