1. 2/4/2014PHY 770 Spring 2014 -- Lecture 61 PHY 770 -- Statistical Mechanics 12:30-1:45 PM TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course Webpage: http://www.wfu.edu/~natalie/s14phy770http://www.wfu.edu/~natalie/s14phy770 Lecture 6 -- Chapter 4 Review of Thermodynamics – continued 1.Thermodynamics of phase transitions 2.Phase equilibria; Clausius-Clapeyron equation

2. 2/4/2014PHY 770 Spring 2014 -- Lecture 62

3. 2/4/2014PHY 770 Spring 2014 -- Lecture 63

4. 2/4/2014PHY 770 Spring 2014 -- Lecture 64

5. 2/4/2014PHY 770 Spring 2014 -- Lecture 65 Thermodynamics of phase equilibria and transitions Initially, focus on one component systems with multiple phases Example: water Phase I: Solid Phase II: Liquid Phase III: Gas

6. 2/4/2014PHY 770 Spring 2014 -- Lecture 66 Phase diagram of water (http://www1.lsbu.ac.uk/water/phase.html)http://www1.lsbu.ac.uk/water/phase.html

7. 2/4/2014PHY 770 Spring 2014 -- Lecture 67 Comments about phase transitions at constant T and P (or more generally T and Y).  G I (T,Y)=G II (T,Y) and  I (T,Y)=  II (T,Y)  Coexistence line defined by Y I-II coexist (T).  In this case, the coexistance of three phases is only possible at a point in the Y,T plane.  Phase transition can be first order when G has discontinuous first derivatives  Phase transition can be second order when G has continuous first derivatives

8. 2/4/2014PHY 770 Spring 2014 -- Lecture 68

9. 2/4/2014PHY 770 Spring 2014 -- Lecture 69 Thermodynamic description of the equilibrium between two forms “phases” of a material under conditions of constant T and P

10. 2/4/2014PHY 770 Spring 2014 -- Lecture 610 Example of phase diagram :

11. 2/4/2014PHY 770 Spring 2014 -- Lecture 611 Phase diagram for water:

12. 2/4/2014PHY 770 Spring 2014 -- Lecture 612 piston T,P A B Consider a two phase system at constant T and P Note: A and B denote different phases (previously I and II)

13. 2/4/2014PHY 770 Spring 2014 -- Lecture 613 piston T,P A B

14. 2/4/2014PHY 770 Spring 2014 -- Lecture 614 P T g A > g B g A < g B

15. 2/4/2014PHY 770 Spring 2014 -- Lecture 615

16. 2/4/2014PHY 770 Spring 2014 -- Lecture 616 Example – liquid – solid transition in water G T P constant Liquid Solid Melting T m

17. 2/4/2014PHY 770 Spring 2014 -- Lecture 617

18. 2/4/2014PHY 770 Spring 2014 -- Lecture 618 More details

19. 2/4/2014PHY 770 Spring 2014 -- Lecture 619

20. 2/4/2014PHY 770 Spring 2014 -- Lecture 620

21. 2/4/2014PHY 770 Spring 2014 -- Lecture 621

22. 2/4/2014PHY 770 Spring 2014 -- Lecture 622 Approximate liquid-gas vaporization curve from Clausius- Clapeyron equation: P

23. 2/4/2014PHY 770 Spring 2014 -- Lecture 623 The van der Waals equation of state -- More realistic than the ideal gas law; contains some of the correct attributes for liquid-gas phase transitions.

24. 2/4/2014PHY 770 Spring 2014 -- Lecture 624 Some motivation for van der Waals equation of state Johannes Diderik van der Waals – Ph. D. Thesis written in 1873 (The Netherlands) -- received Nobel Prize in 1910 General potential between two particles:

25. 2/4/2014PHY 770 Spring 2014 -- Lecture 625 Substancea (10 -30 eV m 3 )b (10 -30 m 3 ) water9.5550.7 SO 2 11.994.7 CO 2 6.371.3 O2O2 2.3852.9 Ar2.3653.8 N2N2 2.3664.3 H2H2 0.42844.3 4 He0.059739.4 From: Baierlein, Thermal Physics

26. 2/4/2014PHY 770 Spring 2014 -- Lecture 626 P/P c V/V c T/T c =1 T/T c >1 T/T c <1 Gas Liquid

27. 2/4/2014PHY 770 Spring 2014 -- Lecture 627 V/V c P/P c Decreasing values of T

28. 2/4/2014PHY 770 Spring 2014 -- Lecture 628 P   unphysical

29. 2/4/2014PHY 770 Spring 2014 -- Lecture 629 

30. 2/4/2014PHY 770 Spring 2014 -- Lecture 630 Behavior of the thermodynamic potentials for the van der Waals equation of state

31. 2/4/2014PHY 770 Spring 2014 -- Lecture 631 Behavior of the thermodynamic potentials for the van der Waals equation of state

32. 2/4/2014PHY 770 Spring 2014 -- Lecture 632

33. 2/4/2014PHY 770 Spring 2014 -- Lecture 633 Gibbs chemical potential at coexistence point liquid gas

34. 2/4/2014PHY 770 Spring 2014 -- Lecture 634

35. 2/4/2014PHY 770 Spring 2014 -- Lecture 635 Analysis of gas-liquid coexistence conditions

36. 2/4/2014PHY 770 Spring 2014 -- Lecture 636 Analysis of gas-liquid coexistence conditions -- continued

37. 2/4/2014PHY 770 Spring 2014 -- Lecture 637

38. 2/4/2014PHY 770 Spring 2014 -- Lecture 638 P/P c V/V c liquid gas liquid & gas P-V diagram for van der Waals material at T/T c =0.9 

39. 2/4/2014PHY 770 Spring 2014 -- Lecture 639

40. 2/4/2014PHY 770 Spring 2014 -- Lecture 640 Phase diagram for van der Waals material P/P c T/T c 1 1 gas liquid 0.9 0.65