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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

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

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

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

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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

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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

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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

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

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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

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

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

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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)

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

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

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

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

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

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

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

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

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

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

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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.

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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:

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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

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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