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PHY 770 -- Statistical Mechanics 12:30-1:45 P M TR Olin 107

PHY 770 -- Statistical Mechanics 12:30-1:45 P M TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course Webpage: http://www.wfu.edu/~natalie/s14phy770. Lecture 5 -- Chapter 3 Review of Thermodynamics – continued Continue the analysis of t hermodynamic stability Examples.

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PHY 770 -- Statistical Mechanics 12:30-1:45 P M TR Olin 107

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  1. PHY 770 -- Statistical Mechanics 12:30-1:45 PM TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course Webpage: http://www.wfu.edu/~natalie/s14phy770 Lecture 5 -- Chapter 3 Review of Thermodynamics – continued Continue the analysis of thermodynamic stability Examples PHY 770 Spring 2014 -- Lecture 5

  2. PHY 770 Spring 2014 -- Lecture 5

  3. Summary of thermodynamic potentials PHY 770 Spring 2014 -- Lecture 5

  4. Derivative relationships of thermodynamic potentials PHY 770 Spring 2014 -- Lecture 5

  5. Equilibrium properties of thermodynamic potentials • At equilibrium dS0 and Smaximum • At equilibrium dU0 and U(S,X,{Ni})minimum • At equilibrium dH0 and H(S,Y,{Ni})minimum • At equilibrium dA0 and A(T,X,{Ni})minimum • At equilibrium dG0 and G(T,Y,{Ni})minimum • At equilibrium dW0 and W(T,X,{mi})minimum PHY 770 Spring 2014 -- Lecture 5

  6. Stability analysis of the equilibrium state   Assume that the total system is isolated, but that there can be exchange of variables A and B. PHY 770 Spring 2014 -- Lecture 5

  7. Stability analysis of the equilibrium state   Note that this result does not hold for non-porous partition. PHY 770 Spring 2014 -- Lecture 5

  8. Stability analysis of the equilibrium state – multi-partioned box PHY 770 Spring 2014 -- Lecture 5

  9. Stability analysis of the equilibrium state – multi-partioned box PHY 770 Spring 2014 -- Lecture 5

  10. Stability analysis of the equilibrium state – multi-partioned box PHY 770 Spring 2014 -- Lecture 5

  11. Stability analysis of the equilibrium state – multi-partioned box 0 PHY 770 Spring 2014 -- Lecture 5

  12. Stability analysis of the equilibrium state – multi-partioned box PHY 770 Spring 2014 -- Lecture 5

  13. Stability analysis of the equilibrium state • Note that at equilibrium, Stotal= maximum •  DStotal≤ 0 ≥ 0 After a few more steps -- PHY 770 Spring 2014 -- Lecture 5

  14. Stability analysis of the equilibrium state -- continued Le Chatelier’s principle: If a system is in stable equilibrium, then any spontaneous charge in its parameters must bring about processes which tend to restore the system to equilibrium. By assumption, the fluctuations of each variable is independent so that we can examine each term separately. PHY 770 Spring 2014 -- Lecture 5

  15. Stability analysis of the equilibrium state -- continued Contributions from fluctuations in the chemical potentials PHY 770 Spring 2014 -- Lecture 5

  16. Example 3.10 from Reichl: • Consider a system at constant P,T containing two kinds • of particles A and B with the following form for the Gibbs free energy: PHY 770 Spring 2014 -- Lecture 5

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