Thermodynamics and Statistical Physics

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Presentation transcript:

Thermodynamics and Statistical Physics Lecture 14 Methodologies of statistical mechanics. (Chapter 4 in STP) Microcanonical ensemble Canonical ensemble 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Microstate count for N particles in d-dimensions – microcanonical distribution 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Boltzmann entropy function 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

N1,V1 N2,V2  N,V=N1+N2,V1+V2 N1/V1=N2/V2=N/V 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble: Eb Es 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble (continued) 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble (continued) 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble: 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble continued – average energy of system: Heat capacity for canonical ensemble: 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

First Law of Thermodynamics for canonical ensemble - Pressure associated with state s 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

=0 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Recap: 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Canonical ensemble 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14

Example: Canonical distribution for free particles 5/13/2019 PHY 341/641 Spring 2012 -- Lecture 14