Physics 418: Statistical Mechanics I
Prof. S. Teitel ----- Spring 2004

Lecture Notes

My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from - they are not in general carefully prepared for others to read. I make no guarentees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.

The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.

  • Lecture 1 - Basic postulates of classical thermodynamics; the entropy and maximum entropy principal; extensive and intensive variables; thermal, mechanical and chemical equilibrium

  • Lecture 2 - Concavity of the entropy; equations of state; Euler and Gibbs-Duhem relations; minimum energy principal

  • Lecture 3 - Legendre transformations

  • Lecture 4 - Other Thermodynamic Potentials: Helmholtz and Gibbs free energies, enthalpy, the grand potential; extremum principals for free energies; Maxwell relations

  • Lecture 5 - Response functions and the relations between them; specific heats, compressibilities, coeficient of thermal expansion; stability and convexity or concavity of free energies

  • Lecture 6 - Kinetic theory of the ideal gas; Maxwell velocity distribution; ensembles and Liouville's theorem

  • Lecture 7 - The Microcanonical Ensemble and Entropy; entropy of an ideal gas

  • Lecture 8 - The entropy of mixing and Gibbs' paradox; indistinguishable particles; the canonical ensemble and partition function

  • Lecture 9 - The canoncial partition function and the Helmholtz free energy; the equivalence of the canonical and microcanonical ensembles; the ideal gas in the canonical ensemble

  • Lecture 9 Appendix - Derivation of Stirling's formula; entropy of the ideal gas in the microcanonical vs. canonical ensembles; average energy vs. most probable energy in the canonical ensemble

  • Lecture 10 - Virial and equipartition theorems; applications: Law of Dulong and Petit, Curie paramagnetism

  • Lecture 11 - Entropy and information theory

  • Lecture 12 - Grand canonical ensemble: grand partition function and grand potential, particle number and energy fluctuations

  • Lecture 13 - Grand canonical ensemble for non-interacting degrees of freedom; Quantum ensembles and the density operator

  • Lecture 14 - Quantum grand canonical ensemble; quantum statistics, fermions and bosons; two particle density matrix

  • Lecture 15 - Quantum N-particle canonical partition function; quantum grand canonical partition functions for fermions and bosons

  • Lecture 16 - Occupation numbers in quantum and classical grand canonical ensemble; the classical limit of quantum ensembles

  • Lecture 17 - Chemical equilibrium; Debye model for specific heat of a solid; black body radiation

  • Lecture 18 - Energy and pressure of ideal quantum gases, the non-degenerate limit, Sommerfeld model for electrons in a metal

  • Lecture 19 - Sommerfeld model continued: finite temperature expansion, chemical potential, specific heat

  • Lecture 20 - Pauli paramagnetism, Landau diamagnetism

  • Lecture 21 - Landau diamagnetism continued

  • Lecture 22 - Bose Einstein condensation

  • Lecture 23 - Bose Einstein condensation, thermodynamic properties

  • Lecture 24 - Superfluid 4He and BEC in laser cooled gases

  • Lecture 24.5 - Classical ideal gas with internal degrees of freedom

  • Lecture 25 - Non-ideal classical gas: the Mayer cluster expansion

  • Lecture 26 - The virial expansion and Van der Waal's equation of state

  • Lecture 27 - Van der Waal's equation of state and the liquid-gas phase transition; Maxwell's construction

  • Lecture 28 - Behavior at the liquid-gas critical point in the Van der Waal theory; critical exponents

Last update: Wednesday, August 22, 2007 at 8:53:22 AM.