Department of Physics and Astronomy
PHYS 3850/7850
Fall Semester 2012
Class 5:30 pm - 6:45 pm MW Natural Science Center 272 Jan 09, 2012 - April 30, 2012

Instructor: Mark Stockman
Office: 406 Science Annex (by appointment)
Phone: (678)457-4739 (worldwide mobile)
Web site:
Grading: 30% midterm exam, 70% final exam (subject to change)

Final Exam: Monday, April 30 from 4:15 pm to 6:45 pm in the regular classroom Text: Roger Bowley and Mariana Sanchez, Introductory Statistical Mechanics, Oxford University Press, Oxford, New York, 1999 or later.

Basic Rules of the Class Room

These rules are designed to allow students to get the maximum benefit for their time and money spent. The physical attendance of lectures is not required but strongly recommended. If you happen to be late, enter class, do not apologize, quietly take your seat and start working. If you need to leave, do so also as quietly as possible, do not ask permission. Timely submission of home assignments is required. The home assignments are due in one week after they are given. They will not be graded but you will be given detailed solutions in writing, and you will be welcome to discuss them either in class or at the office.
Do not talk in class even in a low voice since it is disruptive (asking a fellow student a brief question is admissible, but should be kept to the minimum). Do not hesitate to interrupt the lecturer with any questions or comment, since it is beneficial for the class. (Do not assume that your question is too trivial to ask -- it may well be not so trivial. Many students may have a similar problem. No questions and comments in class will affect your grades in any way. Please, your question is very important -- ask it!)
At the exams, you may not use any notes or books, unless specifically allowed. You may briefly (for not more than five minutes) leave the class room after one hour of work without asking permission. You should bring your calculator (no data banks) and pen or pencils. The paper needed will be given to you. The date and time of the final exam cannot be changed.


1. Thermodynamics: Introduction and the First Law

  1. Definitions
  2. Macroscopic and microscopic description
  3. Partitions (walls): adiabatic vs. diathermal, rigid vs. flexible, etc.
  4. Equilibria and  principal possibility of a process in thermodynamics
  5. Internal energy, work and heat.
  6. Perfect and imperfect differentials
  7. Isothermal and adiabatic processes
  8. Carnot cycle
2. Entropy and the Second Law
  1. The Second Law
  2. Carnot theorem.
  3. Entropy as a function of state
  4. Entropy and the Second Law
  5. Maximum of entropy and equilibrium.
  6. Fundamental relations. Entropy of ideal gas.
  7. Energy and enthalpy (heat function)
  8. Van der Waals fluid.
  9. Mixing ideal gases. Entropy of mixture.
  10. Joule process (expansion into vacuum)
  11. Maximum work theorem.
  12. Equilibria and maximum of entropy
  13. Thermodynamic identities. Maxwell identities. Reduction of derivatives, method of Jacobians.
3. Introduction to Statistics 4. Introduction to Statistical Mechanics
    1. Statistical expression for entropy (Boltzmann, S=kB Log W )
    2. Entropy of spins on a lattice
    3. Entropy for vacancies in a crystal
    4. The second law and thermodynamic fluctuations
5. Gibbs Method: Canonical Ensemble
  1. Entropy and the number of available sates for an isolated system (microcanonical ensemble). Microcanonical distribution.
  2. System in contact with thermal reservoir. Entropy and Gibbs distribution.
  3. Alternative way to derive the Gibbs distribution: Principle of maximum disorder
  4. Boltzmann formula for entropy
  5. Partition function. Helmholtz free energy  and thermodynamics.
  6. Two-level system
  7. Monatomic ideal gas.
  8. Rotational and vibrational contributions.
  9. Equipartition
  10. Thermodynamic equilibria and minima of potentials
  11. Einstein and Debye heat capacity.*
6-8. Identical particles
    1. Identical particles in quantum mechanics.
    2. Pauli theorem on spin and statistics. Fermi-Dirac and Bose-Einstein statistics.
    3. Molecule with identical atoms
    4. Classical ideal gas and Maxwell distribution
    5. Black body radiation (photon gas) and Planck distribution.
    6. Thermodynamics of the photon gas.
    7. Einstein and Debye heat capacity of solids
9,10. Gibbs method: Grand Canonical Ensemble
  1. Chemical equilibria and chemical potentials
  2. Grand canonical ensemble and the grand canonical potential (or, grand potential).
  3. Fermi gas. Grand partition function. Fermi distribution and Fermi energy.
  4. Thermodynamic properties at T=0 and T<<EF.
  5. Application to astrophysics. Equilibria of stars.*
  6. Bose systems. Bose condensation.
  7. Black body radiation revisited. Photons and Planck distribution.
4. Dielectric and magnetic systems*
  1. Polarization and electrostatic energy.*
  2. Dielectrics with fixed external potentials. Free energy of dielectrics.*
  3. Microscopic models of dielectrics. Rigid and induced dipoles.*
  4. Thomas-Fermi approximation for interacting electron gas. Debye screening. Plasmons.*
  5. Thermodynamics of magnetics.
  6. Pauli paramagnetism and Landau diamagnetism. Quantum oscillations.*

*) Time permitting (usually not taught unless the students express specific and significant interest)