Department of Physics and Astronomy
STATISTICAL AND THERMAL
Fall Semester 2012
- 6:45 pm
09, 2012 - April 30, 2012
Instructor: Mark Stockman
Monday, April 30 from 4:15 pm to 6:45 pm in the
Text: Roger Bowley and Mariana Sanchez, Introductory
Mechanics, Oxford University Press, Oxford, New York, 1999 or later.
Office: 406 Science Annex
Phone: (678)457-4739 (worldwide mobile)
Web site: http://www.phy-astr.gsu.edu/stockman/
Grading: 30% midterm exam, 70% final exam (subject to change)
Basic Rules of the Class Room
These rules are designed to allow
students to get the maximum benefit
their time and money spent.
The physical attendance of lectures is not required but strongly
If you happen to be late, enter class, do not apologize, quietly
seat and start working. If you need to leave, do so also as
possible, do not ask permission. Timely submission of home
is required. The home assignments are due in one week after they
given. They will not be graded but you will be given detailed
in writing, and you will be welcome to discuss them either in
at the office.
Do not talk in class even in a low voice since it is
(asking a fellow student a brief question is admissible, but
kept to the minimum). Do not hesitate to interrupt the lecturer
questions or comment, since it is beneficial for the class. (Do
that your question is too trivial to ask -- it may well be not so
Many students may have a similar problem. No questions and
class will affect your grades in any way. Please, your question is very important -- ask
At the exams, you may not use any notes or books, unless
allowed. You may briefly (for not more than five minutes) leave
room after one hour of work without asking permission. You should
your calculator (no data banks) and pen or pencils. The paper
be given to you. The date and time of the final exam cannot be
1. Thermodynamics: Introduction and the First Law
2. Entropy and the Second Law
- Macroscopic and microscopic description
- Partitions (walls): adiabatic vs. diathermal,
- Equilibria and principal possibility of a process in
- Internal energy, work and heat.
- Perfect and imperfect differentials
- Isothermal and adiabatic processes
- Carnot cycle
3. Introduction to Statistics
- The Second Law
- Carnot theorem.
- Entropy as a function of state
- Entropy and the Second Law
- Maximum of entropy and equilibrium.
- Fundamental relations. Entropy of ideal gas.
- Energy and enthalpy (heat function)
- Van der Waals fluid.
- Mixing ideal gases. Entropy of mixture.
- Joule process (expansion into vacuum)
- Maximum work theorem.
- Equilibria and maximum of entropy
- Thermodynamic identities.
of derivatives, method of Jacobians.
4. Introduction to Statistical Mechanics
- Probability: intuitive and axiomatic formulations
- Independent and mutually excluding events
- Combinatorial probability: Arrangements, permutations, and
5. Gibbs Method: Canonical Ensemble
- Statistical expression for entropy (Boltzmann, S=kB Log W )
- Entropy of spins on a lattice
- Entropy for vacancies in a crystal
- The second law and thermodynamic fluctuations
6-8. Identical particles
- Entropy and the number of available sates for an isolated
ensemble). Microcanonical distribution.
- System in contact with thermal reservoir. Entropy and
- Alternative way to derive the Gibbs distribution:
- Boltzmann formula for entropy
- Partition function. Helmholtz free energy and
- Two-level system
- Monatomic ideal gas.
- Rotational and vibrational contributions.
- Thermodynamic equilibria and minima of potentials
- Einstein and Debye heat capacity.*
9,10. Gibbs method: Grand Canonical Ensemble
- Identical particles in quantum mechanics.
- Pauli theorem on spin and statistics. Fermi-Dirac and
- Molecule with identical atoms
- Classical ideal gas and Maxwell distribution
- Black body radiation (photon gas) and Planck distribution.
- Thermodynamics of the photon gas.
- Einstein and Debye heat capacity of solids
4. Dielectric and magnetic systems*
- Chemical equilibria and chemical potentials
- Grand canonical ensemble and the grand canonical potential
- Fermi gas. Grand partition function. Fermi distribution
- Thermodynamic properties at T=0 and T<<EF.
- Application to astrophysics.
- Bose systems. Bose condensation.
- Black body radiation revisited. Photons and Planck
- Polarization and electrostatic
- Dielectrics with fixed external
energy of dielectrics.*
- Microscopic models of dielectrics.
- Thomas-Fermi approximation for
gas. Debye screening. Plasmons.*
- Thermodynamics of magnetics.
- Pauli paramagnetism and Landau
*) Time permitting (usually not taught
unless the students express specific and significant interest)