PHYS 7850/3850
STATISTICAL AND THERMAL PHYSICS
Syllabus

Prerequisite: Phys 2211-2212 or equivalent.

Textbook: Roger Bowley and Mariana Sanchez, Introductory Statistical Mechanics, Oxford University Press, Oxford, New York, 1999 or later.
 
Contents: 

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 as fundamental problems of 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

  1. Probability: intuitive and axiomatic formulations
  2. Independent and mutually excluding events
  3. Combinatorial probability: Arrangements, permutations, and combinations
  4. Distributions

4. Introduction to Statistical Mechanics

  1. Statistical expression for entropy
  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 idtribution: 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 paramegnetism and Landau diamagnetism. Quantum oscillations.*

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