Course Identification

The course will deal with thermodynamic quantities such as energy, entropy, free energy, heat capacity, equilibrium constants and rate constants, with emphasis on polyatomic molecules as well as some discussion of metals, Bose-Einstein condensates, vibrations in crystals.and phase transitions. A key component of the course is the connection between the macroscopic thermodynamic description and the microscopic statistical mechanical theory.that underlies it.

1. Thermodynamics, Fundamentals (first and second law of thermodynamics, variational statement of the second law, Legendre transforms, Maxwell relations, Gibbs-Duhem equation).
2. Conditions for Equilibrium and Stability (multiphase and multicomponent equilibrium, the chemical potential, the Gibbs phase rule)
3. Statistical Mechanics (the connection between microscopic (statistical mechanics) and macroscopic (thermodynamics), microcanonical and canonical ensembles, partition functions, fluctuations, variational development of equilibrium distribution functions, the Gibbs entropy formula)
4. Non-Interacting (Ideal) Systems. I. (canonical partition functions for translation, rotation and vibration in molecules, the heat capacity, the equilibrium constant and the rate constant)
5. Non-Interacting (ideal) Systems. II. (Bose and Fermi statistics, photon gas, phonons, electrons in metals, Bose-Einstein condensation)
6. Statistical Mechanical Theory of Phase Transitions (Ising model, lattice gas, mean field theory, renormalization group theory).

Upon successful completion of the course, the student will be able to:

1. Explain thermodynamics from two viewpoints: the macroscopic, postulational viewpoint and the microscopic viewpoint.
2. Develop both an intuitive and a quantitative understanding of the origin of the various partition functions.
3. Describe how the different thermodynamic variables can be calculated from the partition functions.
4. Understand the microscopic origin of entropy, heat capacity, equilibrium constants, phase transitions and other thermodynamic quantities.

1. Introduction to Modern Statistical Mechanics, Chandler
2. Supplementary: Statistical Mechanics, McQuarrie
3. Thermodynamics, Callen