Course Syllabus

Properties of gases: Ideal gas equation of state, van der Waals equation, pressure-volume diagrams, critical point, law of corresponding states, virial coefficients, simple models (hard spheres, square well potential, hard sphere potential with attractive tail, Lennard-Jones potential).

Canonical ensemble and Boltzmann factor: Concept of statistical ensemble, Boltzmann factor, partition function, internal energy, heat capacity at constant volume. Contributions to molecular partition function, internal energy and heat capacity from translational, electronic, vibrational and rotational degrees of freedom. The equipartition principle.

The first law of thermodynamics. Mechanical work, reversible processes, exact and inexact differentials, state functions, internal energy function, first law. Reversible isothermal, isobaric and adiabatic expansions. Free expansion. Enthalpy, heat capacity at constant pressure.

The second law of thermodynamics. Entropy. The Carnot and Otto cycles. Statistical mechanical definition of entropy. Microscopic interpretation of heat, work, and entropy changes.

The third law of thermodynamics. Discontinuity of entropy across phase transitions.

Helmholtz and Gibbs free energies. Legendre transforms. Maxwell's relations.

Phase equilibria. Phase diagrams, phase coexistence, phase transitions. Chemical work and chemical potential. General conditions of equilibrium. The Clausius-Clapeyron equation. Microscopic determination of chemical potential.

Liquid-liquid and liquid-solid solutions. Euler relations. The Gibbs-Duhem equation. Raoult's law and ideal solutions. Vapor pressure and chemical potentials in binary solutions. Osmotic pressure.

Kinetic theory of gases. The Maxwell-Boltzmann distribution.

Kinetics of chemical reactions. Rate laws, Arrenius plots. Classical transition state theory. Barrier recrossing and quantum tunneling effects. Stability conditions and phase transitions. Identical particle exchange effects. Superfluidity and Bose-Einstein condensation.

In addition to the material specified above, you should be comfortable with the mathematical operations used in the various procedures performed in class, in the examples covered in the book, and in homework problems. The math chapters included in the book and the lecture slides offer useful reviews of such tools.