Statistical Mechanics and Thermodynamics

For systems in a heat bath we obtain the Gibbs canonical distribution and explain the concepts of the partition function and the free energy. The ideal gas law is then obtained, and extended to the van der Waals equation of state. The vibrational, rotational and electronic partition functions are obtained for molecular systems. For open thermodynamic systems under a fixed pressure the grand-canonical Gibbs ensemble is  introduced with the concepts of the chemical potential and the enthalpy. Finally, the quantum systems with the Bose-Einstein and Fermi statistics are reviewed.