Statistical Mechanics and Thermodynamics (Concise Lecture Notes in Physical Chemistry Book 2)

After a brief introduction into the probability theory, the main principles of Statistical Mechanics are systematically developed from the first principles for the equilibrium theory. The course proceeds from a mechanistic description of molecular and atomic motion for macroscopically large physical chemical systems to introduce the concepts of thermodynamical ensembles. For an isolated system, described by the micro-canonical ensemble, the laws of Thermodynamics are derived from the principle of a priori equal probabilities of micro-states in the thermodynamic limit. The concepts of the entropy, temperature and heat capacity are introduced. We proceed to systems in a heat bath and obtain the Gibbs canonical distribution and explain the concepts of the partition function and the free energy. The ideal gas law is then obtained, as well as its corrections are calculated, leading to the van der Waals equation of state. The vibrational, rotational and electronic partition functions are obtained for molecular systems. The concept of an open thermodynamic system under a fixed pressure, and the grand-canonical Gibbs ensemble associated with it, are further introduced, along with the concepts of the chemical potential and the enthalpy. Finally, the quantum systems with the Bose-Einstein and Fermi statistics are reviewed.