Learning Outcomes
On completion, the students should be able to;
1. describe an ideal gas on the basis of classical statistics;
2. explain the basic concepts of statistical mechanics, including entropy, its statistical
interpretation and relation to disorder, and the statistical origin of the second law of
thermodynamics;
3. illustrate the canonical and grand-canonical partition functions for systems in thermal
equilibrium, and use them to obtain thermodynamic quantities of interest;
4. describe the implications of the indistinguishability of particles for systems of non-interacting
quantum particles;
5. deduce the Bose-Einstein and Fermi-Dirac distribution functions, and apply them to calculate
the properties of Bose and Fermi gases, for example in the context of White Dwarf stars and
black-body radiation;
6. explain the physical origin of Bose-Einstein condensation, to characterise it quantitatively, and
to explain the experiments confirming Bose-Einstein condensation.
Course Contents
Basic theory of thermodynamics. Basic of probability theory. Microstates and macrostates. The
concept of ensembles. Statistical interpretation of entropy and temperature. Isolated systems and
the microcanonical ensemble. Statistical physics of non-isolated systems. Derivation of the
Boltzmann distribution and canonical ensemble. The partition function in thermodynamics. Noninteracting systems. Equipartition theorem. Density of states. Grand canonical ensemble. FermiDirac and Bose-Einstein distributions. The ideal Fermi gas. Fermi energy. Heat capacity. The ideal
Bose gas. Black body radiation. Bose-Einstein condensation.
