Systems with a very large number of degrees of freedom: the need for statistical mechanics. Macrostates, microstates and accessible microstates. Fundamental postulate of equilibrium statistical mechanics.
Probability distributions. Microcanonical ensemble, Boltzmann's formula for entropy. Canonical ensemble, partition function, free energy. calculation of thermodynamic quantities. Classical ideal gas. Maxwell-Boltzmann distribution, equipartition theorem. Paramagnetism, Langevin and Brillouin functions, Curie's law.
Quantum statistics: systems of identical, indistinguishable particles, spin, symmetry of wavefunctions, bosons, Pauli's exclusion principle, fermions. Grand canonical ensemble. Bose-Einstein and Fermi-Dirac distributions. Degeneracy. Free electron gas, Pauli paramagnetism. Blackbody radiation. Bose-Einstein condensation. Einstein model of lattice vibrations. phonons, Debye's theory of the specific heat of crystals.
Phase diagrams, phase equilibria and phase transitions. Mean-fjeld theory of liquid-gas transition (Van der Waals model) and ferromagnet-paramagnet transition (Weiss' molecular field theory). Heisenberg exchange interaction and the origin of ferromagnetism. Elementary ideas on Ising and Heisenberg models of ferromagnetism.
- Teacher:
- Teacher: ashwin Ashwin Joy