(A) THERMODYNAMICS
– Axiomatic formulation of Thermodynamics: Axiomatic introduction to the laws of Thermodynamics.
– Thermodynamic potentials: Thermodynamic potentials, Legendre transformations, Maxwell relations. Exercises.
– Applications I – Study of simple systems: Relation between heat capacities, ideal gas, elastic rod, electrochemical cell, piezoelectric and magnetocaloric effects. Problems.
-Applications II – Irreversible processes: Joule expansion, Thomson expansion. Problems.
– Phase equilibrium: Thermodynamic equilibrium and equilibrium criteria. Multiphase systems (real pure substances), phase equilibrium, phase transitions, Clausius-Clapeyron equation. Order of phase transitions. Problems.
(B) STATISTICAL PHYSICS
– Axioms of Statistical Physics – Microcanonical ensemble: Equilibrium in an isolated system.
– Canonical ensemble: Equilibrium of a system in a thermal reservoir. Partition function, Boltzmann distribution, energy, relative energy fluctuations, Helmholtz free energy. General definition of entropy. Problems using the microcanonical and canonical ensemble.
– Paramagnetism: Paramagnetic material in a heat reservoir. Energy, entropy, heat capacity, magnetization, magnetic susceptibility. Isolated paramagnetic material. Negative temperatures. Problems.
– Second Law of Thermodynamics for infinitesimal transformations. Third Law. Formulations and experimental verification. Adiabatic cooling. Problems.
– Heat capacity of solids due to lattice vibrations: Einstein model. Density of states. Debye model. Problems.
– Classical Ideal Gas: Energy, partition function, entropy, heat capacity, equation of state of a classical ideal gas, entropy of mixing (Gibbs paradox). Criterion for classical approximation. Classical statistical mechanics. Equipartition theorem. Problems.
– Introduction to Quantum Statistics – Blackbody radiation: Photon partition function, Planck’s law, properties of blackbody radiation. Problems.
– Ideal Quantum Gas: Quantum statistics – Grand canonical ensemble, Fermi-Dirac and Bose-Einstein distributions, classical limit.
– Fermion gas: Free electron model in metals.
– Bose-Einstein condensation: Bose gas at low temperature. Problems in quantum statistics.