Course Plan:

No. Topic
1 Thermodynamic potentials: Gibbs free energy; per molecule and per unit volume thermodynamic potentials.
2  First order phase transitions: experimental observations; thermodynamic phases; free energy per unit volume;
conditions for phase separation; local and global stability of a thermodynamic phase; graphical representation.
3 Molecular interactions: hard-core repulsion; Van der Waals attraction; induced dipole; electronic and dipole
polarizability; estimations of Van der Waals attraction for simple molecules; Lennard-Jones potential.
4 Incorporation of molecular interactions into free energy: phase coexistence; common tangent construction;
phase diagrams; spinodal and binodal lines; critical temperature; Clausius-Clapeyron equation.
5 Van der Waals gas: free energy; pressure; spinodal; critical point; estimations of critical temperature;
approximation of binodal far from the critical point.
6 Van der Waals gas near the critical point: free energy; binodal line; first and second-order phase transition;
critical opalescence; nucleation and growth; surface energy; critical nucleous.
7 Ferromagnet-paramagnet second-order phase transition; Landau theory of phase transitions.
8 Kinetic theory of gases: characteristic velocities; kinetic derivation of pressure of ideal gas; 
Maxwell distribution of velocities.
9 Diffusion and random walks on a lattice model: mean-square displacement; diffusion coefficient;
the diffusion equation for random walks; diffusion as transport phenomenon; derivation of Fick's
laws from microscopic considerations; self- diffusion and collective diffusion coefficients.
10 Diffusion in gas: random walks; distribution of free paths; mean free path; mean square displacement
of a molecule; self-diffusion coefficient; diffusion in concentration gradient; derivation of Fick's laws;
equivalence of self-diffusion and collective diffusion coefficients for gases.
11 Other linear transport phenomena in gases: heat conductivity; Fourier law; thermalization; thermal
conductivity coefficient; momentum transport; viscosity; mobility of molecules in the external field;
Einstein relation; detailed balance.
12 Quantum gases: limits of classical approach to gases; bosons and fermions;
Fermi-Dirac and Bose-Einstein statistics; Boltzmann gas as extrapolation of classical gas.
13 Fermions: density of states; Fermi energy; total energy and pressure of fermion gas at zero temperature;
heat capacity of fermion gas.
14 Bosons: Bose-Einstein condensation; physical origin and derivation; relation to superfluidity and superconductivity.