Thermodynamics and statistical mechanics 2

Syllabus

• Thermodynamic potentials: Gibbs free energy; per molecule and per unit volume thermodynamic potentials.
• 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.  
• 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.
• Incorporation of molecular interactions into free energy: phase coexistence; common tangent construction; phase diagrams; spinodal and binodal lines; critical temperature; Clausius-Clapeyron equation.  
• Van der Waals gas: free energy; pressure; spinodal; critical point; estimations of critical temperature; approximation of binodal far from the critical point.    
• 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.  
• Ferromagnet-paramagnet second-order phase transition; Landau theory of phase transitions.  
• Kinetic theory of gases: characteristic velocities; kinetic derivation of pressure of ideal gas;  Maxwell distribution of velocities.
• 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.  
• 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.
• 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.  
• Quantum gases: limits of classical approach to gases; bosons and fermions; Fermi-Dirac and Bose-Einstein statistics; Boltzmann gas as extrapolation of classical gas.
• Fermions: density of states; Fermi energy; total energy and pressure of fermion gas at zero temperature; heat capacity of fermion gas.  
• Bosons: Bose-Einstein condensation; physical origin and derivation; relation to superfluidity and superconductivity.

Sources:

1. C. Kittel and H. Kroemer, Thermal Physics
2. F. Reif F, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, NY 1965, QC 175.R43