Statistical Thermodynamics and Phase Equilibria

35 lessons, pages 3701–3735.

  1. Thermodynamic Ensembles: Choosing the Constraints — Microcanonical, canonical and grand canonical descriptions
  2. The Microcanonical Ensemble and Entropy — Counting accessible states and deriving temperature from S(E,V,N)
  3. The Canonical Ensemble and Energy Fluctuations — Boltzmann probabilities, partition functions and variance
  4. The Grand Canonical Ensemble — Particle exchange, chemical potential and the grand partition function
  5. Connecting Ensemble Potentials — From entropy to Helmholtz energy and grand potential
  6. The Thermodynamic Limit and Ensemble Equivalence — Why large systems suppress relative fluctuations
  7. Classical Gas Partition Functions Revisited — Translational states, indistinguishability and the ideal-gas free energy
  8. Maxwell–Boltzmann Speed Distribution — Speed probabilities, characteristic speeds and molecular energy
  9. Energy Equipartition and Its Boundaries — Quadratic degrees of freedom and quantum freeze-out
  10. Rotational Heat Capacity of Molecules — Rigid-rotor sums and low- and high-temperature limits
  11. Vibrational Heat Capacity and Einstein Modes — Harmonic oscillator populations and characteristic temperature
  12. Heat Capacity of Solids: Einstein and Debye Models — Optical oscillators, acoustic modes and low-temperature trends
  13. Electronic and Magnetic Contributions to Heat Capacity — Two-level systems, Schottky peaks and state degeneracy
  14. Fluctuation Formula for Heat Capacity — C_V from the variance of canonical energy
  15. Molecular Partition Functions and Spectroscopic Data — Translation, rotation, vibration and electronic factors
  16. Real Gases and the Virial Expansion — Second virial coefficient and pair interactions
  17. Configurational Integrals and Intermolecular Forces — Pair potentials and the origin of nonideal pressure
  18. Chemical Potential from Particle Exchange — Adding particles in canonical and grand canonical descriptions
  19. Statistical Basis of Reaction Equilibrium — Partition functions, standard states and reaction constants
  20. Phase Coexistence as Equality of Chemical Potential — Stability and material exchange between phases
  21. Clapeyron and Clausius–Clapeyron Revisited — Exact coexistence slopes and vapour-pressure approximations
  22. First-Order and Continuous Phase Transitions — Latent heat, order parameters and response-function anomalies
  23. Critical Points and Supercritical Fluids — Vanishing phase distinction, compressibility and critical opalescence
  24. The Gibbs Phase Rule with Reactions — Components, phases and independent equilibrium constraints
  25. Reading One-Component Phase Diagrams — Coexistence curves, metastability and triple points
  26. Binary Vapour–Liquid Equilibrium — Bubble and dew curves, tie lines and phase compositions
  27. Azeotropes and Distillation Limits — Activity deviations and composition-fixed boiling points
  28. Binary Liquid–Liquid Equilibrium — Miscibility gaps, binodals and critical solution temperatures
  29. Binary Solid–Liquid Equilibrium — Eutectics, liquidus lines and lever-rule fractions
  30. Ternary Phase Diagrams and Tie Lines — Triangular composition coordinates and two-phase regions
  31. Lever Rule and Material Balance Workshop — Phase fractions from composition tie lines
  32. Statistical Models of Phase Separation — Mixing entropy, interaction parameters and free-energy curvature
  33. Nucleation and Metastability — Free-energy barriers, supersaturation and delayed transitions
  34. Advanced Phase Equilibrium Problems — Chemical potentials, phase rule and diagram interpretation
  35. Statistical Thermodynamics and Phase Equilibria Review — Connecting ensembles, heat capacities and phase diagrams