1. First and Second laws of thermodynamics, Temperature, Thermal equilibrium, Variational Statement of Second law, and Energy minimization
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2. Legendre Transforms, Helmholtz & Gibbs Free Energies, Enthalpy, and Maxwell Relations
3. Gibbs Duhem Relation and Intensive Variables, Degrees of Freedom Calculations, Chemical and Mechanical Equilibriums, Gibbs Phase Rule, Stability Condition, Phase Diagrams, and The Clausius-Clapeyron relation
4. Connecting Delta H vap to microscopic bond strengths, The Central Limit Theorem, Basic Foundations of Statistical Mechanics
5. 6. Foundations of statistical mechanics, density of states, vs degrees of freedom, fragility of quantum states of macroscopic systems, relations of thermodynamics to statistical mechanics (entropy and the second law), the ideal gas law from S=k ln W, the canonical ensemble, relations of thermodynamics to statistical mechanics (Helmholtz free energy), and the collection of 2-level atoms using both the canonical and microcanonical ensembles
7. Review of the canonical ensemble, application to the quantum harmonic oscillator, the Equipartition Theorem with examples for an Ideal Gas and in Generalized Ensembles and The Grand Partition Function
8. Application of the Grand Partition Function, the Fermi-Dirac distribution and limit considerations, the Grand Potential, entropy for one and many systems for the grand partition function, and beginning discussions of Quantum Statistics
9. Continuing discussions of Quantum Statistics with examples from a 2-state system with coherent superposition and in the classical mixture, application of the density matrix to quantum statistics, the Von Neumann Entropy, general formalism of non-interacting ideal gasses, wave functions of Fermions and Bosons, constructing multiple wave functions from single particle states, and using the chemical potential instead of a constrained sum
Note: there might be a typo on the very last line, will investigate
10. Identical Particle Wavefunctions, Wavefunction for Bosons and Fermions, Bose-Einstien and Fermi-Dirac Distributions, Energy State Degeneracies, the Gibbs Paradox, and the Density of States
11. An example of the Density of States in a 3D particle in a box of side lengths L with periodic boundary conditions, Thermal DeBroglie Wavelength, some computations of the expectation value of the energy and the pressure for an ideal gas, and the Sakur-Tetrode Equation
12. The partition function of the Harmonic Oscillator in phase space, discussions of the classical limit (including chemical potential), the Reduced Distribution Function, pair correlation function definition, and the Maxwell Distribution of Velocities (in an ideal gas)
13. N-particle distribution for an ideal gas, the mean free path, the probability of transmitting a particle through material, susceptibility, and partition function molecules including internal degrees of freedom
14. Chemical Equilibrium in Gasses, The Law of Mass Action, The Saha Equation
14.b. Further on Gas of a Diatomic Molecule
15. The low temperature limit of ⟨n(ε)⟩ for fermions and bosons, The Fermi Level, The Sommerfeld Model, and relation to the Fermi Level, Isothermal Compressibility, Correction to the Sommerfeld Expansion, Fermi-Dirac calculus, the Sommerfeld Lemma, and an example for a 3D electron gas
Note: There is a typo on the last page; it should be Φ=g(ε)
16. Statistical Limit of White Dwarf Stars (Black Body Application), Statistical Model of the Atom, The Thomas Fermi Equation and Thomas Fermi Binding Energy
17. Photon Gas, Phonon Gas, Fermi Dirac & Bose Einstein Statistics, Planck Distribution, Fluctuations of Atomic Positions in a Cold Solid, Application to the Thermodynamics of Blackbody Radiation, Planck's Formula for distribution of energy over the blackbody spectrum, Total Energy Density in a cavity, Rayleigh-Jean's Law, Energy Density for a Black Body, and Net Rate flow of radiation per unit area of opening
18. Thermodynamic Behavior of an Ideal Bose Gas, Bose-Einstein Functions, Virial Expansion and Virial Coefficients, Bose-Einstein Condensate, Characteristic Temperature, Normal vs Condensed phase and low vs high temperature limits, Constant P + varying V as a function of T systems, Constant V + varying P as a function of T systems, Constant T + varying P as a function of V systems, relation to heat capacities and entropy S, and comparisons to ideal gas limit
20. (done, take pic)
Note: 19 skipped, it's more fun with BEC's and can be read up on in Pathria
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