Free Energy
– Helmholtz free energy; Definition, F:= U – TS , and physical interpretation.
– Gibbs free energy; Definition, G:= U – TS + PV , and physical interpretation.
– Thermodynamic potentials: Use of H, F, and G to calculate the energy needed for transformations at constant pressure and/or temperature.
– Thermodynamic identities: Using the form of the identity for energy,

dF = –SdT – PdV + μdN   and   dG = –SdT + VdP + μdN .

– Gibbs-Duhem relations: Expressions for G = μN and U = TS – PV + μN as examples.

Thermodynamic Potentials and Equilibrium
– Isolated systems: Entropy tends to increase, dS ≥ 0.
– Thermal equilibrium with environment: Helmholtz free energy tends to decrease, dF ≤ 0.
– Thermal and mechanical equilibrium: Gibbs free energy tends to decrease, dG ≤ 0.

Types of Thermodynamic Variables
– In terms of behavior for composite systems: Extensive (additive) vs intensive variables.
– In terms of role in the theory: Thermodynamic potentials, 1st-order quantities (in extensive-intensive conjugate pairs), 2nd-order quantities, etc; Physical meaning of each type.

Phase Transformations of Pure Substances
– Phases: Concept; Main examples for fluids characterized by T, V, P and related variables; Distinguishing gases and liquids from the behavior of isothermal lines in P-V plane.
– Phase diagrams: Concept; Triple points, critical points; Apperance for water.
– Clausius-Clapeyron equation: For phase boundary, dP/dV = ΔS/ΔV= L/TΔV ; Condition in terms of thermodynamic potentials that determines when phase transitions occur.

van der Waals Model

– Idea: Simple model for non-ideal gas that takes interactions between molecules into account.
– Equation of state: (P + aN ²/V ²)(V–Nb) = NkT, or P = (NkT/(V–Nb)) – aN ²/V ²; Meaning of the parameters a and b; [no need to remember the equation]; Shape of isotherms.
– Phase transition: Qualitative behavior; Maxwell construction (how to use it, why it works).