Chapter 4: Free Energy and Thermodynamic Equilibrium

Free Energy and Thermodynamic Equilibrium begins by distinguishing between the two primary free energy functions: Helmholtz Free Energy, which represents the maximum work available from a system, and Gibbs Free Energy, which is pivotal for understanding non-mechanical work and predicting reaction feasibility under constant temperature and pressure. The text explores the mathematical integration of the First and Second Laws of Thermodynamics to derive fundamental relationships for internal energy, enthalpy, and entropy. A significant portion of the discussion is dedicated to establishing the specific criteria for equilibrium, identifying the thermodynamic potentials that drive natural, spontaneous processes versus unnatural ones across various conditions. The summary explains how to assess the feasibility of reactions by analyzing the interplay between enthalpy and entropy changes, alongside the temperature and pressure dependence of free energy using concepts like fugacity. It further elaborates on essential mathematical tools, including the Gibbs-Helmholtz equations for calculating free energy from calorimetric data, and Maxwell’s Relations, which link theoretical state functions to measurable physical properties like thermal expansion and compressibility. Practical metallurgical applications are highlighted through the Clausius-Clapeyron equation, which models phase transformations such as melting, vaporization, and allotropic changes. The chapter also covers empirical approximations like Richard’s Rule and Trouton’s Rule for estimating entropy during phase changes. Finally, the content concludes with an examination of the Third Law of Thermodynamics, detailing Nernst’s Heat Theorem, the concept of complete internal equilibrium, and the method for determining the absolute entropy of pure substances at absolute zero.