Computational Tools for Thermodynamic Teaching in Chemical and Metallurgical Engineering Courses

Thermodynamics is considered, among many engineering students, a very difficult branch of physics, especially regarding phase equilibria modeling, which usually often requires the use of commercial software and/or complex algorithms, rarely available for the general public. The present article provides new and simple Python numerical codes for calculating condensed phase equilibria, using pure metals and an alloy (Cu–Ni) as example, for a validity and consistency check, results were compared with both literature data and Thermo-Calc software's simulations. All parameters for computing pure metal's molar Gibbs energies and chemical activities for liquid and solid solutions were extracted from SSOL3 (SGTE) database. Regarding the pure metals (Bi, Cu, Nb, Ni, Pd, Pt, Sb, Ta, and Th), excellent agreement with literature values has been achieved in all cases, also including the solid–solid transition found for thorium. Regarding the Cu–Ni alloy phase equilibrium behavior, the proposed algorithm has also resulted in a quantitative agreement with literature experimental data and equilibrium liquidus temperatures and solid phase compositions calculated with Thermo-Calc software together with the SSOL2 database. The authors believe that the proposed algorithms could be of valuable use as teaching tools in metallurgical or chemical engineering courses, for example, through computational exercises to predict equilibrium conditions (transition temperatures, phase compositions) and or thermodynamic properties (molar Gibbs energy, enthalpy, and entropy), as exemplified by the activities proposed in the two exercise lists provided as Supporting Information. It is important to note that, although only metallic systems have been explored as examples, the same logic and thermodynamic principles can be applied to other phase equilibria problems involving inorganic condensed phases, for which accurate molar Gibbs energy models can be constructed or obtained from reliable databases.