Course content

This course provides a broad and coherent introduction to thermodynamics and phase equilibria as they apply to real materials and industrial processes. The teaching progresses from the basic laws of thermodynamics to entropy, free energies, chemical potential, and activities, and then uses these concepts to analyse solutions, reactions, and equilibria in gases, liquids, and solids.

The fundamental theoretical framework is included because it is essential for later application, but it is not the primary focus. The course emphasises interpretation. Students learn to use thermodynamic quantities to explain material behaviour, to understand how driving forces influence processes, and to relate free energy changes to phase stability, reactions, and microstructural development. Principles familiar from the introductory course in thermodynamics will serve as the foundation, but the objective here is to apply thermodynamics as an analytical tool for understanding materials.

A major component of the course concerns the thermodynamics of solutions. Students work with ideal, regular, and subregular solution models; activities and activity coefficients; partial molar quantities; Raoult’s and Henry’s laws; and the Gibbs-Duhem equation. The selection of standard states for different systems is discussed, together with the implications for the interpretation of real material behaviour.

The course then applies these principles to phase equilibria. Students learn to construct and interpret unary, binary, and ternary phase diagrams, and to relate these diagrams to free energy curves, phase stability, invariant reactions, and phase transformations. Gas-metal equilibria and oxidation behaviour are addressed through Sievert’s law, interaction coefficients, Wagner’s equation, and the use of Ellingham diagrams.

Examples throughout the course are drawn from metals, alloys, oxides, and other inorganic materials. The overall aim is to use thermodynamics to understand how materials behave and how processes evolve under different conditions.

Learning outcome

Upon successful completion of the course, the students will be able to:

Thermodynamic principles

• Define thermodynamic systems, processes, state functions, and equilibrium.
• Apply the First, Second, and Third Laws to real materials.
• Calculate enthalpy, entropy, and free energy changes from heat capacities and phase change data.
• Identify the direction of spontaneous change using free energy and entropy criteria.

Solutions and mixtures

• Describe ideal and non-ideal solutions and apply Raoult’s and Henry’s laws.
• Use activity, activity coefficients, fugacity, and partial molar properties in practical calculations.
• Apply the Gibbs-Duhem equation and understand assumptions and limitations of common solution models.
• Use regular and subregular solution models to interpret and predict behaviour in liquid and solid solutions.

Chemical potential and reaction equilibria

• Relate chemical potential to stability and to the driving force for reactions and phase changes.
• Evaluate reaction equilibria from standard free energy data.
• Use Sievert’s law for gas solubility in metals and apply interaction coefficients in dilute alloys.

Phase diagrams

• Apply the Gibbs phase rule to determine degrees of freedom and constraints.
• Construct simple binary phase diagrams from thermodynamic models.
• Interpret unary, binary, and ternary phase diagrams and extract relevant information.
• Recognise and describe phase boundaries, tie lines, invariant reactions, and three-phase triangles.
• Use the lever rule to calculate phase compositions and phase fractions.
• Interpret Ellingham diagrams and relate them to oxidation and selective reduction.

Learning methods and activities

The course is taught through lectures and problem-solving. HSC Chemistry is used to calculate thermodynamic data and to investigate equilibria. Relevant exercise material is distributed weekly.

Teaching is in English, and both the semester test and the exam are given in English. Students may answer in English or Norwegian. The total workload is approximately 200 hours.

Recommended previous knowledge

Chemical Thermodynamics equivalent to TKJ4162 Physical Chemistry: Chemical Thermodynamics or IMAK1004 Chemical Thermodynamics for Engineers

Course materials

Svein Stølen and Tor Grande, Thermodynamics of Materials, John Wiley & sons, Ltd (2004). Lecture notes and exercises.

Credit reductions