Thermodynamics of mixtures

Thermodynamics of mixtures

Two-phase flow is a 2nd semester elective specialised course held at University of Ljubljana, Slovenia.


2. semester - University of Ljubljana, Slovenia


prof.dr. Iztok Golobič

Course Points (ECTS)


Contact Information

University of Ljubljana, Slovenia

Course Overview

Module objective

The objective of this course is to provide the students with the fundamental knowledge to be able to understand and thermodynamically describe mixtures and processes involving mixtures.

The students will earn competences enabling them to understand the processes involving bi- and multicomponent mixtures in different states of matter. This will enable them to understand and deepen their work on processes in process engineering, providing them with the foundation for an in-depth study of narrower professional fields of energy and process engineering.

Knowledge outcome

Successfully executed study obligations in the Thermodynamics of mixtures course enable the students to understand and describe the basic processes involving mixtures. Based on the knowledge and understanding the description of processes involving mixtures, being fundamental for the procedures in process engineering, the students in possession of fundamental knowledge will be able to participate in further in-depth studies of processes in energy and process engineering, as well as to solve complex problems in this field in a wider working environment.

Syllabus outline

  • Introduction, mixtures of ideal gases, mixtures of gases and vapours, moist air, Mollier h-x diagram, dry- and wet-bulb temperature;
  • Conservation of mass and energy in psychrometric systems, heating and cooling, mixing of moist air flows, humidification and dehumidification, evaporative cooling, air conditioning, cooling tower, drying;
  • Gibbs free energy and chemical potential, main Gibbs equation;
  • Real mixtures, equations of state for pure matter, equations of state for mixtures;
  • Gibss' phase rule, phase diagrams, chemical potential of real fluids, fugacity and fugacity coefficient, activity and activity coefficient, ideal solutions, excess quantities;
  • Vapor–liquid equilibrium in a mixture, equilibrium and stability;
  • Thermodynamic processes involving mixtures, exergy analysis;
  • Chemical reactions and combustion, Hess' law, enthalpy of formation, fuel cells;
  • Chemical and phase equilibria, using equilibrium criteria for chemical reactions;
  • Transport properties of matter, databases of thermodynamic material properties of pure matters and mixtures.

Monitoring of student progress

  • two colloquia
  • written and oral examination 


[1] M.J. Morgan, H.N. Shapiro, Fundamentals of Engineering Thermodynamics. 6th Edition, John Wiley & Sons, New York, 2007 - selective chapters
[2] K.Stephan, F.Mayinger, Thermodynamik. Band 2: Mehrstoffsysteme un chemishe Reaktionen. 14.neubearbeitete und erweiterte Auflage, Springer, Berlin, 1999 - selective chapters
[3] J.M. Smith, H.C. Van Ness, M.M. Abbot, Introduction to Chemical Thermodynamics. 7th Edition, McGraw-Hill, New York, 2005 - selective chapters
[4] M. Oprešnik, Termodinamika zmesi. 3. predelana izdaja, Fakuleta za strojništvo, Univerza v Ljubljani, Ljubljana 1988.
[5] A. Bejan, Advanced Engineering Thermodynamics. Third Edition, John Wiley &Sons, Hoboken, 2006 - selective chapters
[6] B.E. Poling, J.M. Prausnitz, J.P. O'Connel, The Properties of Gases and Liquids. 5th Edition, McGraw-Hill, New York, 2001 – selective chapters