Thermodinamics of Real Processes

NAME OF THE COURSE Thermodinamics of Real Processes



Year of study


Course teacher

Prof Vanja Martinac

Credits (ECTS)


Associate teachers

ScD Jelena Jakić
Assoc Prof Miroslav Labor

Type of instruction (number of hours)






Status of the course


Percentage of application of e-learning

0 %


Course objectives

The aim of the course is that students acquire knowledge in applying the basic laws of thermodynamics and advanced mathematical methods to solutions of chemical engineering problems.

Course enrolment requirements and entry competences required for the course


Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

After passing the exam, students are expected to:
- evaluate the thermodynamic properties of the pure substances, mixtures and solutions based on the pressure, temperature and composition
- select the required literature thermodynamic data and theoretical relationships to describe the dependence of various thermodynamic properties of real gases, mixtures and solutions on pressure and temperature
- apply different types of phase diagrams, tables and numerical expressions to display thermodynamic properties of real gases and solutions
- calculate the thermodynamic properties of real fluids using the equations of state
- calculate the thermodynamic properties of real solutions using a model of the activity coefficient
- apply the acquired knowledge of thermodynamic and advanced mathematical methods to solve chemical engineering tasks

Course content broken down in detail by weekly class schedule (syllabus)

1st week: General consideration. Thermodynamic probability and Boltzman equation.
2nd week: Volumetric properties of real fluids. Equations of state of a real gas and mixture.
3rd week: The principle of corresponding states and thermodynamic similarity. Critical compressibility factor. Application to gases and liquids.
4th week: Improved principle of corresponding states. Pitzer correlation - acentric factor.
5th week: Calculation of the pVT-properties, the comparison equations.
6th week: Thermodynamic properties of real fluids - fugacity and fugacity coefficient
7th week: Methods of calculating fugacity.
8th week: Thermodynamic of real solutions – volume, enthalpy and entropy of mixing, causes of non-ideality of real solutions, regular and athermal solutions.
Exam (I preliminary exam)
9th week: Partial molal quantities. Methods of calculation of partial molal quantities in binary mixtures.
10th week: Partial fugacity and partial fugacity coefficient
11th week: Excess functions. Activity and activity coefficient, standard state for pure gases, liquids and solids and components of gas and liquid mixtures. Activity and activity coefficients from the Gibbs energy.
12th week: Activity coefficient models for liquid mixtures.
13th week: The third law of thermodynamics and calculation of equilibrium transformation. Heterogeneous reactions-changes in reagents’ surface area.
14th week: Introduction to thermodynamics of open systems - work, energy and heat, enthalpy, partial molal quantities, heat in open system, relation between entropy and heat, affinity, thermodynamic functions of non-equilibrium states, entropy balance - entropy production and entropy flow in open system, dissipation function, relation between reaction rates and the affinities.
15th week: Thermodynamic analysis of elastic deformation of a solid. Equation of state for elastic deforming axis. Caloric properties. Thermodynamic deformation processes. Application of thermodynamic theory to man and society.
Exam (II preliminary exam)
Numeric examples demonstrating the topics covered are analysed during the course and make an integral part with lectures.
During exercises, examples from engineering practice are solved using PC and available software.
Laboratory exercises:
1. Thermal storage of solar energy
2. Partial molar quantities
3. Vapour-liquid equilibrium

Format of instruction:

Student responsibilities


Screening student work (name the proportion of ECTS credits for eachactivity so that the total number of ECTS credits is equal to the ECTS value of the course):

Class attendance




Practical training


Experimental work







Seminar essay






Oral exam




Written exam






Grading and evaluating student work in class and at the final exam

Continuous assessment through partial preliminary exams (twice in a semester) allows for exemption from the written exam. The passing threshold is 60%. Partial preliminary exams are not mandatory. Preliminary exams are not eliminatory.
Each passed preliminary exam participates with 18% in the rating. Attendance to lectures and seminars for 80%-100% is 5% of the grade. Activity in lab excercises is 5% of the grade. The oral exam participates with 54 %.
A written and an oral exam are held in the examination periods. The oral exam is mandatory for all students, and the written exam is mandatory if a student is not exempt from it. A passed preliminary exam also participates with 10% in the summer examination period. The written exam participates with 36%, and the oral one with 54%. Students who have not passed the written exam through preliminary exams take the full exam (final exam) consisting of the written and the oral exam in regular examination periods. The passing threshold is 60%. The written exam form participates in the rating with 46% and oral one with 54%..
Ratings: 60%-70% - satisfactory, 71%-80% - good, 81%-90% - very good,
91%-100% - excellent.

Required literature (available in the library and via other media)


Number of copies in the library

Availability via other media

J. M. Smith, H. C. Van Hess, M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, 7th Ed., McGraw-Hill, New York, 2005.


S. I. Sandler, Chemical, Biochemical and Engineering Thermodynamics, 4th Ed., Wiley, New York, 2006.


M. J. Moran, H. N. Shapiro, D. B. Daisie, M. B. Bailey, Fundamentals of Engineering Thermodynamics, 7th Ed., Wiley, New York, 2010.


P. Ahuja, Chemical Engineering Thermodynamics, PHI Learning, New Delhi, 2009.


N. Petric, V. Martinac, Kemijsko-inženjerska termodinamika, Termodinamika realnih procesa, Kemijsko-tehnološki fakultet, Split, 1998.


M. Labor, Termodinamika realnih procesa, Seminar, ppt prezentacija, on line (2014-02-20), Kemijsko-tehnološki fakultet, Split, 2014.


on line

V. Martinac, J. Jakić, Vježbe iz termodinamike, on line (2011-11-15), Kemijsko-tehnološki fakultet, Split, 2010.


on line

Optional literature (at the time of submission of study programme proposal)

B. E. Poling, J. M. Prausnitz, J. P. O’Connell, The Properties of Gases and Liquids, 5th Ed., McGraw-Hill, New York, 2001.
M. Graetzel, P. Infelta, The bases of Chemical Thermodynamics, Vol. 1. & Vol. 2., Universal Publishers, Florida, 2000.

Quality assurance methods that ensure the acquisition of exit competences

Quality assurance will be performed at three levels:
(1) University Level;
(2) Faculty Level by Quality Control Committee;
(3) Lecturer’s Level.

Other (as the proposer wishes to add)