Risorse bibliografiche
Risorsa bibliografica obbligatoria
Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2021/2022
Tipo incarico Dottorato
Docente Beretta Gian Paolo Maria
Cfu 5.00 Tipo insegnamento Monodisciplinare

Corso di Dottorato Da (compreso) A (escluso) Insegnamento

Programma dettagliato e risultati di apprendimento attesi

The course will meet one morning per week starting in February till the end of May.

Lecture hours usually start at 9:00 and end around 13:30 with one half-hour break.

There will be a midterm exam and a final oral exam.

The midterm exam will require each student to answer three questions about the first part of the course by submitting three prerecorded videos (max-5-minutes-each).

Final oral exams will be held in presence (or, if necessary, online) on two fixed dates immediately after the end of the course, typically at the end of May, no other dates available. Please take a note and read below in the section "Note Sulla Modalità di valutazione"



A concise review of general thermodynamics concepts, with emphasis on rigorous developments of foundational concepts such as the definition of entropy for nonequilibrium states, and on the meaning of exergy, followed by a presentation of analytical methods of equilibrium thermodynamics, of homogeneous and heterogeneous, reacting and non-reacting systems, and a general introduction on the methods of and non-equilibrium thermodynamics, designed to allow a unified understanding of simple and complex transport phenomena for future energy engineering applications.



The first part of the course provides a brief review of general thermodynamics concepts, such as the definition of entropy, the properties of pure substances, the meaning of exergy, the definition of the so-called second-law efficiency. This part will end with a pass/fail written midterm examination.

The second part of the course focuses on the properties of ideal and nonideal gas mixtures and solutions, liquid-vapor, liquid-liquid and membrane equilibria for binary systems, chemical equilibrium and chemical kinetics of reacting gas mixtures and flows.

The third part introduces to the methods of non-equilibrium thermodynamics, the local and constrained equilibrium assumptions that underlie the description of multicomponent flows, the diffusion of energy, mass, and momentum, the Onsager reciprocal relations, and the concept of cross effects. This part will end with an overview of thermodiffusive and thermoelectric effects.


Reference texts

Two thirds of the course material is covered in the reference text:

Gyftopoulos and Beretta, Thermodynamics. Foundations and Applications, Dover 2005.

One third of the course material is covered in a set of instructor's viewgraphs.


Suggested preliminary reading

In preparing for the quick review in the first part, and for preliminary reading and reference in preparation for the midterm examination:

Suggested sections of the book Gyftopoulos and Beretta, Thermodynamics. Foundations and Applications, Dover: Chapters 1 to 17. Many details and proofs will not be requested. The viewgraphs used during the lectures define the required contents.

The following text in italian may be useful (for those who can read it! sorry!):

Beretta, Le Nozioni di Base della Termodinamica, Edizione preliminare per i corsi di Fisica Tecnica, Terza Edizione, 2008, Casa Editrice Cartolibreria SNOOPY s.n.c., via Bligny n.27, 25133 Brescia, Tel. e Fax 0302006331

The following text may be useful as additional for the last part of the course and connections with advanced fluid mechanics and heat transfer:

Kjelstrup, Bedeaux, Johannessen and Gross, Non-Equilibrium Thermodynamics for Engineers, World Scientific 2010.


Note Sulla Modalità di valutazione

Midterm around the 4th useful week of classes (offered only once, no repeats*)

Final oral exam at the end of the course (the student can choose between only two fixed available dates to be announced the first day of class, NO OTHER DATES AVAILABLE, no repeats). Students are advised to take a note and block these dates on their calendar.  If they miss these dates, the next available dates will be in May of the following year!

Intervallo di svolgimento dell'attività didattica
Data inizio
Data termine

Calendario testuale dell'attività didattica

Risorsa bibliografica obbligatoriaE.P. Gyftopoulos and G.P. Beretta, Thermodynamics: Foundations and Applications, Editore: Dover, Anno edizione: 2005, ISBN: 0-486-43932-1
Risorsa bibliografica facoltativaKjelstrup, Bedeaux, Johannessen and Gross, Non-Equilibrium Thermodynamics for Engineers, Editore: World Scientific, Anno edizione: 2010, ISBN: 981-4322-15-6

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Note Docente
schedaincarico v. 1.7.2 / 1.7.2
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