Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Papalexandris Miltiadis;
Language
English
Main themes
- Elaboration of a general theoretical framework of irreversible phenomena having as starting points the kinetic theory of gases and classical thermodynamics
- Presentation of the classical theory of Onsager-Prigogine. Presentation of more recent theories such as Rational Thermodynamics (theory of Truesdell & Noll) and Extended Thermodynamics (theories of Jou & Lebon and of Müller).
Aims
At the end of this learning unit, the student is able to : | |
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With respect to the reference AA of the programme of studies "Masters degree in Mechanical Engineering", this course contributes to the development and acquisition of the following skills
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The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
- Summary of equilibrium thermodynamics: first thermodynamic axiom (principle of energy conservation), absolute temperature and entropy, second thermodynamic axiom, Gibbs relation, equations of Euler & Duhem, thermodynamic potentials and Legendre transformations, stability of equilibrium states, evolution principles, thermochemistry.
- Classical theory of irreversible thermodynamics (theory of Eckart-Onsager-Prigogine): local equilibrium, balance laws and constitutive relations, entropy production, thermodynamic fluxes and forces, Onsager-Casimir reciprocal relations. Applications: Fourier-Navier-Stokes equations for Newtonian fluids, thermodiffusion.
- Study of thermo-electric phenomena: Hall effect, Seebeck and Peltier effects, Nerst and Ettinghausen effects, Joule and Thomson heats.
- Kinetic theory of gases. Derivation of the Boltzmann equation. Collision operator. Relations between mascroscopic variables and kinetic theory. H-theorem. Collision invariants, Maxwell-Boltzmann distribution and derivation of balance laws. Justification of local equilibrium hypothesis. Theory of fluctuations of Einstein. Derivation of the Onsager-Casimir reciprocal relations.
- Introduction to rational thermodynamics. material memory, objectivity, Clasius-Duhem inequality, material-frame indifference, constitutive relations. Application in thermo-elastic materials, comparison with the linear theory of Eckart-Onsager-Prigogine. Liu's method of Lagrange multipliers and extended theories.
- Stationary states: criteria for minimum of entropy production and minimum of dissipated energy. Introduction to stability theory. Rayleigh-Bénard instability.
Teaching methods
- Course lectures
- Sessions of exercises
Evaluation methods
Written exam, with open books and notes. The score on the course will be determined solely on the score on the exam.
Online resources
Bibliography
- M.V Papalexandris, Thermodynamics of Irreversible Phenomena: Lecture notes, 2018. Hand-written notes and exercies (in English). Mandatory, available on the moodle site of the course.
- G. Lebon, D. Jou & J. Casas-Vasquez, Understanding Non-equilibrium Thermodynamics, Springer, 2008. Mandatory, available on the e-books of the library in electronic form.
- Additional notes on the kinetic theory of gases from the book of Chapman & Cowling, Recommended, available on the moodle site of the course.
- D. Kondepudi & I. Prigogine, Modern Thermodynamics, Wiley, 1999. Recommended.
- S.R. De Groot and P. Mazur, Non-equilibrium Thermodynamics, Dover, 1984. Recommended.
Teaching materials
- M.V Papalexandris, Thermodynamics of Irreversible Phenomena: Lecture notes, 2018. Hand-written notes and exercies (in English), available on the moodle site of the course.
- G. Lebon, D. Jou & J. Casas-Vasquez, Understanding Non-equilibrium Thermodynamics, Springer, 2008, available on the e-books of the library in electronic form.
Faculty or entity
MECA
