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Programme (detailed contents):

Introduction : Mathematic for thermodynamics : partial derivatives, Jacobian, exact and inexact differential, Legendre transform, extensive and intensive properties.

I-Part : Formalism of the thermodynamic of the equilibrium states :

  • Postulates for simple systems
  • Fundamental equations of simple systems
  • States equation of simple systems
  • Calorimetric coefficients of simple systems
  • Legendre transform of simple systems
  • New equilibrium conditions of simple systems
  • Stability conditions of simple systems
  • Generalisation of the thermodynamics to complex systems

II-Part : Applications

  • Perfects gases
  • Mixture of perfect gases
  • Real gases
  • Liquids
  • Solids
  • State transformation
  • Phase diagram
  •  Superficial and interfacial phenomena
  • Energy and efficiency.

III-Part : Irreversible processes

  • Formalism
  • Matter transport (diffusion)

v  Heat transport (conduction)





v  The main concepts will be introduced in a series of lectures (20), and illustrated by a series of tutorial class (10).

v  First intermediate test will be realised after the first third of the course, and the second test after two-thirds of the course.

Main difficulties for students:

Difficulty in acquiring the main principles, and using them to treat real problems.


At the end of this module, the student will have understood and be able to explain (main concepts) :
Laws of thermodynamics, equilibrium and stability conditions, state transitions, phase
diagram, energy, heat, work, matter/heat transport and exchange.
The student will be able to:
The student will be able to grasp different concepts, assimilate them, extract them
from their context in order to use them in real-life situations.

Needed prerequisite


Basic level in mathematical analysis: function of several variables, integration, differential equations

Some basic ideas of thermodynamics.

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...


Thermodynamics and an Introduction to Thermostatistics Herbert B. Callen Ed. John Wiley and Sons (WIE) ; 2n.