Thermodynamics 2

This module completes and formalizes the notions of thermodynamics introduced in EU Thermodynamics 1, by exploring several aspects in greater depth: thermodynamic potentials defined on the basis of Legendre transformations, thermodynamics of open systems, pure-body phase transitions and irreversible processes, with incursions at the microscopic level to provide an insight into the physical foundations of the theory.

• Use differential forms and their properties in thermodynamics.
• Draw up an energy balance and entropy balance for a compound thermodynamic system.
• Predict the macroscopic properties of simple physical models (e.g. perfect gas, real gas, harmonic solid).
• Apply methods for solving ordinary differential equations to thermodynamic problems (e.g. pressure in a compressible fluid).
• Perform an energy and entropy balance for an open system
• Integrate a diffusion equation in simple cases.
• Establish the link between the macroscopic and microscopic description of a system

• UE thermodynamics 1:
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• Notions of Newtonian dynamics
  • Conservative forces
  • Kinetic and potential energy
  • Harmonic oscillators
• Maths
  
  
  • Derivatives, integrals, limited developments 
  • Differential forms

Terminal control

• Equilibrium thermodynamics
  • Reminders: Thermodynamic systems. Variables and state functions: equations of state, intensivity, extensivity, additivity. Notion of equilibrium and local equilibrium. Thermodynamic transformations: quasi-static vs. reversible. Work and heat and their elementary expressions. Internal energy.
  • Axiomatic presentation: First principle: statement and consequences, link with calorimetry. Dulong and Petit's law. Second principle: statement and consequences. Fundamental equation and equations of state. Thermal equilibrium. Third principle.
  • Thermodynamic potentials: Helmoltz potential (free energy) and Gibbs potential (free enthalpy) and applications. Enthalpy. Legendre transformations. Phase diagrams. Clausius-Clapeyron equation and applications.
  • Thermodynamics of open systems: Expression of the first and second principles for open systems. Chemical potential. Application to chemical transformations
  • Phase transitions: concavity and convexity of thermodynamic potentials. Response functions. Applications. Phase transitions: first-order and continuous transitions.
  • Transport phenomena: thermodynamic forces. Local energy and entropy balance. Diffusion equation. Coupling of irreversible phenomena: application to themoelectric effects.
• Microscopic aspects
  • Internal energy: conservation and equipartition of energy
  • Pressure and temperature: elements of gas kinetic theory
  • Entropy: microscopic interpretation, microstates and macrostates