Licence 3 CPES Modélisation et numérique en sciences de la matière Chemistry

Thermodynamics: micro and macroscopic aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, in the case of chemical reactions, it enables us to predict the direction of their evolution and their state of equilibrium. In the first years of the bachelor's degree, we focus on describing the principles of thermodynamics and their direct application to chemistry in the case of simple single-phase equilibrium reactions or reactions between homogeneous phases. This teaching unit will extend this knowledge in two directions.

First, we'll generalize this macroscopic thermodynamic framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. Equilibrium breaks and displacements will also be studied.

Next, we'll look at the link with the microscopic world, where matter is described at the atomic scale. We'll show that the evolution predicted by thermodynamics is statistical in nature, with the equilibrium state corresponding to the most probable macroscopic state given the constraints applied to the system. This will enable us to deduce the macroscopic thermodynamic properties of a physico-chemical system from its microscopic description.

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A first part of the module will consist of presenting metals and alloys through crystallography (from the "ideal" crystalline solid to defects and solid solutions), then a second part will be devoted to their characterization by X-ray diffraction and the last part will address their synthesis through their solid/liquid binary diagram (description and construction) and the different transformations in the solid state.

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This UE is a continuation of the mathematics courses of L1 and the 1st^{semester of} L2. The mathematical tools necessary for the physicist in integration theory, functional transformations, complex variables and distributions will be presented.

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This module is an introduction to the concepts and methods of the statistical physics of equilibrium systems, with a bottom-up approach: start with examples and then give the general principles. It draws heavily on Harvey Gould and Jan Tobochnik's course. A historical introduction to the construction of Brownian motion theory forms the final chapter of the course.

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The aim of this course is to introduce the basics of physical hydrodynamics. The kinematic aspects are dealt with first: Euler and Lagrange formalism, analysis of the motion of an element of fluid volume, introduction of current and potential velocity functions, and applications to different types of flow. In the following section on fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of perfect fluids, followed by the Navier-Stokes equation describing the flow of viscous Newtonian fluids. This will lead to the definition of the stress tensor and the Reynolds number, enabling us to deduce whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids : displacement field, expansion and deformation tensors.

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This course builds on the basic concepts acquired in Quantum Mechanics in Semester 5. The course is structured around the following main themes: extension of the wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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