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

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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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 UE represents the natural continuation of the UEs in classical Newtonian mechanics.

In the first part of the course, we take Classical Mechanics from the principle of least action to two new formulations: the Lagrangian formalism and the Hamiltonian formalism. We study the link between physical symmetries and conservation laws (E. Noether's theorem) and introduce Poisson brackets, which allow us to write the classical laws of temporal evolution of physical quantities in a form that already prefigures those of quantum mechanics.

In the second part of the course, starting from an examination of the experimental limits of classical mechanics, a new theory of mechanics is introduced: Quantum Mechanics. This is a theory that is conceptually completely different from previous classical theories, based on a description of physical phenomena in terms of probabilities and therefore no longer deterministic. It's a radical paradigm shift that has turned physics on its head over the last century, enabling a deeper understanding of physical nature, with fundamental and practical spin-offs that have radically changed the lives of mankind (atomic physics, chemistry, nuclear energy, transistors, LASERS, to name but a few). 

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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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