Syllabus
A. Thermodynamics A.1. Basic concepts Description of state, state functions, internal and external state parameters. Adiabatic process, work, heat, heat capacity, latent heat, thermodynamics coefficients. Thermodynamic equilibrium, empirical temperature. Equations of state, examples (ideal gas, van der Waals gas, surface tension, paramagnet, rubber, thermal radiation). Relaxation, equilibrium and non-equilibrium processes. Polytropic processes. A.2. Three laws of thermodynamics Differentials of the functions of state, heat as the Pfaffian differential form, conditions of its integrability. Internal energy, formulations of the first law of thermodynamics. Carnot’s theorems, the second law of thermodynamics for equilibrium and non-equilibrium processes, Clausius inequality. Carnot cycle, its P-V diagram, and T-S diagram. Efficiency of the Carnot machine. Thermodynamic definition of the absolute temperature and of the entropy. Principle of the maximal work. Nernst-Planck theorem and its consequences. A.3. Termodynamic potentials and their applications Analytic formulation of thermodynamics, natural variables, Legendre transformation, physical meaning and calculation of the potentials U, F, H, a G, their geometrical interpretation. Gibbs-Helmholtz equations, Maxwell relations. Relation between the thermal and the caloric equation of state, integration of the equation of state. Expansion into vacuum, Joule-Kelvin expansion. Mixing entropy, Gibbs paradox. A.4. Phase transitions and chemical equilibrium Conditions of equilibrium and stability, direction of natural processes, thermodynamic inequalities. Ehrenfest equations, Clausius-Clapeyron equation. Landau theory, scaling laws and critical exponents, relations between critical exponents. Gibbs phase rule, examples of phase diagrams. Chemical potential, its calculation for the ideal gas. Chemical equilibrium, affinity of a chemical reaction, reaction heat, law of acting mass. A.5. Selected applications of the equilibrium thermodynamics Thermodynamics of the thermal radiation. Mean field theory of magnetic phase transition. Thermodynamics of an electromagnet. Adiabatic demagnetization. Analogies between fluids and magnets. Thermodynamics of a capacitor. Termodynamics of an elastic continuum. B. Statistical physics B.1. Aims and tools of the statistical description Macroscopic, mesoscopic, and microscopic description of the physical system. Pure and mixed state, phase space, distribution function, density matrix. Liouville equation and its solution for the harmonic oscillator and for the two-level system. Ergodic principle, information entropy, Boltzmann formula for the entropy. Random walks, Brownian motion, Langevin equation. Relaxation processes, Ehrenfest model, statistical interpretation of the second law of thermodynamics. B.2. Gibbs equilibrium ensembles Microcanonical ensemble, phase extension. Canonical ensemble, method of maximal entropy, calculation of the state sum, fluctuation of the internal energy, calculation of the Helmholtz free energy. Ensemble averaging, microscopic derivation of the equations of state. Ensembles with a variable number of particles, T-P ensemble. B.3. Classical ideal and real gas Maxwell-Boltzmann distribution, equipartition theorem, virial theorem, van der Waals equation of state, Langevin model of paramagnetism. B.4. Quantum ensembles of non-interacting particles Role of the quantum statistics in the evaluation of the entropy. Gibbs paradox. Bose-Einstein distribution, boson condensation, Planck law for the thermal radiation. Heat capacity of a solid, phonons. Fermi-dirac distribution. Degenerated gas of electrons, its internal energy and heat capacity. Classical limit of the quantum distributions.
Annotation
The lecture presents standard introductory material of phenomenological thermodynamics and statistical physics. In its first part, the three laws of thermodynamics are discussed together with the thermodynamic potentials, conditions of equilibrium and stability, and theory of phase transitions.
Next, the formalism of linear nonequilibrium thermodynamics is developed. The second part of the lecture focuses on the statistical approach to the study of microscopically defined classical and quantum many-particle systems.
The Gibbs' method of statistical ensembles yields the first-principle calculation of measurable macroscopic properties. The general formalism is adopted to the study of both ideal and real gases, magnetic and dielectric systems, and quantum systems of noninteracting particles.
Finally, the lecture presents introduction to the nonequilibrium statistical physics resulting in analysis of the Liouville equation and description of the relaxation processes.