Syllabus
* Basic concepts of thermodynamics
The macroscopic system, thermodynamic equilibrium. Description of the equilibrium state, extensive and intensive variables, empirical temperature, equations of state (ideal and van der Waals gas, ideal paramagnet).
* First law of thermodynamics
Work, internal energy, heat. The first law of thermodynamics. Fundamental thermodynamic processes, heat capacities and other coefficients of the linear response.
* Second law of thermodynamics
Carnot and other thermodynamic cycles, reversible and irreversible processes, thermodynamic devices. Formulations of the second law due to Clausius, Kelvin and Carathéodory. Absolute temperature, Clausius inequality, entropy.
* Entropy
Properties of entropy as the new axioms of thermodynamics. Pfaffian forms, fundamental equation. The entropy of open systems, entropy and statistical physics.
* Thermodynamic potentials
The conditions of equilibrium and stability. Legendre transformation, Maxwell relations, homogeneity and Gibbs-Duhem relation. Maximum work theorem.
* Phases and phase transitions
Phase equilibrium, Gibbs rules, chemical equilibrium. Liquid-gas system, Clausius-Clapeyron equation, latent heat, van der Waals equation and Maxwell construction. Continuous phase transitions and critical phenomena.
* The third law of thermodynamics
Planck's and Nernst's formulations, main consequences.
* Mathematical statistics and probability theory
Probability, stochastic variables, distribution function (binomial, Poisson, Gaussian distributions), the law of large numbers, central limit theorem.
* Basic theoretical concepts of statistical physics
Phase space, phase volume, microscopic and macroscopic states, statistical description, Liouville theorem. Boltzmann entropy.
* Principles of statistical description of thermodynamic processes
The principle of equal probability, microcanonical ensemble. Interaction of the system with a thermal bath, canonical and great canonical statistical ensemble, fluctuations of thermodynamic quantities. Gibbs entropy. Maxwell-Boltzmann distribution.
Annotation
Basic concepts of thermodynamics, empirical temperature, the first and second law of thermodynamics, entropy, absolute temperature, thermodynamic potentials and Maxwell relations; the third law of thermodynamics, systems with more phases and chemical equilibrium. Basic theory of probability, distribution function in phase space, equilibrium statistical distributions, statistical thermodynamics.
For the 3rd year of the TF study.