Syllabus
1. The aim and scope of thermodynamics (TD). Fundamental concepts. Relations of TD to other fields.
2. Required mathematical knowledge. Functions of many variables. Partial differentiation. Perfect differential. Pfaff's forms.
3. Zeroth law of TD. Thermodynamic postulates, equilibrium state, relaxation processes. Empirical temperature. Measuring of temperature.
4. First law of TD and its consequences. First law of TD, heat. Joule experiment. Ideal gas. Equations of state. Joule-Thompson experiment. Enthalpy. Polytrophic processes.
5. Second law of TD and its consequences. Different formulations of the second law of TD. Carnot theorem, Carnot's cycle. Thermodynamic temperature. Entropy. Thermodynamic potentials, Maxwell's relations, "magic" square. Simple applications.
6. Third law of TD. Different formulations of the third law of TD. Consequences of the third law.
7. Open systems and phase transitions. Basic notions. Chemical reactions. Gibbs paradox. Equilibrium in homogeneous and heterogeneous system. Gibbs phase rule. Phase equilibrium, phase transitions and phase diagrams. Clausius-Clapeyron equation.
8. The subject of statistical physics (StPh) and basic concepts. The relation of StPh to thermodynamics. Microstates and macrostates. The description of states of many-particle systems in classical Sph. The configuration, momentum and phase spaces. Phase trajectory. Phase volume.
9. The concept of statistical ensemble. Distribution function. The time and ensemble mean values of physical quantities. Ergodical hypothesis. The Liouville's theorem and its consequences for the nature of distribution function.
10. Microcanonical, canonical and grand canonical distribution. The relation between distributions. Statistical integral (partition function) and calculation of free energy and internal energy of the system. The relations of statistical to thermodynamical quantities. Maxwell and Maxwell-Boltzmann distributions. Grand canonical partition function. Chemical potential.
11. Entropy. Statistical definition of entropy. The relation of entropy to phase volume and spectral density g(E). Connection between statistical and thermodynamic perception of entropy.
12. Quantum canonical distribution. Implications of quantum mechanics and transition from classical to quantum StPh. Quasi-quantum view. Quantum partition function. Fermi-Dirac and Bose-Einstein distributions.
13. Applications. Equations of state of perfect and imperfect gases. System of non-interacting harmonic oscillators. Equipartition theorem. Distribution function for particles in the field. Density distribution of a gas in the gravitational field. Energy mean value of system of noniteracting harmonic oscillators and two-energy-level systems. Blackbody radiation, photon gas and Planck’s law, comparison with classical physics. Heat capacity of crystals (Einstein’s and Debye’s model, comparison with classical model).
Annotation
Lecture of fundamentals of thermodynamics and statistical physics for future physics teachers.