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# Theoretical physics III WM-FI-501

1. Introduction to the phenomenological thermodynamics: thermodynamic parameters and processes. The first law of thermodynamics. Classical thermodynamic ideal gas. The second law of thermodynamics. Entropy. Carnot cycle.

2. Conditions of thermodynamic equilibrium. State functions. Helmholtz and Gibbs free Energy. Maxwell's relations. Chemical potential. The van der Waals equation of state.

3. Phase space in classical physics. Phase volume. Continuity equation. Liouville theorem. Phase space in quantum physics. Phase volume of the harmonic oscillator. The density of states per unit of energy.

4. Thermodynamic probability. Entropy in statistical physics. The micro-canonical ensemble. Canonical ensemble. The Gibbs distribution.

5. Partition function. Ensemble average for the energy. Relationship between the canonical ensemble and thermodynamics. Grand canonical ensemble. Grand canonical partition function. Average number of particles. Grand potential.

6. Classical thermodynamic ideal gas. Entropy. Average energy per particle. Pressure. Gibbs paradox. Theorem of equipartition of energy.

7. Quantum ideal gases. Temperature of degeneration. Fermions and bosons. Distributions of Fermi-Dirac and Bose-Einstein. Classical limit of high temperature. Maxwell-Boltzmann distribution.

8. Black body thermal radiation. Experimental facts. State density function for photons. Planck distribution. Wien's displacement law and Stefan-Boltzmann law. Thermodynamic state functions for a black body photon gas. Specific heat and entropy. The isothermal process. Cosmic microwave background.

9. Free electron model. Drude model of electrical conduction. Density of states. Electron gas at 0 K. Fermi energy. Concentration of electrons. Fermi velocity. Electron gas at temperature T > 0 K. Fermi temperature.

10. Semiconductors. Band structure of semiconductors. Electron effective mass. Intrinsic semiconductors. Effective density of states . Fermi level and band structure. Doped semiconductors.

11. Bose-Einstein condensation. Critical temperature. Chemical potential. Doppler laser cooling of atoms. Magnetic trap. Evaporative cooling. Thermodynamic parameters of Bose–Einstein condensate.

12. The heat capacity of solids . Einstein's theory of specific heats. Canonical partition function of independent phonons. Specific heat at the limits of high and low temperatures. Debye's model. Debye's maximum frequency. Density of states. Internal energy. Electron heat capacity.

13. Fluctuations and thermodynamics. Gaussian distribution. The average fluctuations of the square energy. Fluctuations in the grand canonical ensemble. Particle number fluctuations. Nyquist noise. Landauer's principle.

14. Brownian motion. Mean squared displacement of the particles. Einstein-Smoluchowski's expression. Random walk. Diffusion. Diffusion coefficient.

15. Phase transitions. Ising Model for ferromagnetism. Order parameter. The single-spin energy. Internal energy. Specific heat. The Ginzburg-Landau theory. Minimizing of the potential. Phase transition in the external field. Susceptibility. Critical exponents.

## Subject level

## Learning outcome code/codes

## Learning outcomes

Explains the problems of statistical mechanics and the relationship with the experimental physics. Solves the problems of statistical mechanics. Uses the formalism of statistical mechanics to describe the laws and processes in nature.

## Assessment criteria

Assessed knowledge of the theory and the ability to solve problems. Two tests are planned, a written and oral exam.

## Bibliography

1. K. Huang, Podstawy fizyki statystycznej, PWN 2006

2. R. Hołyst, A. Poniewierski, A. Ciach, Termodynamika dla chemików, fizyków i inżynierów, Wydawnictwo UKSW 2005

3. L. D. Landau, J. M. Lifszyc, Fizyka statystyczna. Cz. 1, wyd. 2, PWN, Warszawa, 2011

4. R. C. Tolman, The principles of statistical mechanics, Dover, New York, 1979.

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