Cardinal Stefan Wyszynski University in Warsaw - Central Authentication System
Strona główna

Theoretical physics III

General data

Course ID: WM-FI-501
Erasmus code / ISCED: (unknown) / (unknown)
Course title: Theoretical physics III
Name in Polish: Fizyka teoretyczna III
Organizational unit: Faculty of Mathematics and Natural Sciences. School of Exact Sciences.
Course groups:
ECTS credit allocation (and other scores): (not available) Basic information on ECTS credits allocation principles:
  • the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS;
  • the student’s weekly hourly workload is 45 h;
  • 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes;
  • weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS;
  • work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load.

view allocation of credits
Language: English
Subject level:


Learning outcome code/codes:

FIZ2_W01; FIZ2_W02; FIZ2_W03; FIZ2_W07; FIZ2_W08; FIZ2_U01; FIZ2_U04; FIZ2_U09; FIZ2_U15; FIZ2_U16; FIZ2_K02

Short description:

Introduction to the statistical description of three base assembles of many particles and the connection with the principles of thermodynamics. Microscopic understanding of the entropy, partition and thermodynamic functions. The application of statistical physics and distributions to classical and quantum ideal gases. Introduction to fluctuating phenomena.

Full description:

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.


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.

Efekty kształcenia i opis ECTS:

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 methods and assessment criteria:

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

Practical placement: (in Polish)


This course is not currently offered.
Course descriptions are protected by copyright.
Copyright by Cardinal Stefan Wyszynski University in Warsaw.
ul. Dewajtis 5,
01-815 Warszawa
tel: +48 22 561 88 00
contact accessibility statement USOSweb (2022-09-30)