Theoretical Physics 4A (Statistical Mechanics and Thermodynamics)

1) Statistical foundation of the thermodynamics

Microcanonical ensemble, assumption of equal probability, density operator, partition function and entropy, heat and work, temperature, Maxwell-Boltzmann distribution, equipartition theorem, laws of thermodynamics, reversible and irreversible processes, canonical and grand canonical ensembles.

2) Phenomenological thermodynamics

Basic definitions, heat engine and thermodynamic cycle, thermodynamic potentials and stability, Maxwell relations, cooling of gases, Joule–Thomson effect, phases and phase transitions in one-component systems, Clausius–Clapeyron relation, osmosis, van der Waals equation, multicomponent systems.

3) Statistical physics of specific systems in equilibrium

Non-interacting quantum gas: basics, classical limit, gas of molecules, ideal Fermi gas, degenerate Fermi gas, ideal Bose gas, Bose–Einstein condensation, photons, thermodynamics of radiation, phonons, magnetism, Ising model, virial expansion, van der Waals equation.

4) Non-equilibrium thermodynamics

Basic definitions of kinetic theory, Boltzmann equation, Brownian motion, fluctuation-dissipation theorem, particles and heat diffusion, Einstein relation.

After successful participation in this module students are able

1. to explain basic concepts and relations of temperature and heat
2. to understand basics of statistical mechanics and their implications on thermodynamics
3. to describe ideal gases and ideal quantum gases
4. to understand essential properties and different descriptions of interacting gases and fluids as well as to describe their behavior at phase transitions
5. to gain insight into the non-equilibrium thermodynamics

PH0005, PH0006, PH0007, MA9201, MA9202, MA9203, MA9204

Lecture: presentation

Tutorial: The tutorial is held in small groups. In the tutorial the weekly exercises are presented by the students and the tutor. They also provide room for discussions and additional explanations to the lectures.

The courses of the module are offered during the winter semester only. Students taking the repeat exam after the summer semester may visit the courses to PH0012 Theoretical Physics 4B (Thermodynamics and Elements of Statistical Mechanics) to recapitulate the contents at least in parts.

Blackboard or beamer presentation

concurrent material on webpage/moodle

• M. Kardar, Statistical Physics of Particles, Cambridge University Press
• F. Reif, Fundamentals of statistical and thermal physics, Mc Graw-Hill
• T. Fließbach, Statistische Physik, Spektrum, Akad. Verlag
• W. Nolting, Band 6: Statistische Physik
• F. Schwabl, Statistische Mechanik
• Landau, Lifshitz, Pitajewski, Band 5: Statistische Physik, Teil 1

There will be an oral exam of about 40 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Determination of the chemical potential of a perfect gas in the canonical ensemble
• Presentation of properties of the Ising model

After successful participation in the tutorials a certificate ("Übungsschein") is issued as mid-term. Successful participation is active participation in the tutorials and at least 50% of exercise points.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0) if a certificate ("Übungsschein") is present before the oral exam.