SubjectsSubjects(version: 901)
Course, academic year 2021/2022
Physical Chemistry IV (Statistical Thermodynamics) - MC260P105
Title: Fyzikální chemie IV (Statistická termodynamika)
Czech title: Fyzikální chemie IV (Statistická termodynamika)
Guaranteed by: Department of Physical and Macromolecular Chemistry (31-260)
Faculty: Faculty of Science
Actual: from 2017
Semester: winter
E-Credits: 3
Examination process: winter s.:
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Note: enabled for web enrollment
Guarantor: RNDr. Peter Košovan, Ph.D.
Teacher(s): RNDr. Peter Košovan, Ph.D.
Is co-requisite for: MC260C105
Is incompatible with: MC260P129
Annotation -
Last update: RNDr. Peter Košovan, Ph.D. (13.10.2020)
The course introduces basic concepts of Statistical Thermodynamics as a discipline based on atomistic description of matter and quantum-mechanical description of atoms. We introduce postulates, methods to calculate thermodynamic functions of ideal gas, ideal crystal and liquids based on a small number of basic information about the molecular structure and interactions. Starting from 2016/2017 the lecture is supplemented by non-compulsory exercises (MC260C105). These will cover some more complicated derivations which were not sufficiently covered in the lecture. The exercises will also include an individual project, focused on solving one specific problem by means of statistical thermodynamics.

If there are students who do not speak Czech, then the lectures are given in English. All lecture notes are in English.

The course is primarily dedicated to advanced master and PhD students. Prior knowledge within the scope of bachelor courses is required in the fields of mathematics, physics, chemical thermodynamics, statistics and quantum mechanics.

In the time of covid-19 restrictions, the lectures will be held online by means of a videoconference. Recording of the lectures will be made available to students via google drive.
Literature -
Last update: RNDr. Peter Košovan, Ph.D. (10.09.2013)

Main coursebook:

D. McQuarrie: Statistical Mechanics (Harper & Row, New York)

Other reading:

D. Chandler: Introduction to Modern Statistical Mechanics (Oxford University Press)

T. Boublík: Statistická termodynamika (Academia, in Czech language)

Requirements to the exam -
Last update: RNDr. Peter Košovan, Ph.D. (13.10.2020)

Oral exam within the scope of the sylabus. In the time of covid-19 restrictions it is possible to the the oral exam by a videoconference.

Syllabus -
Last update: RNDr. Peter Košovan, Ph.D. (02.10.2013)

1. Basic definitions, postulates (probability, ensemble). Link to thermodynamics, statistics and quantum mechanics. Canonical ensemble.

2. Micro-canonical and grand-canonical ensemble. Overview of characteristic functions and expressions for p, V, S, E in different ensembles.

3. Monoatomic ideal gas -- non-interacting particles. Fermi-Dirac, Bose-Einsetein and Maxwell-Boltzmann statistics.

4.-5. Diatomic and polyatomic molecules. Zero point energy. Translational, rotational, vibrational, electronic and nuclear contributions to thermodynamic functions. Equilibrium constant. Mixture of ideal gases.

6. Real gas -- interacting particles. Intermolecular potentials. Virial expansion. Virial coefficients from Mayer functions. Virial coefficients for pair potentials.

7. Statistico-mechanical theory of fluids. Quasi-classical approach -- pair correlation function. Van der Waals equation and Kirkwood equation. Perturbation methods.

8. Simulation methods: Molecular Dynamics and Monte Carlo. Distribution functions and thermodynamic functions and methods for their computation.

9. Ideal crystal. Frequency distribution. Enstein and Debye model of a crystal. Heat capacity and temperature limits. One-dimensional case, phonons.

10. Ising model. Phase transitions, fluctuations and long-range correlations. Mean field and renormalization group theories.

11. Thermodynamics at interfaces. Theory of adsorption. Intermolecular interactions at surfaces. Langmiur and BET isotherms. Distribution functions for selected geommetries.

12. Non-equilibrium thermodynamics. Liouville operator, time-dependent ensemble average. Boltzmann equation. Time-correlation functions. Absorption of radiation.

If desired, the advanced topics in the second part of the syllabus can be modified to meet individual needs of the participating students.

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