COURSE GOALS: Understanding the relationship between thermodynamics and statistical physics. Acquiring the basic concepts of the statistical description of a system in the thermodynamic limit: entropy, thermodynamic potentials, ensemble, single-particle distributions, and fluctuations.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics;
1.2. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena);
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem;
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.3. use mathematical methods to solve standard physics problems;
3. MAKING JUDGEMENTS
3.1. develop a critical scientific attitude towards research in general, and in particular by learning to critically evaluate arguments, assumptions, abstract concepts and data;
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely;
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information;
5.2. remain informed of new developments and methods in physics, informatics and education;
5.3. develop a personal sense of responsibility for their professional advancement and development;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
By the end of the course, the student should be able to:
1. understand abstract thermodynamics at the elementary level of the theory of functions of several variables;
2. explain the difference between thermodynamics and theoretical mechanics, i.e. thermalization as a real physical process;
3. explain the role of thermalization and the Liouville theorem in the foundations of statistical physics;
4. explain the physical construction of thermodynamic potentials through the energy of interaction of a system and the outside world;
5. understand the statistical interpretation of thermodynamic potentials, particularly the entropy and Massieu functions;
6. explain the role of the chemical potential and its qualitative behaviour in the classical and quantum limits;
7. describe four ideal gases (fermions, bosons, light, sound) qualitatively and quantitatively, in the classical and quantum limits;
8. expound the basic properties of gas liquefaction within the van der Waals approach
1. Thermodynamics as an autonomous discipline
1.1. Introduction. Basic concepts.
1.2. First law. Engines.
1.3. Second law. Reversibility and entropy.
1.4. Thermodynamic potentials.
1.5. Practical calculations.
2. Introduction to statistical physics
2.1. Basic considerations.
2.2. The ensemble as a universal random model.
2.3. Connection with thermodynamics.
3. Canonical and grand canonical ensembles
3.1. Canonical ensemble.
3.2. Grand canonical ensemble.
3.3. Sums over states as generating functions.
3.4. Classical ideal gas.
3.5. Maxwell distribution and equipartition of energy.
4. Quantum statistical physics
4.1. Basic considerations.
4.2. Ideal fermion gas.
4.3. Ideal boson gas.
5. Examples and models
5.1. Barometric formula.
5.2. Two-atom molecules.
5.3. Heat capacity of crystals.
5.4. Van der Waals model of gas liquefaction.
REQUIREMENTS FOR STUDENTS:
Students should pass two out of three tests spread out during the course.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Students are admitted to an oral examination if they have passed a written one. They are admitted to the written examination if they have passed two out of three above-mentioned tests. If they have passed all tests with grade 4 or 5, the grade in the written examination is increased by one.
- R. Stowe, An Introduction to Thermodynamics and Statistical Mechanics, Cambridge University Press 2014, ISBN: 9781107694927
- C. Kittel, Elementary Statistical Physics, Dover 2004, ISBN 0486435148.
- R. Kubo et al., Statistical mechanics: an advanced course with problems and solutions, North-Holland, Amsterdam 1988, ISBN 0444871039.
- Skripta: http://www.phy.hr/dodip/notes/statisticka.html