- Department: Physics
- Module co-ordinator: Prof. Rex Godby
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2018-19
- See module specification for other years: 2019-20
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Occurrence | Teaching cycle |
---|---|
A | Autumn Term 2018-19 |
In Statistical Mechanics we will develop formalisms of equilibrium statistical mechanics from fundamental considerations of the microscopic states available to the system, and relate statistical mechanics to the classical thermodynamical descriptions of heat, work, temperature and entropy. Statistical mechanics will be used to derive formulae for the internal energy, entropy, specific heat, free energy and related properties of classical and quantum-mechanical systems, and to apply these formulae to a variety of realistic examples.
Learning outcomes: at the end of this module successful students will be able to:
Discuss, at the level of detail given in the lectures, how the results of statistical mechanics may be derived from fundamental statistical considerations and how they are related to classical thermodynamics;
Apply the definitions and results of statistical mechanics to deduce physical properties of the systems studied in the lectures and other systems of similar complexity, drawing in part on your knowledge of the microstates of simple systems from core courses in quantum mechanics and solid state physics.
Please note, students wishing to take this module should take the prerequisite modules listed above (Thermodynamics & Solid State II - PHY00031I; Quantum Physics II - PHY00032O; and Mathematics II - PHY00030I) or the appropriate equivalent modules.
Syllabus
Microstates: microstates (quantum states) and macrostates of a system, degeneracy W, density of states, illustration for a set of N harmonic oscillators, principle of equal equilibrium probability of an isolated system, term “microcanonical ensemble” [1 lecture]
Thermal equilibrium, temperature: statistical nature of equilibrium illustrated for 2 sets of N harmonic oscillators, definition of temperature, Boltzmann distribution, partition function Z, term “canonical ensemble” [2]
Entropy: general statistical definition of entropy S, law of increase of entropy, entropy of isolated system in internal equilibrium (“microcanonical ensemble”), entropy of system in thermal equilibrium with a heat bath (“canonical ensemble”), Helmholtz free energy F; equivalence of classical and statistical entropy [2.5]
Elementary applications: Vacancies in solids; two-level systems (including magnetic susceptibility of dilute paramagnetic salt), simple harmonic oscillator (partition function, heat capacity). [2]
Vibrational heat capacity of solids: Quantisation of phonon modes, labelling of modes using wavevector k; Einstein and Debye models [2]
Ideal gas: Partition function of monatomic gas, classical gas law, Maxwell-Boltzmann speed distribution, molecular gases (rotation and vibration), classical limit of occupation numbers [2]
Systems with variable number of particles: Grand canonical ensemble, chemical potential, Gibbs distribution [1.5]
Identical particles: Fermions and bosons, Fermi and Bose distributions, Bose-Einstein condensation, with applications to free-electron metals and nuclear physics (fermions), and liquid 4He and superconductivity (bosons) [3]
Black body radiation: Energy density, pressure [1]
The classical limit: Phase space, classical equipartition theorem [1]
Comprehensive lecture notes should be taken down from the blackboard during lectures, and will be supplemented by a small number of handouts. These handouts, together with audio recordings of lectures, interactive apps, a record of problems set, and similar information, will also be made available through the VLE.
Task | Length | % of module mark |
---|---|---|
Essay/coursework Physics Practice Questions |
N/A | 14 |
University - closed examination Statistical Mechanics |
1.5 hours | 86 |
None
Task | Length | % of module mark |
---|---|---|
University - closed examination Statistical Mechanics |
1.5 hours | 86 |
Physics Practice Questions (PPQs) - You will receive the marked scripts via your pigeon holes. Feedback solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback solutions are provided, normally detailed comments will not be written on your returned work, although markers will indicate where you have lost marks or made mistakes. You should use your returned scripts in conjunction with the feedback solutions.
Exams - You will receive the marks for the individual exams from eVision. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor.
Advice on academic progress - Individual meetings with supervisor will take place where you can discuss your academic progress in detail.
Statistical Mechanics
Waldram JR: The theory of thermodynamics (Cambridge University Press)***
Bowley R and Sánchez M: Introductory statistical mechanics (Oxford University Press)***
Glazer M and Wark J: Statistical Mechanics: A Survival Guide (Oxford University Press)***
Mandl F: Statistical physics (Wiley)**
Reif F: Fundamentals of statistical and thermal physics (McGraw-Hill)**
Blundell SJ and KM: Concepts in Thermal Physics (Oxford University Press)*
Swendsen RJ: An Introduction to Statistical Mechanics and Thermodynamics (Oxford University Press 2012)*