Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
Occurrence | Teaching cycle |
---|---|
A | Autumn Term 2021-22 |
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 Statistical Mechanics Assignment 1 |
N/A | 40 |
Essay/coursework Statistical Mechanics Assignment 2 |
N/A | 60 |
None
Task | Length | % of module mark |
---|---|---|
Essay/coursework Statistical Mechanics Assignment 1 |
N/A | 40 |
Essay/coursework Statistical Mechanics Assignment 2 |
N/A | 60 |
Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.
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)*