Module overview
Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In the course the basic principles of statistical mechanics will be introduced with applications to the physics of matter.
Linked modules
Pre-requisite: PHYS1013
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Microcanonical ensemble (e.g. enumerate microstates for some simple physical systems)
- How Bose-Einstein condensation leads to unique states of matter at low temperatures
- Microscopic definition of entropy and temperature
- Canonical ensemble, and applications to some simple physical systems immersed in a heat bath (temperature)
- Chemical potential
- Probabilistic interpretation of entropy, heat and work
Subject Specific Practical Skills
Having successfully completed this module you will be able to:
- Employ quantum mechanics for a correct statistical description in terms of Fermi and Bose gases and their applications
- Distinguish between Bose and Fermi gases and their ground states
Syllabus
- Revision of the basics laws of thermodynamics
- Brief summary of combinatorics and probabilities
- Discussion of basic concepts, notions and postulates of statistical mechanics e.g. microstates vs macrostates, notion of ensemble and postulate of equal a priori probability and ergodicity
- Microcanonical ensemble (isolated system). From where a microscopic definition of entropy and temperature emerges.
- Canonical ensemble (system in a heat reservoir). Uncover the free energy F as the natural thermodynamic potential.
- Discuss the equivalence of microcanonical and canonical ensemble in the thermodynamic limit.
- Applications: paramagnetism, heat capacity of solids (phonons);
- Grand canonical ensemble (systems with a variable numbers of particles); Discussion of the chemical potential;
- Discussion of indistinguishable particles in quantum mechanics and introduce the two types of particles: bosons and fermions
- Applications: Fermi gases; zero point pressure, zero point energy, discuss the free fermion electron model
- Bose gases: Black body radiation, Bose-Einstein condensation
Learning and Teaching
Teaching and learning methods
Lectures and problem classes.
| Type | Hours |
|---|---|
| Revision | 10 |
| Completion of assessment task | 10 |
| Lecture | 36 |
| Preparation for scheduled sessions | 18 |
| Wider reading or practice | 46 |
| Follow-up work | 18 |
| Tutorial | 12 |
| Total study time | 150 |
Resources & Reading list
Textbooks
R,Baierlein. Thermal Physics. Cambridge.
S Blundell and K Blundell Ð (2006). Concepts in Thermal Physics. Oxford University Press.
Assessment
Assessment strategy
Course work worth 20% of the module mark will be set and assessed in the normal way. In the event that a course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that piece of course work. Please note that documentary evidence will normally be required before these can be considered.
The final exam is worth 80% of the module mark.
Referral Method: By examination, the final mark will be calculated both with and without the coursework assessment mark carried forward, and the higher result taken.
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Problem Sheets | 20% |
| Examination | 80% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Coursework marks carried forward | 20% |
| Examination | 80% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 80% |
| Coursework marks carried forward | 20% |
Repeat Information
Repeat type: Internal & External