Statistical Mechanics - course unit details - MPhys Physics - full details (2025 entry)

Duration: 4 years
Year of entry: 2025
UCAS course code: F305 / Institution code: M20

Key features:
Scholarships available
Accredited course

Typical A-level offer: A*A*A including specific subjects
Typical contextual A-level offer: A*AA including specific subjects
Refugee/care-experienced offer: AAA including specific subjects
Typical International Baccalaureate offer: 38 points overall with 7,7,6 at HL, including specific requirements

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Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £36,500 per annum. For general information please see the undergraduate finance pages.

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All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

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Course unit details:
Statistical Mechanics

Course unit fact file
Unit code	PHYS20352
Credit rating	10
Unit level	Level 2
Teaching period(s)	Semester 2
Available as a free choice unit?	No

Overview

Statistical Mechanics

Pre/co-requisites

Unit title	Unit code	Requirement type	Description
Properties of Matter	PHYS10352	Pre-Requisite	Compulsory
Introduction to Quantum Mechanics	PHYS20101	Pre-Requisite	Compulsory

Aims

• To develop the statistical basis of classical thermodynamics

• To deepen the appreciation of the link between the microscopic properties of individual atoms or other particles and the macroscopic properties of many-body systems formed from them

• To demonstrate the power of statistical methods in different areas of physics

• To use the methods of quantum mechanics and statistical physics to calculate the behaviour of gases of identical particles, and to apply the results to a set of important physical system.

Learning outcomes

On completion successful students will be able to:

1. Explain the basic concepts of statistical mechanics, including entropy, its statistical interpretation and relation to disorder, and the statistical origin of the second law of thermodynamics;

2. Construct the canonical and grand-canonical partition functions for systems in thermal equilibrium, and use them to obtain thermodynamic quantities of interest.

3. Demonstrate an understanding of the implications of the indistinguishability of particles for systems of non-interacting quantum particles

4. Write down the Bose-Einstein and Fermi-Dirac distribution functions, and apply them to calculate the properties of Bose and Fermi gases, for example in the context of White Dwarf stars and black-body radiation.

5. Explain the physical origin of Bose-Einstein condensation, to characterize it quantitatively, and to explain the experiments confirming Bose-Einstein condensation

Syllabus

1.The statistical theory of thermodynamics (approximately 5 lectures)

Basic of probability theory; microstates and macrostates; the concept of ensembles; the statistical interpretation of entropy and temperature; isolated systems and the microcanonical ensemble

2. Statistical physics of non-isolated systems (approximately 8 lectures)

Derivation of the Boltzmann distribution and the canonical ensemble; the independent-particle approximation; the partition function and its connection with thermodynamics; examples of non-interacting systems (paramagnet set of harmonic oscillators – quantum and classical , ideal gas, classical and quantum rotors). Equipartition theorem; Density of states. Grand-canonical ensemble and chemical potential.

3. Quantum gases (approximately 10 lectures)

Fermi-Dirac and Bose-Einstein distributions. The ideal Fermi gas: Fermi energy. Electronic heat capacity. White Dwarf stars. The ideal Bose gas: Photon gas blackbody radiation (Stefan’s Law and the Planck formula). Bose-Einstein condensation.

Assessment methods

Method	Weight
Other	10%
Written exam	90%

* Other 10% Tutorial Work/attendance

Feedback methods

Feedback is through weekly tutorials and marked tutorial work.

Study hours

Scheduled activity hours
Assessment written exam	1.5
Lectures	24
Tutorials	4

Independent study hours
Independent study	70.5

Teaching staff

Staff member	Role
Judith McGovern	Unit coordinator

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