Module: Statistical Physics

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Statistical Physics
Module Code	PS302 (ITS) / PHY1049 (Banner)
Faculty	Science & Health	School	Physical Sciences
Module Co-ordinator	Huw Leggate
Module Teachers	Timo Gans
NFQ level	8	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
Array

Description

The aims of the module are to analyse the behaviour of large number of quantum particles using statistical methods and to show how these can be used to calculate the structure and properties of solids, liquids, gases and light.

Learning Outcomes

1. Explain the fundamental nature of the concepts of temperature and entropy at both the macroscopic and microscopic levels and their relationship.
2. Predict the microscopic states of systems of bosons and fermions and their total energy in the quantum and classical limits.
3. Outline the results of the particle-in-the-box model and notably the concept of density of states and its role in statiscal mechanics
4. Explain how the macroscopic properties of localised and classical particles can be obtained using the concept of partition function.
5. Outline the properties of the fermion gas in general and of the degenerate electron gas, in particular, to obtain a basic model for the structure of metals.
6. Outline the basic properties of the boson gas, in general, and of the photon gas in particular.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	In class instruction using computerised presentations.
Tutorial	6	Numerical problems and worked examples. Integrated with lecture series
Independent Study	95	Study of course material, preparation of in class tests, revision for end of semester examination
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Lecture Series: Review of Classical Thermodymanics/Reformulation in terms of total differentials and partial derivatives
Macroscopic state of thermodynamic systems, First and Second laws: Temperature and entropy, Intensive (U,V,N) and Extensive (T,P,mu) variables, Definition and importance of chemical potential mu, Gibbs-Duhem equation, Total differential of internal energy U, Thermodynamic potentials, Free energy F and thermostats.

Lecture series: states of systems of quantum particles
Microstates of individual particles, configurations of systems of particles. Distinguishable and indistinguishable particles, most probable configuration, fluctuations. Bosons, fermions and classical limit (Maxwell-Boltzmann)

Tutorials and Worked problems
Counting, Arrangements and Combinations, Distributions (mean, variance, moments, Binomial, Poisson, Gaussian, Central Limit Theorem), classical vs quantum (indistinguishability) behaviour, Stirling approximation, Degeneracy/statistical weight of a quantum system (atom of hydrogen).

Lecture Series: Methods of Statistical Physics
Postulates, Extremum Principle, Lagrange multipliers, Work and heat, Statistical interpretation of entropy (Boltzmann postulate and Boltzmann constant), temperature and pressure

Lecture Series: Maxwell-Boltzmann Distribution
The partition function, Definition, Partition function and thermodymanics, Domains of validity of M.B statistics for quantum systems, Applications of Maxwell-Boltzmann distribution: The two-level system, The ideal monoatomic gas, The one-dimensional harmonic oscillator, Internal degrees of freedom, The diatomic molecule, The chemical potential of an ideal diatomic gas, Equilibrium conditions and dissociation

Tutorials and Worked problems
Maths: Gaussian integrals, gamma integrals and geometric series, Ideal gas law in terms of Boltzmann constant, number density of particles, partial pressures, Ideal gas and MB equilibrium, MB distribution of molecular velocities, Properties of ideal gas, Rigid rotator energy spectrum and partition function/temperature dependence, Gas of harmonic oscillators: spectrum, partition function, thermodynamic properties, Harmonic solid/Einstein temperature/Dulong-Petit law, Dissociation equilibrium of H2 molecule, Ionisation equilibrium of H atom/Saha-Boltzmann equation, Spin-flip system/paramagnets: order/disorder, partition function, entropy and magnetisation energy, adiabatic cooling and cryogenics

Lecture Series: Quantum Statistics
The Ideal Fermion Gas, General Properties, Applications:Free electron theory of metals, Model for the atomic nucleus, White dwarf stars. The Ideal Boson Gas, General Properties, Applications: The Photon Gas, The Bose-Einstein Condensation

Tutorials and Worked Problems
Basic calculations of Fermi energy from electron density data, Total energy of the free electron gas, Blackbody radiator, Temperature dependence of Blackbody spectrum

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	First in class test: problem with 3/4 short numerical questions. On counting and particle in box model only.	10%	Week 5
In Class Test	Second in class test: problem with 3/4 short numerical questions. On Maxwell-Boltzmann chapter only	10%	Week 10

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

Mike Glazer and Justin Wark: 2001, Statistical Mechanics A Survival Guide, First edition, Chapters 1-9, Oxford University Press, 0 19 850815 8,
Jean-Paul Mosnier/Moodle Notes/DCU: 2009, Statistical Physics,
F. Mandl: 2002, Statistical Physics, Second Edition, 2002 reprint, Chapters 1-7, 9-11, Wiley,
L.D. Landau and E.M. Lifshitz: 2001, Statistical Physics, 3rd Edition, part1, Butterworth Heinemann,

Other Resources

None