Description

This module builds upon the PHY2023 Thermal Physics module taken by students at Stage 2. It emphasises four aspects of statistical physics by applying them to a number of physical systems in equilibrium. Firstly, it is shown that a knowledge of the thermodynamic state depends upon an enumeration of the accessible quantum states of a physical system; secondly, that statistical quantities such as the partition function can be found directly from these states; thirdly, that thermodynamic observables can be related to the partition function, and fourthly, that the theoretical results relate to experimental observations.

Module Aims

This module aims to give students an understanding of how the time-symmetric laws of quantum mechanics obeyed by all systems can be linked, through a chain of statistical and thermodynamic reasoning, to the (apparently time-asymmetric) natural processes occurring in macroscopic systems. It also furnishes the theoretical background in statistical mechanics that can be drawn on in other modules e.g. PHYM003 Condensed Matter II.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. describe the role of statistical concepts in understanding macroscopic systems;
  2. deduce the Boltzmann distribution for the probability of finding a system in a particular quantum state;
  3. apply statistical theory to determine the magnetisation of a paramagnetic solid as a function of temperature;
  4. deduce the Einstein and Debye expressions for the heat capacity of an insulating solid and compare the theory with accepted experimental results;
  5. deduce the equation of state and entropy for an ideal gas;
  6. extend the theory to deal with open systems where particle numbers are not constant;
  7. deduce the Fermi-Dirac and Bose-Einstein distributions;
  8. describe superfluidity in liquid helium, Bose-Einstein condensation and black body radiation;
  9. deduce the heat capacity of a electron gas;
• Discipline Specific Skills and Knowledge:
  10. apply the laws of thermodynamics and statistical mechanics to a range of physical systems
• Personal and Key Transferable / Employment Skills and Knowledge:
  11. information retrieval from the WWW;
  12. communication skills via discussions in classes;
  13. Meet deadlines for completion of work to be discussed in class and must therefore develop appropriate time-management strategies.

Syllabus Plan

1. Introduction
   aims and methods of thermodynamics and statistical mechanics; differences between thermodynamics and mechanics
2. Thermodynamic equilibrium
   internal energy; hydrostatic and chemical work; heat; the first law of thermodynamics
3. Reversible, irreversible and quasistatic processes
   entropy; the Clausius and Kelvin statements of the second law
4. Criteria for equilibrium
   enthalpy; the Helmholtz and Gibbs free energies; the grand potential
5. Statistical mechanics
   microstates and macrostates; assumption of equal a priori probabilities
6. The canonical ensemble and the Boltzmann distribution
   partition functions; derivation of thermodynamic quantities
7. Systems in contact with a heat bath
   vacancies in solids; paramagnetism
8. Reversible quasistatic processes
   statistical meaning of heat and work; Maxwell's relations; the generalised Clausius inequality; Joule-Thomson effect; the thirdlaw of thermodynamics
9. Heat capacity of solids
   the Einstein and Debye models
10. Partition function for ideal gas
    validity of classical statistical mechanics; Maxwell velocity distribution; kinetic theory; approach to equilibrium
11. Diffusion of particles between systems
    the grand canonical ensemble; the grand partition function; application to the ideal gas; chemical reactions
12. Quantum gases
    Bose-Einstein, Fermi-Dirac and Boltzmann statistics; Black-body radiation; Bose-Einstein condensation; The degenerate electron gas
13. A selection of more-advanced topics:
    phase equilibria; Monte Carlo methods; mean-field theory of second-order phase transitions; the kinetics of growth

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Goodstein D.L. (2002), States of Matter, Dover, ISBN 978-0-486-49506-4

Supplementary texts:

• Bowley R. and Sanchez M. (1996), Introductory Statistical Mechanics, Oxford Science Publications, ISBN 0-19-851794-7
• Mandl F. (1988), Statistical Physics (2^nd edition), John Wiley, ISBN 978-0-471-91533-1

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phym001

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous