Statistical Physics - 2024 entry

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 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.

I. Introduction

aims and methods of thermodynamics and statistical mechanics; differences between thermodynamics and mechanics

II. Thermodynamic equilibrium

internal energy; hydrostatic and chemical work; heat; the first law of thermodynamics

III. Reversible, irreversible and quasistatic processes

entropy; the Clausius and Kelvin statements of the second law

IV. Criteria for equilibrium

enthalpy; the Helmholtz and Gibbs free energies; the grand potential

V. Statistical mechanics

microstates and macrostates; assumption of equal a priori probabilities

VI. The canonical ensemble and the Boltzmann distribution

partition functions; derivation of thermodynamic quantities

VII. Systems in contact with a heat bath

vacancies in solids; paramagnetism

VIII. Reversible quasistatic processes

statistical meaning of heat and work; Maxwell's relations; the generalised Clausius inequality; Joule-Thomson effect; the thirdlaw of thermodynamics

IX. Heat capacity of solids

the Einstein and Debye models

X. Partition function for ideal gas

validity of classical statistical mechanics; Maxwell velocity distribution; kinetic theory; approach to equilibrium

XI. Diffusion of particles between systems

the grand canonical ensemble; the grand partition function; application to the ideal gas; chemical reactions

XII. Quantum gases

Bose-Einstein, Fermi-Dirac and Boltzmann statistics; Black-body radiation; Bose-Einstein condensation; The degenerate electron gas

XIII. A selection of more-advanced topics:

phase equilibria; Monte Carlo methods; mean-field theory of second-order phase transitions; the kinetics of growth

An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.

 

Physics Modules with PHY Codes

Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.

ELE:

 

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