Study information

# Statistical Physics - 2023 entry

MODULE TITLE CREDIT VALUE Statistical Physics 15 PHYM001 Dr Luis A. Correa (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
 Number of Students Taking Module (anticipated) 70
DESCRIPTION - summary of the module content
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.

AIMS - intentions of the module

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) (see assessment section below for how ILOs will be assessed)

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 - summary of the structure and academic content of the module
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
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 22 128
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning & teaching activities 20 hours 20×1-hour lectures Scheduled learning & teaching activities 2 hours 2×1-hour problems/revision classes Guided independent study 30 hours 5×6-hour self-study packages Guided independent study 16 hours 4×4-hour problem sets Guided independent study 82 hours Reading, private study and revision

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Guided self-study (0%) 5×6-hour packages (fortnightly) 1-13 Discussion in class
4 × Problems sets (0%) 4 hours per set (fortnightly) 1-13
Solutions discussed in problems classes.

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 0 100
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Final Examination 100% 2 hours 30 minutes (January) 1-10 Mark via MyExeter, collective feedback via ELE and solutions.

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Whole module Written examination (100%) 1-10 August/September assessment period

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

RE-ASSESSMENT NOTES
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.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
ELE:

Type Author Title Edition Publisher Year ISBN
Set Goodstein, D.L. States of Matter Dover 2002 978-0486495064
Extended Bowley, R. and M. Sanchez Introductory Statistical Mechanics Oxford Science Publications 1996 0-19-851794-7
Extended Mandl, F. Statistical Physics 2nd John Wiley 1988 978-0-471-91533-1
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES PHY2023
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING 7 No Thursday 15th December 2011 Thursday 26th January 2023
KEY WORDS SEARCH Physics; Statistical Mechanics; Thermodynamics; Heat; Einstein; Quantum states; Partition function