PHYM001 Statistical Physics 2017-18
Dr E. Mariani

Delivery Weeks: T1:01-11
Level: 7 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 70 students (approx)

### 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 and PHYM007 Low-Dimensional Physics.

### 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:
1. apply the laws of thermodynamics and statistical mechanics to a range of physical systems
• Personal and Key Transferable / Employment Skills and Knowledge:
1. information retrieval from the WWW;
2. communication skills via discussions in classes;
3. 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

Description Study time KIS type
20×1-hour lectures 20 hours SLT
2×1-hour problems/revision classes 2 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 82 hours GIS

#### Assessment

Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-13 Discussion in tutorials
0% 4 × Problems sets 4 hours per set Fortnightly 1-13 Solutions discussed in problems classes.
100% Final Examination 2 hours 30 minutes January 1-10 Mark via MyExeter, collective feedback via ELE and solutions.

### 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:

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules Thermal Physics (PHY2023) none

#### Re-assessment

Re-assessment is not available except when 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

Notes: See Physics Assessment Conventions.

#### KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 22 hrs
GIS - guided independent study 128 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%

#### Miscellaneous

 IoP Accreditation Checklist Not applicable to this module. Availability MPhys and PGRS only Distance learning YES (see PHYM011) Keywords Physics; Statistical Mechanics; Thermodynamics; Heat; Einstein; Quantum states; Partition function. Created 01-Oct-10 Revised 18-Feb-14