PHYM001 
Statistical Physics 
201718 

Dr E. Mariani 


Delivery Weeks: 
T1:0111 

Level: 
7 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
24 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 timesymmetric
laws of quantum mechanics obeyed by all systems can be linked, through a chain
of statistical and thermodynamic reasoning, to the (apparently timeasymmetric)
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 LowDimensional Physics.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 describe the role of statistical concepts in understanding macroscopic
systems;
 deduce the Boltzmann distribution for the probability of finding
a system in a particular quantum state;
 apply statistical theory to determine the magnetisation of a
paramagnetic solid as a function of temperature;
 deduce the Einstein and Debye expressions for the heat
capacity of an insulating solid and compare the theory
with accepted experimental results;
 deduce the equation of state and entropy for an ideal gas;
 extend the theory to deal with open systems where particle
numbers are not constant;
 deduce the FermiDirac and BoseEinstein distributions;
 describe superfluidity in liquid helium, BoseEinstein condensation
and black body radiation;
 deduce the heat capacity of a electron gas;

Discipline Specific Skills and Knowledge:
 apply the laws of thermodynamics and statistical mechanics to a range of physical systems

Personal and Key Transferable / Employment Skills and Knowledge:
 information retrieval from the WWW;
 communication skills via discussions in classes;
 Meet deadlines for completion of work to be
discussed in class and must therefore develop appropriate
timemanagement strategies.
Syllabus Plan

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

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

Reversible, irreversible and quasistatic processes
entropy; the Clausius and Kelvin statements of the second law

Criteria for equilibrium
enthalpy; the Helmholtz and Gibbs free energies; the grand potential

Statistical mechanics
microstates and macrostates; assumption of equal a priori probabilities

The canonical ensemble and the Boltzmann distribution
partition functions; derivation of thermodynamic quantities

Systems in contact with a heat bath
vacancies in solids; paramagnetism

Reversible quasistatic processes
statistical meaning of heat and work; Maxwell's relations;
the generalised Clausius inequality; JouleThomson effect;
the thirdlaw of thermodynamics

Heat capacity of solids
the Einstein and Debye models

Partition function for ideal gas
validity of classical statistical mechanics; Maxwell velocity
distribution; kinetic theory; approach to equilibrium

Diffusion of particles between systems
the grand canonical ensemble; the grand partition function;
application to the ideal gas; chemical reactions

Quantum gases
BoseEinstein, FermiDirac and Boltzmann statistics;
Blackbody radiation; BoseEinstein condensation;
The degenerate electron gas

A selection of moreadvanced topics:
phase equilibria; Monte Carlo methods; meanfield theory of
secondorder phase transitions; the kinetics of growth
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
82 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
113 
Discussion in tutorials

0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
113 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
110 
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
Prerequisite Modules 
Thermal Physics (PHY2023) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
110 
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 
01Oct10 
Revised 
18Feb14 