PHYM001 - Module Description

MODULE TITLE	Statistical Physics					CREDIT VALUE	15
MODULE CODE	PHYM001		MODULE CONVENER			Dr L.A. Correa

DURATION	TERM	1	2	3	Number Students Taking Module (anticipated)		70
	WEEKS	T1:01-11

DESCRIPTION – summary of the module content (100 words)

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 – 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)

On successful completion of this module you 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 Fermi-Dirac and Bose-Einstein distributions;
describe superfluidity in liquid helium, Bose-Einstein 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 time-management strategies.

SYLLABUS PLAN – summary of the structure and academic content of the module

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

22 hours

Guided independent study

128 hours

Placement/study abroad

0 hours

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS