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Outline:

This module aims to establish a secure structural foundation to an understanding of statistical thermodynamics, which is essential to the study of processes at the microscopic level and of condensed matter physics. The module: reviews concepts in classical thermodynamics, and presents the basic ideas and methods appropriate for the description of systems containing very many identical particles; compares and contrasts the statistical mechanics of ideal gases comprised of bosons, fermions, and classical particles; develops the statistical mechanics of systems of harmonic oscillators; applies the statistical framework to form an appreciation of the thermal and electrical properties of solids.

Aims:

The main aim of this module is to provide a statistical mechanical foundation to the classical laws of thermodynamics, with an emphasis on their application to understand the thermodynamic properties of matter. The specific objectives are as set out in the module outline. Most of the objectives involve establishing the properties of gases of various types, and then using this to study electromagnetic radiation, electrons in metals, superconductors, white dwarfs, neutron stars, as well as the more prosaic gases and condensable vapours.Ìý

•ÌýÌý ÌýTo review concepts in classical thermodynamics, and to present the basic ideas and methods appropriate for the description of systems containing very many identical particles
•ÌýÌý ÌýTo compare and contrast the statistical mechanics of ideal gases comprised of bosons, fermions, and classical particles
•ÌýÌý ÌýTo develop the statistical mechanics of systems of harmonic oscillators
•ÌýÌý ÌýTo apply the statistical framework to form an appreciation of the thermal and electrical properties of solids

Intended Learning Outcomes:

On successful completion of PHAS0024 a student will be able to:

•ÌýÌý Ìýstate and understand the four laws of thermodynamics
•ÌýÌý Ìýunderstand that the state of a system in thermodynamic equilibrium can be described by func¬tions of state, and distinguish between isothermal/adiabatic and reversible/irreversible processes
•ÌýÌý Ìýunderstand and manipulate the equation of state
•ÌýÌý Ìýexplain the difference between a thermodynamic macrostate of the system and an atomistic microstate of a system
•ÌýÌý Ìýenumerate the microstates for simple systems of indistinguishable quantum particles
•ÌýÌý Ìýexpress the mean value of a thermodynamic function in terms of the probability distribution of microstates
•ÌýÌý Ìýpostulate that the a priori probabilities of a system being in anyone of its accessible microstates are equal for an isolated system
•ÌýÌý Ìýargue that the entropy is the logarithm of the statistical weight of a system, and give Boltzmann's definition of entropy
•ÌýÌý Ìýstate the condition for equilibrium in an isolated system
•ÌýÌý Ìýobtain definitions of temperature, pressure and chemical potential in terms of entropy
•ÌýÌý Ìýderive the Boltzmann distribution for a system in equilibrium with a heat bath
•ÌýÌý Ìýrelate the average energy and the Helmholtz free energy of the system to the partition function
•ÌýÌý Ìýstate the definition for equilibrium in a system in contact with a heat bath
•ÌýÌý Ìýunderstand the significance of the Gibbs free energy in multi-component systems
•ÌýÌý Ìýderive the Clausius-Clapeyron equation and understand its application to phase transitions
•ÌýÌý Ìýderive the partition function for a quantum oscillator
•ÌýÌý Ìýderive the density of momentum and energy states of a single free particle
•ÌýÌý Ìýstate the definition of a boson and a fermion in terms of the spin of the particles, and the occupation of single particle states
•ÌýÌý Ìýderive the Bose-Einstein (BE), Fermi-Dirac (FD), and Maxwell¬ Boltzmann (MB) distribution functions
•ÌýÌý Ìýexplain the role played by the chemical potential in these derivations, and be familiar with the partition function
•ÌýÌý Ìýapply BE statistics to the case of a photon gas, and obtain Planck's Law of the energy density of black-body radiation, and sketch the temperature dependence of this energy spectrum
•ÌýÌý Ìýunderstand the physics and behaviours of BE condensation and superfluidsÌý
•ÌýÌý Ìýapply FD statistics to a free electron gas, and white dwarf and neutron stars
•ÌýÌý Ìýexpress the criterion for validity of the classical regime in terms of occupation numbers of single particle energy levels
•ÌýÌý Ìýdetermine the average kinetic energy of an ideal gas molecule, and obtain the equation of state of an ideal gas by differentiating the Helmholtz free energy with respect to volume
•ÌýÌý Ìýdetermine the heat capacity of phonons in a solid
•ÌýÌý Ìýdetermine the electrical conductivity of conductor and semi-conductors

Teaching and Learning Methodology:

This module is delivered via weekly lectures supplemented by a series of problem solving tutorials and additional discussion.

In addition to timetabled lecture and PST hours, it is expected that students engage in self-study in order to master the material. This can take the form, for example, of practicing example questions and further reading in textbooks and online.