This course is given to all second year physicists
and is examined on paper A1 at the end of the second year.
I gave this lecture course up until the end of Hilary Term 2011.
In this course we introduce the subject of
statistical mechanics. This is
a thermodynamic theory in which account is taken of
the microscopic properties of individual atoms or
molecules analysed in a statistical fashion.
Statistical mechanics allows macroscopic properties to be calculated from
the statistical distribution of the microscopic behaviour
of individual atoms and molecules.
Boltzmann factor. Partition function and its relation to internal
energy, entropy, Helmholtz energy, heat capacities and equations
of state. Quantum states and the Gibbs hypothesis (non-examinable).
Density of states. Application to: the spin-half paramagnet;
simple harmonic oscillator (Einstein model of a solid); perfect gas;
vibrational excitations of a diatomic gas; rotational excitations of
a heteronuclear diatomic gas. Equipartition of energy. Bosons and
fermions: Fermi-Dirac and Bose-Einstein distribution functions
for non-interacting, indistinguishable particles. Partition function
for bosons and fermions when the particle number is not restricted
and when it is: microcanonical, canonical and grand canonical
ensemble (non-examinable). Chemical potential. High-temperature
limit and the Maxwell-Boltzmann distribution. Simple treatment
of fluctuations (non-examinable). Low-temperature limit
for fermions: Fermi energy and low-temperature limit of the heat
capacity; application to electrons in metals and degenerate stars.
Low-temperature limit for boson gas: Bose-Einstein condensation:
calculation of the critical temperature of the phase transition;
heat capacity; relevance to superfluidity in helium. The photon
gas: Planck distribution, Stefan-Boltzmann law. Kirchhoff's law
- Course-related links
I have written a book, together with
Professor Katherine Blundell,
``Concepts in Thermal Physics''
which was published by Oxford University Press in 2006 (2nd edition 2010, now available).
This covers kinetic theory, thermodynamics, statistical mechanics and applications in astrophysics, atmospheric physics, information theory and many other areas.
Other recommended textbooks are listed in the first course handout.
- Thermodynamics-related links
(Updated: July 2012)