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PH3012   Thermal and Statistical Physics

Academic year(s): 2019-2020

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF Level 9

Semester: 2

Planned timetable: 12 noon odd Mon, 2.00 pm even Tue, 12 noon Wed & Fri

The aim of this module is to cover at honours level the principles and most important applications of thermodynamics and statistical mechanics. The syllabus includes: equilibrium; the equation of state; the classical perfect gas; discussion of experimental results that lead to the three laws of thermodynamics; idealised reversible engines; the Clausius inequality; the classical concept of entropy and its connection to equilibrium; thermodynamic potentials; Maxwell's relations; open systems and the chemical potential; phase transitions and the Clausius-Clapeyron equation for first order transitions; higher order phase transitions; the connection between statistical physics and thermodynamics; the Boltzmann form for the entropy; microstates and macrostates; the statistics of distinguishable particles; the Boltzmann distribution; the partition function; statistical definition of the entropy and Helmholtz free energy; statistical mechanics of two-level systems; energy levels and degeneracy; quantum statistics: Bose-Einstein and Fermi-Dirac distributions; density of states; black-body radiation; Bose-Einstein condensation; Fermi energy; quantum gases and the classical limit; Maxwell-Boltzmann distribution; equipartition of energy; negative temperatures.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass 4 modules from {PH2011, PH2012, MT2501, MT2503} and ( pass at least 1 module from {PH3081, PH3082} or pass 2 modules from {MT2506, MT2507} )

Learning and teaching methods and delivery

Weekly contact: 3 lectures or tutorials.

Scheduled learning hours: 36

Guided independent study hours: 114

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 80%, Coursework = 20%

As defined by QAA
Written examinations : 80%
Practical examinations : 0%
Coursework: 20%

Re-assessment: Oral Re-assessment, capped at grade 7


Module coordinator: Dr I Leonhardt
Module teaching staff: Dr I Leonhardt, Dr A Rost

Additional information from school


Thermodynamics and Statistical Physics provide complementary approaches to understanding many-body states of matter. This course introduces the fundamental ideas and methods of both approaches and applies these to systems in thermal equilibrium, covering systems of both quantum mechanical and classical particles. Physical examples are used throughout to develop the ideas in a concrete way.


Aims & Objectives

To present the fundamental ideas and methods of Thermodynamics and Statistical Physics, and to develop these through simple examples and applications. The presentation includes:


  • Laws of thermodynamics
  • Thermodynamic potentials and Maxwell's relations
  • Application to simple thermodynamic systems
  • Phase transitions and introduction to Landau theory
  • Statistical ensemble of distinguishable particles and Boltzmann entropy
  • Counting for particles with quantum statistics
  • Important examples of statistical physics: paramagnets, heat capacity in crystals, ideal classical and quantum gases, Bose-Einstein condensation, and electrons in metals. White dwarfs and neutron stars.


Learning Outcomes

By the end of the course the students will be expected to:


  • State the laws of thermodynamics in their various forms and explain their physical significance.
  • Derive and state Maxwell's relations and apply them to problems in thermodynamics.
  • State the thermodynamic potentials and recognize the most appropriate potential for application to a particular problem.
  • Have a basic appreciation of the thermodynamics of first and second order phase transitions.
  • Derive and state the Boltzmann, Fermi-Dirac and Bose-Einstein distributions.
  • Know the key links between thermodynamics and statistical physics and apply these to problems.
  • Be able to explain the importance and significance of the partition function, and be able to construct partition functions for systems and extract thermodynamic properties from them.



Zeroth and first laws of thermodynamics, ideal gas illustrating a simple equation of state, thermal equilibrium, quasistatic and reversible processes. Second law of thermodynamics. Maxwell’s relations. Overview of the thermodynamic potentials. Conditions for equilibrium. 3rd law of thermodynamics. Phase transitions.

Microstate, macrostate, statistical weight, postulate of equal a priori probability, equilibrium postulate, Boltzmann form for the entropy. Statistics of distinguishable particles, Boltzmann distribution, partition function, general definition of the entropy, Helmholtz free energy. The statistical mechanics of a two level system. Quantum statistics: Bose-Einstein and Fermi-Dirac, density of states, black-body radiation, Bose-Einstein condensation, Fermi energy. De Broglie wavelength and quantum behaviour, gases in the classical limit, Maxwell-Boltzmann distribution.



PH3081 or PH3082 or (MT2506 and MT2507)






Continuous Assessment = 20%, 2 Hour Examination = 80%


Additional information on continuous assessment etc.


Please note that the definitive comments on continuous assessment will be communicated within the module.  This section is intended to give an indication of the likely breakdown and timing of the continuous assessment. 


This module is part of the core JH programme, and as such there is a summary of deadlines etc on the School’s Students and Staff web pages.   Students have compulsory tutorials every two weeks, with hand-in tutorial work counting for 20% of the module mark.


Accreditation Matters

This module contains material that is or may be part of the IOP “Core of Physics”.  This includes

Probability distributions

Black body radiation

Entropy, free energies and the Carnot Cycle

Kinetic theory of gases and the gas laws to Van der Waals equation

Statistical basis of entropy

Maxwell-Boltzmann distribution

Bose-Einstein and Fermi-Dirac distributions

Density of states and partition function


Recommended Books

Please view University online record:


General Information

Please also read the general information in the School's honours handbook that is available via