Programme And Module Handbook
Course Details in 2025/26 Session

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Module Title LI Statistical Physics and Entropy
SchoolPhysics and Astronomy
Department Physics & Astronomy
Module Code 03 17296
Module Lead Dr Vincent Boyer
Level Intermediate Level
Credits 10
Semester Semester 1
Pre-requisites LC Electromagnetism and Temperature and Matter - (03 19750)
Restrictions BSc/MSci Physics, Physics & Astrophysics, Physics & Space Research, Physics with Particle Physics, Theoretical Physics, Theoretical Physics & Applied Mathematics, Physics with Biomedical Physics, Physics with Business Management. Also available to BNat Sci students as an option.
Contact Hours Lecture-24 hours
Guided independent study-76 hours
Total: 100 hours

The laws of Thermodynamics underpin everything from life itself to the evolution of the universe. Moreover, they also address fundamental problems such as the “arrow of time”. Although Thermodynamics was developed in the nineteenth century, modern developments have reinforced Einstein’s view that it is "the only physical theory of universal content which I am convinced will never be overthrown.” Whilst statistics allow us to calculate the macroscopic properties of a system from microscopic theory, Thermodynamics has a power all of its own, even when we don’t understand the microscopic physics. The central idea that links the two approaches is the concept of entropy, the understanding of which lies at the heart of this module. The main topics are organised as follows:
1. Statistical Physics: Kinetic theory and molecular collisions; Mean free-path, diffusion and the random walk; Binomial, Poisson and Gaussian distributions.
2. Thermal Equilibrium: Microstates, macrostates and Boltzmann entropy; Temperature and the Boltzmann distribution; Equipartition, harmonic oscillators, black-body radiation, stimulated emission and lasers.
3. Classical Thermodynamics: 1st Law and 2nd Law (Clausius & Kelvin); Reversible & irreversible processes; Reversible heat, latent heat and heat capacity; Carnot cycle, heat engines and refrigerators; Functions of state, Gibbs & Helmholtz free energies and enthalpy; Thermodynamics of rubber elasticity, surface tension and liquid-vapour equilibrium; Maxwell Relations and Joule-Kelvin effect; Absolute Zero and the 3rd Law of Thermodynamics.
4. Advanced Topics: Perpetual Motion and Maxwell’s Demon; Information, Gibbs entropy and negative temperatures; Introduction to quantum statistics of identical particles.

Learning Outcomes

By the end of the module the student should be able to:

Analyse simple physical systems using Boltzmann statistics;
Solve problems for molecular collisions, diffusion and the random walk;
Find microstates, macrostates and Boltzmann entropy of simple systems;
Find entropy changes for reversible and irreversible processes;
Use 1st & 2nd laws to analyse ideal heat engines and refrigerators;
Find Gibbs free energy, entropy and enthalpy of simple systems;
Derive and apply Maxwell Relations where needed;
Apply the 3rd Law to systems near Absolute Zero.

Assessment 17296-01 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%)
17296-02 : Assessed problems : Coursework (20%)
Assessment Methods & Exceptions Coursework (20%); 1.5 hour Examination (80%)
Other None
Reading List