F11TS - Thermodynamics and Statistical Mechanics

Course leader(s):

Robert Andrew Weston (Edinburgh, September)

Aims

This course aims to equip students with the key approaches and mathematical techniques of thermodynamics and statistical mechanics, to illustrate them with a variety of applications, and to show how they can be used to model and understand aspects of the Earth's atmosphere.

Syllabus

1. Mathematical Foundations (1.1 1. Differential 1-forms, 1.2 2. Integrating differential 1-forms, 1.3 3. Using differential 1-forms in thermodynamics)

2. The Laws of Thermodynamics (2.1 1. Physical terminology, 2.2 2. The zeroth law, 2.3 3. The 1st law, 2.4 4. The 2nd law, 2.5 5. The 3rd law)

3. Entropy and Heat Engines (3.1 1. Kelvin's Statement of the 2nd Law, heat engines & heat pumps, 3.2 2. Irreversibility and increase of entropy, 3.3 3. Equilibrium and the maximum entropy principle)

4. Thermodynamics Potentials and Maxwell Relations (4.1 1 Legendre Transformation, 4.2 2 Thermodynamic Potentials, 4.3 3 Physical Importance, 4.4 4 Maxwell Relations, 4.5 5 Chain Rules for Partial Differentiation)

5. Heat Capacity and the Ideal Gas (5.1 1 Heat Capacity, 5.2 2 The Ideal Gas, 5.3 3 Real Gases and Phase Transitions)

6. Foundations of Statistical Mechanics (6.1 1 Macrostates and Microstates, 6.2 2 From Time Averages to Expectation Values, 6.3 3 Revision of Probability, 6.4 4 Distributions and Ensembles, 6.5 5 The Methodology of Statistical Mechanics)

7. Entropy and the Microcanonical Ensemble (7.1 1 The Statistical Definition of Entropy, 7.2 2 Isolated Systems with fixed E, V, N - the Microcanonical Ensemble)

8. The Canonical and the Grand Canonical Ensemble (8.1 1 Interacting Systems with fixed T, V, N - the Canonical Ensemble, 8.2 2 Interacting Systems with fixed T, V, µ - the Grand Canonical Ensemble, 8.3 3 Which ensemble should we use?)

9. Application I: the Ideal Gas (9.1 1 Single Particle States, 9.2 2 The Ideal Gas in Statistical Mechanics, 9.3 3 Boson and Fermions)

10. Application II: Boson and Fermion Gases and Planck’s Formula (10.1 1 Ideal Boson and Fermion Gases, 10.2 2 E close to µ ., 10.3 3 The Photon Gas: Planck’s Formula, 10.4 4 Other Applications)

11. Advanced Applications

Learning outcomes

By the end of the course, students should be able to do the following:

state and interpret the four laws of thermodynamics and associated concepts
apply the four laws to describe physical systems including heat engines and heat pumps
manipulate and relate thermodynamics potentials and derive and apply Maxwell Relations
use Boyle’s Law and Charles’ Law to develop the description of ideal gases
develop and apply the fundamental concepts of statistical mechanics including the three ensembles
use statistical mechanics to describe ideal gases and ideal gases of Bosons and Fermions
apply the formalism of thermodynamics and statistical mechanics to analyse a range of more advanced applications

Further details

Curriculum explorer: Click here

SCQF Level: 11

Credits: 15