# Fiches de cours

## Statistical thermodynamics

#### Enseignant(s) :

Hagfeldt Ulf Anders

English

#### Remarque

Seulement en 2018-19

#### Summary

This course enables the acquisition of basic concepts in statistical thermodynamics including the Boltzmann distribution law, partition functions, ensembles, calculations of thermodynamic properties, Bose-Einstein and Fermi-Dirac statistics, metals, semiconductors, p-n junctions and photovoltaics.

#### Content

1. The Boltzmann distribution law

Derivation, Approximation

2. Partition function

The translational, rotational, vibrational and electronic partition functions

3. Thermodynamic functions from statistical thermodynamics

U, CV, heat and work, Entropy, Helmholtz¿ and Gibbs¿ free energies, Chemical potential

4. Ensembles

The canonical ensemble, the canonical partition function, the equilibrium constant

5. Non-ideal gas

Virial coefficients, Intermolecular forces

6. Quantum statistics

Bose-Einstein statistics, Fermi-Dirac statistics, the grand canonical partition function

7. The solid state

Specific heat of crystals, Electronic energy levels and density of states in metals, Fermi level

8. Photon gas and blackbody radiation

Brief introduction

9. Semiconductors

Energy levels, density of states, intrinsic semiconductors, n- and p-doping

10. p-n junctions

Equilibrium. applied bias, diode equation, photovoltaics

#### Learning Outcomes

By the end of the course, the student must be able to:
• Contextualise the connection between quantum mechanics and thermodynamics
• Apply the molecular partition functions
• Derive the vibrational and translational partition function
• Derive and compute thermodynamic functions from partition functions
• Describe the different ensembles
• Describe a non-ideal gas from a statistical thermodynamic point of view
• Apply Fermi-Dirac and Bose-Einstein statistics to solids and photons
• Describe the electronic properties of semiconductors
• Demonstrate the formation of a p-n junction
• Describe the principles of photovoltaics

#### Teaching methods

Lectures with hand outs. Exercises.

Written exam

#### Resources

##### Bibliography

Handouts of Lecture Notes

Recommended book:

Benjamin Widom, Statistical Mechanics: A Concise Introduction for Chemists, Cambridge University Press - 2002, ISBN-13: 978-0521009669

Reference book (deeper in the theories and extra materials):

Donald A. McQuarrie, Statistical Mechanics, University Science Books - 2000, ISBN - 1-891389-15-7.

For introduction and as a reference for classical thermodynamics

Pierre Infelta & Michael Grätzel, Thermodynamique: Principles et Applications. BrownWalker Press - 2006. ISBN - 1-58112-995-5.

### Dans les plans d'études

• Chimie, 2018-2019, Bachelor semestre 5
• Semestre
Automne
• Forme de l'examen
Ecrit
• Crédits
3
• Matière examinée
Statistical thermodynamics
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
1 Heure(s) hebdo x 14 semaines

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction
Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand