# Coursebooks

## Statistical thermodynamics

#### Lecturer(s) :

Hagfeldt Ulf Anders

English

#### 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

UCV, heat and work, Entropy, Helmholtz' and Gibbs' free energies, Chemical potential

4. Ensembles

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

5. Quantum statistics

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

6. Applying partition functions and ensembles

Heat capacity of solids, Computational chemical methods

7. The solid state

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

8.  Semiconductors

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

9. p-n junctions

Equilibrium. applied bias, diode equation, photovoltaics

#### Keywords

Boltzmann distribution

Partition function

Ensembles

Quantum statistics

Semiconductors

p-n junction

#### Learning Prerequisites

##### Important concepts to start the course

Laws of thermodynamics

Equations for quantum energy levels of particle-in-a-box, rotation and vibtration.

#### 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
• Apply Fermi-Dirac and Bose-Einstein statistics to solids
• Demonstrate the formation of a p-n junction
• Describe the principles of photovoltaics

#### Teaching methods

Lectures with hand outs. Exercises.

Written exam

#### Supervision

 Office hours No Assistants Yes Forum No

#### Resources

No

##### Bibliography

Handouts of Lecture Notes and exercises

Reference books:

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

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.

### In the programs

• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
Statistical thermodynamics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks
• Passerelle HES - CGC, 2019-2020, Spring semester
• Semester
Spring
• Exam form
Written
• Credits
3
• Subject examined
Statistical thermodynamics
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
1 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German