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Thermodynamics and Statistical Mechanics

Code: 100157
Credits: 9
2026/2027
Degree programme Type Course
Physics OB 3

Contact lecturer

Name :
Vicenç Mendez Lopez
Email :
vicenc.mendez@uab.cat

Group languages

You can consult this information at the end of the document.

Prerequisites

Some course of introduction to thermodynamics is preferred

Objectives

1. To understand the conditions of a thermodynamical systems 

2. To identify system and environment

3. Distinguish between state variables and process variables

4. To interpret the different kinds of thermal processes

5. To understand the concept of the thermodynamical limit

6. To derive the partition function of a system and find the state equations from it

7. To apply the energy equipartition theorem

8. To distinguish between reversible and irreversible processes

9. To change the fundamental equation of representation

10.To understand the microscopic concept of pressure of a gas

11. Interpret the stability criteria and relate them with the onset of phase ransitions

12. To analyze the first and second order phase transitions. Understand the Landau theory for phase transitions 

13. To construct the Ising model. Apply the mean field approximation, the interactions between nearest neighbours and the method of transfer matrix

14. To distinguish between ideal and real gases. Connect the intermolecular potential with the virial expansion

15. To understand the processes of cooling gases 

16. To interpret the electromagnetic radiation as a gas of bosons and obtain the equations of state

17. Make use of the grancanonical ensable to study the fluctuations in the number of particles and the phase equilibrium

Learning outcomes

  1. Use critical reasoning, show analytical skills, correctly use technical language and develop logical arguments
  2. Transmit, orally and in written format, physical concepts of a certain complexity, making them understandable to non-specialist settings.
  3. Distinguish between the domains of action in thermodynamics and statistical mechanics.
  4. Establish the thermodynamic variables describing equilibrium states for different systems and propose the corresponding Gibbs' equation.
  5. Relate stability criteria to the principles of thermodynamics and verify the stability of a thermodynamic system.
  6. Describe the information contained in the different equations of state within a system.
  7. Describe the properties that differentiate real behaviour from ideal in a gas.
  8. Describe the physical information contained in virial coefficients.
  9. Physically interpret the partial derivatives of the distinct thermodynamic quantities.
  10. Clarify the need for a classic or quantum statistical description for an ideal gas.
  11. Analyse limits at low and high temperature for any given system.
  12. Analyse the information contained in the distinct phase diagrams in equilibrium.
  13. Calculate the number of microstates for classic and discrete systems.
  14. Calculate the partition function of a system in any group.
  15. Deduce the equations of state within a system from the partition function.
  16. Deduce the fundamental equation in different representations.
  17. Calculate the second virial coefficient from the interaction potential.
  18. Identify the social, economic and environmental implications of academic and professional activities within one's own area of knowledge.

Contents


1. Formal structure of thermodynamics


1.0. Review of the laws of thermodynamics
1.1. The fundamental equation
1.2. Euler's form of internal energy. Gibbs-Duhem equation
1.3. Transformed by Legendre. Thermodynamic potentials
1.4. Maxwell relations for a fluid
1.5. Stability conditions

2. Microscopic description of macroscopic systems

2.1. Microstats and Macrostats. Phase space
2.2. Ensembles
2.3. Microcanonical ensemble

2.4 Thermodynamic-Statistical Mechanical Connection
2.5. Application to the ideal monoatomic gas

2.6. Discrete systems

2.7. Statistical entropy

2.8. Maxwell-Boltzmann distribution
2.9. Pressure
2.10. Effusion

3. Canonical ensemble

3.1. Partition function.

3.2. Ideal systems

3.3. Energy degeneration

3.4. The ideal monoatomic gas in a potential
3.5. Equipartition of energy theorem
3.6. Discrete systems
 

4. Magnetic systems

4.1. Thermodynamics of magnetic systems
4.2. Classical paramagnetism
4.3. Spin Paramagnetism 1/2. Microcanonical and canonical treatments
4.4. Adiabatic demagnetization


5. Phase transitions

5.1. Classification. P-V, P-µ and P-T diagrams. Clapeyron equation
5.2. Vapor-condensed phase equilibrium
5.3. The critical point

5.4. Ehrenfest classification of phase transitions

5.5. Second order phase transitions.

6. Ising model
6.1. One-dimensional chain

6.2. One-dimensional open chain

6.3. Meanfield approximation


7. Real gases

7.1. Compressibility factor. Virial expansion
7.2. Interaction potential. Configuration partition function
7.3. Second coefficient of the virial. Van der Waals equation
7.4. Reticular gas

7.5. Corresponding State Law
7.6. Joule and Joule-Kelvin expansions

 

8. Photons

8.1. Statistics of bosons and fermions

8.2 Energy density. Degeneration of states
8.3. Planck distribution
8.4. Equations of state of a photon gas

 

9. Macrocanonical collectivity

9.1. Partition function
9.2. Connection with thermodynamics

9.3. Discrete systems

9.4. Fluctuations

9.5. Ideal systems. The ideal monoatomic gas

9.6. Solid-vapor equilibrium

 


 

Learning activities and methodology

Title Hours ECTS Learning outcomes
Study 136 5.44 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Teaching lectures 45 1.8 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Delivered solved problems in class 5 0.2 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Problems 25 1 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17


  • Classroom activities

Lectures

The lectures will be taught by the theory teacher where the concepts, developments and basic principles of the subject will be presented.

Teaching Problems

The problem's teacher will solve in class some of the problems of the collection that previously the student will have had to try to solve. We will try to make use of dynamical discussions of alternative results.

Tutorial activities

In case of virtual teaching along the seasons of tutorial activites questions of theory and practical will be solved in class



  • Authonomous activities

Study

We have counted that the student must dedicate 2 hours of study for each hour of master class.


  • Supervised activities

Solved problems in class

Up to five 1-hour sessions will be held during problem periods, where students will solve a problem that will be turned in and graded.



SURVEYS

It is planned to leave 15 minutes at the end of class when the institutional surveys need to be answered



Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
First part exam 37,5% 3 0.12 3, 4, 5, 6, 7, 9, 10, 13, 14, 15, 16
Second part exam 37,5% 3 0.12 7, 8, 11, 12, 17
Delivered solved problems in class 25% 5 0.2 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Final exam 75% 3 0.12 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17

Partial exams and final exam

There will be two partial exams. The first one will evaluate the first part of the course while the second will evaluate the rest. in case the mean of the qualifications is less than 4 the student must do the final exam. To be examined in the final exam is compulsery to be examend in the first and second partial exams.


Remedial exam

Those who have been evaluated in the partial exams obtaining a qualification lower than 4 (compulsory) or those who want to improve their marks (optional) may do the remedial exam. In the latter case, the final mark will be the best of the marks obtained from the remidial and partials examams


Delivered of in-class solved problems

The 5 in-class solved problems that are delivered at he end of the class will be graded and will count toward the final course grade. This graded component is not recoverable.



Final Grade

The final grade will be 75% of the exam plus 25% of the in-class problem-solving if the final exam grade is 4.0 or higher. If the test score is less than 4.0 or if the final grade calculated above does not reach 5, the student has another opportunity to pass the course through a make-up exam, which will be held on a date set by the program coordinator. The final grade will be recalculated as before: if the make-up exam grade is 4.0 or higher, the final grade will be 75% of the exam plus 25% of the seminar problems.


Single Assessment

Students who have opted for the single-exam assessment mode must take a final exam consisting of a problem-based test. When they have finished, they will submit the problems assigned by the instructor. These exams will be held on the same day, at the same time, and in the same location as the second midterm exams for the continuous assessment mode.


Use of AI

In this course, the use of Artificial Intelligence (AI) technologies is not permitted in any of its phases. Any graded activity that includes AI-generated passages will be considered an act of academic dishonesty and may result in a partial or full penalty on the activity's grade, or more severe sanctions in more serious cases.


Irregularities on Assessments

The commission of any irregularity on an assessment (academic fraud, plagiarism, or improper use of AI), which could lead to a significant change in the grade, will result in a grade of 0 for that assessment. In the event that multiple irregularities occur in the assessments for the same course, the final grade for that course will be 0. Additionally, disciplinary action may be taken against the student who commits any of these irregularities.




Bibliography

Modern texts

  • Robert H Swendsen, An Introduction to Statistical Mechanics and Thermodynamics (Oxford Univ. Press, 2012)
  • S. K. Roy, Thermal Physics And Statistical Mechanics (New Age International Publishers, 2001)
  • K. Huang, Introduction to Statistical Physics, CRC, 2001
  • D. V. Schroeder, An Introduction to Thermal Physics, Addison Wesley, 2000
  • S. J. Blundell and K. M. Blundell, Concepts in Thermal Physics, Oxford UP, 2006
  • M. Criado-Sancho y J. Casas-Vázquez, Termodinámica química y de los procesos irreversibles, Pearson/Addison Wesley, Madrid, segona edició, 2004.
  • Yi-Chen Cheng, Macroscopic and Statistical Thermodynamics (World Scientific, 2006)

 

Classical texts

  • J. J. Brey, J. de la Rubia, J. de la Rubia, Mecánica Estadística, UNED, 2001
  • R. Kubo, Thermodynamics, North Holland, Amsterdam, 1968.
  • F. Reif, Fundamentals of Statistical Physics and Thermal Physics, McGraw-Hill, 1985
  • D. A. McQuarrie, Statistical Mechanics, Harper Collins, 1976
  • M.W. Zemansky y R.H. Dittman, Calor y Termodinámica, McGraw-Hill, Madrid, 1990. 
  • C.J. Adkins, Termodinámica del equilibrio, Reverté, Barcelona, 1977.
  • P.W. Atkins, La Segunda ley, Prensa científica, Barcelona 1992.

Software

We shall make use of  Python for the simulations activities along the second semester

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan annual morning-mixed
(PAUL) Classroom practices 1 Catalan annual morning-mixed
(TE) Theory 2 Catalan annual morning-mixed
(PAUL) Classroom practices 2 Catalan annual morning-mixed