Thermodynamics
A.Y. 2023/2024
Learning objectives
The aim of the course is to provide the basics of Thermodynamics and to introduce some fundamental quantities, like heat, temperature, internal energy, entropy, and the thermodynamic functions. The course goal is also to show some applications to thermodynamic systems, to describe models for phase transitions and to introduce some elements of classical statistical mechanics.
Expected learning outcomes
At the end of the course, the student will
- know the laws of Thermodynamics;
- have the knowledge and skills necessary for describing thermodynamic systems;
- be able to approach and solve problems involving thermodynamic systems;
- use properly the thermodynamic functions;
- be able to analyze phase transitions with the thermodynamic potentials;
- know the basics of classical statistical mechanics
- know the laws of Thermodynamics;
- have the knowledge and skills necessary for describing thermodynamic systems;
- be able to approach and solve problems involving thermodynamic systems;
- use properly the thermodynamic functions;
- be able to analyze phase transitions with the thermodynamic potentials;
- know the basics of classical statistical mechanics
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Responsible
Lesson period
Second semester
Course syllabus
0. Elements of fluid statics and fluid dynamics
1. The zeroth law of thermodymanics
2. The thermal expansion
3. The heat
4. The kinetic theory of gases
5. The first law of thermodymanics
6. The ideal gases
7. The heat transfer
8. The second law of thermodynamics
9. The entropy
10. The Boltzmann equation
11. The real gases
12. The thermodynamics potentials
13. The statistical mechanics
14. The constant of the entropy
15. The fundamental postulates of thermodynamics
16. The phase transitions
The detailed programme can be found on the Ariel site (https://solivarest.ariel.ctu.unimi.it).
1. The zeroth law of thermodymanics
2. The thermal expansion
3. The heat
4. The kinetic theory of gases
5. The first law of thermodymanics
6. The ideal gases
7. The heat transfer
8. The second law of thermodynamics
9. The entropy
10. The Boltzmann equation
11. The real gases
12. The thermodynamics potentials
13. The statistical mechanics
14. The constant of the entropy
15. The fundamental postulates of thermodynamics
16. The phase transitions
The detailed programme can be found on the Ariel site (https://solivarest.ariel.ctu.unimi.it).
Prerequisites for admission
Knowledge of classical mechanics and of the topics covered in the Mathematical Analysis I and II courses.
Teaching methods
Lectures and Exercises.
Teaching Resources
Course lecture notes:
- S. Olivares, Appunti di Termodinamica (Milano University press)
The pdf file can be downloaded from https://libri.unimi.it/index.php/milanoup/catalog/book/127)
Further bibliography:
- E. Fermi, Thermodynamics.
- M. Planck, Treatise on Thermodynamics.
- P. Mazzoldi, M. Nigro, C. Voci, Fisica Vol. 1 (in Italian).
- H. Callen, Thermodynamics and an Introduction to Thermostatistics.
- The course material (slides, notes, ...) is available on the myAriel website of the course (https://myariel.unimi.it/course/view.php?id=1714).
- S. Olivares, Appunti di Termodinamica (Milano University press)
The pdf file can be downloaded from https://libri.unimi.it/index.php/milanoup/catalog/book/127)
Further bibliography:
- E. Fermi, Thermodynamics.
- M. Planck, Treatise on Thermodynamics.
- P. Mazzoldi, M. Nigro, C. Voci, Fisica Vol. 1 (in Italian).
- H. Callen, Thermodynamics and an Introduction to Thermostatistics.
- The course material (slides, notes, ...) is available on the myAriel website of the course (https://myariel.unimi.it/course/view.php?id=1714).
Assessment methods and Criteria
Learning will be verified through a written test lasting approximately a couple of hours in which you will be asked to solve the Thermodynamics problems proposed by applying the concepts and methodology learned during the teaching. Once the written test has been passed, the final oral exam takes place, which consists of an interview lasting approximately half an hour in which any unclear passages in the writings are discussed and the student must demonstrate that they have acquired the fundamental concepts of thermodynamics and their physical meaning.
The written test will be common to the two editions of the course, while the oral test will be generally held with the specific teacher of each course. During the written and oral exams, the correctness of the approach and methodology will be assessed, as well as the critical sense shown by the student.
The written test will be common to the two editions of the course, while the oral test will be generally held with the specific teacher of each course. During the written and oral exams, the correctness of the approach and methodology will be assessed, as well as the critical sense shown by the student.
FIS/01 - EXPERIMENTAL PHYSICS
FIS/07 - APPLIED PHYSICS
FIS/07 - APPLIED PHYSICS
Practicals: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Olivares Stefano
CORSO B
Responsible
Lesson period
Second semester
Course syllabus
0) Fluid Mechanics: fundamental concepts.
1) Heat, time arrow.
2) Kinetic theory of gases.
3) Statics and dynamics of fluids.
4) Classical statistical mechanics, statistical equilibrium, temperature, ideal gas, thermometers, zeroth law of thermodynamics.
5) Fundamental postulate of thermodynamics. Entropy.
6) Thermodynamic processes, reversibility.
7) First law of thermodynamics.
8) Second and third law of thermodynamics, calorimetric coefficients. Heat engines.
9) Thermodynamic potentials, properties of extensive parameters.
10) Evolution and determination of equilibrium in isolated systems.
11) Evolution and determination of equilibrium in interacting systems.
12) Conditions for stable equilibrium.
13) Pure and homogeneous fluids.
14) Equations of state, ideal gas and real gas, interactions between molecules.
15) Van der Waals equation of state.
16) Coexistence and phase transitions of pure substances; Clausius-Clapeyron equation.
17) Theoretical analysis of phase transitions with thermodynamic potentials and equations of state. Response functions.
18) Blackbody radiation.
19) Heat transfer.
1) Heat, time arrow.
2) Kinetic theory of gases.
3) Statics and dynamics of fluids.
4) Classical statistical mechanics, statistical equilibrium, temperature, ideal gas, thermometers, zeroth law of thermodynamics.
5) Fundamental postulate of thermodynamics. Entropy.
6) Thermodynamic processes, reversibility.
7) First law of thermodynamics.
8) Second and third law of thermodynamics, calorimetric coefficients. Heat engines.
9) Thermodynamic potentials, properties of extensive parameters.
10) Evolution and determination of equilibrium in isolated systems.
11) Evolution and determination of equilibrium in interacting systems.
12) Conditions for stable equilibrium.
13) Pure and homogeneous fluids.
14) Equations of state, ideal gas and real gas, interactions between molecules.
15) Van der Waals equation of state.
16) Coexistence and phase transitions of pure substances; Clausius-Clapeyron equation.
17) Theoretical analysis of phase transitions with thermodynamic potentials and equations of state. Response functions.
18) Blackbody radiation.
19) Heat transfer.
Prerequisites for admission
Mechanics, Mathematical analysis 1 and 2.
Teaching methods
32 hours of theoretical lectures and 24 hours of exercises.
Teaching Resources
E. Fermi, Thermodynamics
R. P. Feynmann, Lectures on Physics
B. Diu et al. Thermodynamique (in French)
H. Callen, Thermodynamics and an Introduction to Thermostatistics
M. Alonso, E. J. Finn, Fundamental University Physics III - Quantum and statistical physics
M. W. Zemansky, R.H. Dittman, Heat and Thermodynamics
C. Mencuccini, V. Silvestrini, Fisica-Termodinamica (in Italian)
S. Rosati, Fisica generale (in Italian)
S. Focardi, I. Massa, A. Uguzzoni, Fisica generale - Termodinamica e Fluidi (in Italian)
R. P. Feynmann, Lectures on Physics
B. Diu et al. Thermodynamique (in French)
H. Callen, Thermodynamics and an Introduction to Thermostatistics
M. Alonso, E. J. Finn, Fundamental University Physics III - Quantum and statistical physics
M. W. Zemansky, R.H. Dittman, Heat and Thermodynamics
C. Mencuccini, V. Silvestrini, Fisica-Termodinamica (in Italian)
S. Rosati, Fisica generale (in Italian)
S. Focardi, I. Massa, A. Uguzzoni, Fisica generale - Termodinamica e Fluidi (in Italian)
Assessment methods and Criteria
Written exam (~2 hours) with 3/4 open problems plus oral exam (~0.5 hour). In the exams, the student has to show to be familiar with the fundamental topics presented during the course and to be able to apply them to solve specific problems of thermodynamics.
FIS/01 - EXPERIMENTAL PHYSICS
FIS/07 - APPLIED PHYSICS
FIS/07 - APPLIED PHYSICS
Practicals: 24 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Grillo Claudio
Educational website(s)
Professor(s)
Reception:
Friday, 9:30-12:30 (by appointment)
Physics Department, via Giovanni Celoria, 16, 20133 Milano
Reception:
by e-mail appointment
Room A/5/C8 - 5th floor LITA building, Dipartimento di Fisica (via Celoria, 16 - 20133 Milano)