#
Thermodynamics

A.Y. 2019/2020

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
(In case of multiple editions, please check the period, as it may vary)

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### CORSO A

Responsible

Lesson period

Second semester

**Course syllabus**

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.

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**

Basics of mechanics and kinetic theory of gases. Basics of analytical calculus.

**Teaching methods**

Lectures and excercises in class

**Teaching Resources**

E. Fermi, Termodinamica - Thermodynamics

R. P. Feynmann, Lectures on Physics

B. Diu et al. Thermodynamique (in francese)

H. Callen, Thermodynamics and an Introduction to Thermostatistics (in inglese)

M. Alonso, E. J. Finn, Fundamental University Physics III - Quantum and statistical physics (in inglese)

M. W. Zemansky, R.H. Dittman, Heat and Thermodynamcs (in inglese)

R. P. Feynmann, Lectures on Physics

B. Diu et al. Thermodynamique (in francese)

H. Callen, Thermodynamics and an Introduction to Thermostatistics (in inglese)

M. Alonso, E. J. Finn, Fundamental University Physics III - Quantum and statistical physics (in inglese)

M. W. Zemansky, R.H. Dittman, Heat and Thermodynamcs (in inglese)

**Assessment methods and Criteria**

Written plus oral examination. Two written exams during the course. If both partial exams are positive they directly allow to access the oral examination, without doing a full written examination. The oral examination is on the programme presented in class and it has a typical duration of 45 minutes.

FIS/01 - EXPERIMENTAL PHYSICS - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

Practicals: 20 hours

Lessons: 32 hours

Lessons: 32 hours

Professor:
Rossi Giorgio

### CORSO B

Responsible

Lesson period

Second semester

**Course syllabus**

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.

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**

Knowledge of classical mechanics and of the topics covered in the Mathematical Analysis I and II courses.

**Teaching methods**

Lectures and Exercises.

**Teaching Resources**

- E. Fermi, Thermodynamics.

- C. Mencuccini, V. Silvestrini, Fisica-Termodinamica.

- 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.

- 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.

**Assessment methods and Criteria**

During the course there will be two on-going written tests, one about halfway through the program and one at the end of the course. In the tests, the student should prove that he/she has become familiar with the concepts introduced during the course and that he is able to apply them to solve specific thermodynamic problems. If both the on-going tests are passed, direct access to the final oral exam is obtained, which consists of an interview of about half an hour in which any unclear passages of the written tests are discussed and the student must show that he/she has acquired the fundamental concepts of Thermodynamics and their physical meaning. Students who have not passed the on-going written tests must take a written exam lasting about a couple of hours in which they should solve the proposed problems by applying the concepts and methodology learned during the course. Also in this case, after passing the written exam, the student can access the oral exam described above. 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 - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

Practicals: 20 hours

Lessons: 32 hours

Lessons: 32 hours

Professor:
Olivares Stefano

### CORSO C

Responsible

Lesson period

Second semester

**Course syllabus**

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.

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 20 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)

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)

**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 - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

FIS/07 - APPLIED PHYSICS - University credits: 0

Practicals: 20 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