81783 - Thermodynamics (A-L)

Learning outcomes

At the end of the course the student acquires a fundamental knowledge of classical thermodynamic and its microscopic interpretation. Basic hints of kinetic theory of gases and statistical thermodynamic will be provided. The student will be able to apply these general concepts to solve problems of thermal phenomena at equilibrium.

Course contents

1. Introduction

1. From systems with a few material points to macroscopic systems
2. The coarse-grain approach and the thermodynamic limit
3. Relationship between the microscopic and macroscopic perspectives: a glimpse into the kinetic theory of gases
4. Intensive and extensive thermodynamic coordinates

2. The Zeroth Law of Thermodynamics and Temperature

1. Thermal equilibrium and the zeroth law
2. Concept of temperature
3. Measurement of temperature
4. The ideal gas thermometer
5. Modern definition of temperature

3. Thermodynamic Systems

1. Thermodynamic equilibrium
2. Equation of state (examples for ideal gases, real gases, and paramagnetic systems)
3. Phase diagrams for pure substances
4. Differential phase transitions

4. Work in Thermodynamics

1. Work in a hydrostatic system
2. Work in composite systems

5. The First Law and Heat

1. Adiabatic work
2. Heat and the first law
3. Heat capacity
4. Molar heat capacities for hydrostatic systems, enthalpy
5. Calorimetry
6. Internal energy of an ideal gas and a real gas
7. Adiabatic transformations of gases

6. Kinetic Theory of Gases

1. Molecular velocity distribution
2. Microscopic interpretation of temperature
3. Mean free path
4. Applications

7. The Second Law and Entropy

1. The "arrow of time"
2. Heat engines and heat-to-work conversion; Kelvin-Planck statement
3. Refrigerators and Clausius statement
4. Equivalence of the two statements of the second law
5. Carnot cycle and theorem
6. Absolute thermodynamic temperature
7. Efficiency of heat engines and refrigerators; real machines
8. Examples of heat engines
9. Clausius theorem and the entropy state function
10. Entropy in selected and notable cases
11. Outline of a thermodynamic transformation. Increase of entropy in the universe; energy degradation
12. Fundamental thermodynamic relation and T-S diagram

8. Thermodynamic Potentials

1. Introduction
2. Internal energy
3. Enthalpy
4. Helmholtz free energy
5. Gibbs free energy
6. Open systems and chemical potential
7. Summary of potentials and Maxwell relations
8. TdS equations
9. Internal energy equations
10. General relation
11. Conditions for thermodynamic equilibrium
12. Gibbs phase rule

9. The Third Law of Thermodynamics

1. Introduction: the absolute value of entropy
2. Nernst and Planck formulations
3. Consequences of the third law: low-temperature physics

10. Elements of Statistical Mechanics

1. Macrostates and microstates
2. Entropy in statistical mechanics

Readings/Bibliography

Basic textbooks:

M. W. Zemansky, Calore e Termodinamica", Zanichelli.

S. Focardi, I. Massa, A. Uguzzoni, M. Villa, "Fisica Generale - Meccanica e Termodinamica, seconda edizione", CEA.

Complementary textbooks:

Stephen Blundell and Katherine Blundell, Concepts in Thermal Physics, 2nd edition, Oxford Univ Press, 2009.

P. Mazzoldi, M. Nigro, C. Voci, "Fisica Volume I, Meccanica-Termodinamica", Edizioni EdiSES.

C. Mencuccini, V. Silvestrini, "Fisica - Meccanica-Termodinamica", CEA.

Exercises textbooks:

M. Villa, A. Uguzzoni, M. Sioli, "Esercizi di fisica. Termodinamica, fluidi, onde e relatività. Come risolvere i problemi", Zanichelli, 2018.

A. Bertin et al., "Problemi d'esame di Fisica Generale - Meccanica e Termodinamica", Edizioni Esculapio.

G. A. Salandin e P. Pavan, "Problemi di Fisica 1", CEA.

S. Longhi et al., "Esercizi di Fisica Generale: Meccanica Termodinamica Elettricità e Magnetismo", Edizioni Esculapio.

C. Mencuccini, V. Silvestrini, "Esercizi di Fisica – Meccanica-Termodinamica", CEA.

Teaching methods

Lectures and exercises. Anonymous quiz using Wooclap.

Assessment methods

General information on the exam:

• The exam consists of a written test and an oral test.
• There are six exam sessions per academic year: three in summer, one in fall and two in winter. No additional sessions are foreseen.
• Enrollment in the exam list by means of AlmaEsami is mandatory.
• In each written test there are two exercises. To pass the test it is necessary to achieve at least 18 marks over 30. During the test - which lasts 2 hours - the use of an electronic calculator is allowed but it is not possible to consult neither textbooks nor notes.
• The result of the written test is valid up to the winter session. It is highly recommended, but not compulsory, to take the oral exam immediately after the written one.
• Students can repeat a written test if they want to improve their mark. However, keep in mind that previous marks will be deleted.
• The final grade that can be achieved is indicatively the average between written and 31 (30 with honors).
• If a student fails the oral exam, or rejects the mark, the commission will decide whether to keep the mark of the written exam. Please note that, according to the university regulations, the rejection of the grade must be accepted at least once by the commission. From the second refusal onwards  the decision is up to the commission itself.

Teaching tools

Course notes on Virtuale

Office hours

See the website of Luca Pasquini

See the website of Tommaso Diotalevi