81783 - Thermodynamics (M-Z)

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

Thermodynamic systems. State of a thermodynamic system. Thermal equilibrium. Zeroth law of thermodynamics. Empirical temperature. Construction of thermometers: Celsius and Kelvin scales. Perfect gas thermometer. States of matter. Ideal and real gas laws. Thermodynamic transformations. Quasi-static transformations. Simple thermodynamic systems. Pressure-volume diagram for pure substances. Phase diagram of water.

Thermodynamic work. Thermodynamic work for isobaric, isochoric and isothermal transformations. Adiabatic work. Internal energy. Heat. First law of thermodynamics. Thermal capacity. Thermal capacity for an hydrostatic system. Two system thermal equilibrium. Thermal reservoir. Latent heat. Calorimeters. Heat transfer: conduction, convection and radiation. Stefan-Boltzmann's law. Black body. Application to the Earth-Sun system. Joule's experiment. Internal energy in perfect and real gases. Mayer's relation. Quasi-static adiabatic transformations. Work in adiabatic transformations.

Elements of kinetic theory of gases. Model Building. Relationship between temperature and molecular kinetic energy. Maxwell-Boltzmann's distribution of molecular speeds. Internal energy and molar thermal capacity predicted by the model. Equipartition theorem. Molar thermal capacities for monoatomic and biatomic gases and for solids. Rotational and vibrational energies and degrees of freedom. Dalton's Law.

Concept of irreversibility. Thermal and refrigerator machines. Thermal efficiency. Kelvin-Planck's statement. Clausius's statement. Equivalence of the two statements. Carnot cycle. Carnot theorem and its corollary. Carnot cycle efficiency for perfect gases. Absolute thermodynamic temperature. Clausius inequality. Entropy. Entropy in isolated systems. Application of the maximum entropy principle: free expansion, heat conduction, processes with friction. Entropy and thermal efficiency. Entropy and energy degradation. TS plane. Entropy for ideal gases.

Thermodynamic Potentials. Helmholtz and Gibbs free energies. Derivation of the Phase Rule. Clapeyron equation. Thermodynamic potentials in non-pV transformations. Chemical potentials.

Elements of classical statistical thermodynamics. Macrostates and microstates. Isolated systems. Microstate counting. Molecular partition function. Boltzmann Entropy. Uninsulated systems. Connections with classical thermodynamics: temperature. Entropy and disorder. Shannon entropy and information. Cosmological arrow of time.

Readings/Bibliography

Basic textbook

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

Complementary textbooks

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

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

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

E. Fermi, "Termodinamica", Boringhieri.

Exercise 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.

Complementary textbooks in English

Andrew Rex, Finn’s Thermal Physics, 3rd edition, CRC press, 2017.

M.W. Zemansky and R.H. Dittman, Heat and Thermodynamics - An intermediate Textbook, 7th edition, McGraw-Hill, 1997.

More advanced textbooks in English

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

Daniel Schroeder, An introduction to Thermal Physics, Oxford Univ Press, 2021.

Ralph Baierlein, Thermal Physics, Cambridge Univ Press, 2010.

Teaching methods

Lectures and exercises.

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 Maximiliano Sioli

See the website of Tommaso Diotalevi