# Thermodynamics—Fundamentals

• Kolumban Hutter
• Yongqi Wang
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

## Abstract

This chapter is devoted to thermodynamics; first, fundamentals are attacked and, second, a field formulation is presented and explored. Class experience has taught us that thermodynamic fundamentals are difficult to understand for novel readers. Utmost caution is therefore exercised to precisely introduce terminology such as ‘states’, ‘processes’, ‘extensive’, ‘intensive’ and ‘molar state variables’ as well as concepts like ‘adiabatic’, and ‘diathermic walls’, ‘empirical’ and ‘absolute temperature’, ‘equations of state’ and ‘reversible’ and ‘irreversible processes’. The core of this chapter is, however, the presentation of the first and second law of thermodynamics. The first law balances the energies. It states that the time rate of change of the kinetic plus internal energies are balanced by the mechanical power of the stresses and the body forces plus the thermal analogies, which are the flux of heat through the boundary plus the specific radiation referred to as energy supply. This conservation law then leads to the definitions of the caloric equations of state and the definitions of specific heats. The Second Law of Thermodynamics is likely the most difficult to understand and it is introduced here as a balance law for the entropy and states that all physical processes are irreversible. We motivate this law by going from easy and simple systems to more complex systems by generalization and culminate in this tour with the Second Law as the statement that entropy production rate cannot be negative. Examples illustrate the implications in simple physical systems and show where the two variants of entropy principles may lead to different answers.

## Keywords

Reversible/irreversible processes Empirical/absolute temperature First, second law of thermodynamics Thermodynamic states—processes Extensive, intensive, molar state variables Adiabatic/non-adiabatic systems Diathermic wall Thermal equations of state vanderWaals gas Caloric equation of state Specific heats

## References

1. 1.
Baehr, H.: Thermodynamik, 6th edn. Springer, Berlin (1988)
2. 2.
Boltzmann, L.: Über die mechanische Bedeutung des zweiten Hauptsatzes der Wärmetheorie. Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften 53, S. 195–220 (19xy)Google Scholar
3. 3.
Born, M.: The Born-Einstein Letters. MacMillan, London (1971)Google Scholar
4. 4.
Bunstead, H.A., Van Name, R.G. (eds.): The Scientific Papers of J. Willard Gibbs, vol. 2. Dover, New York (1961)Google Scholar
5. 5.
Carathéodory, C.: Untersuchungen über die Grundlagen der Thermodynamik. Math. Ann. 67, 355–386 (1909)
6. 6.
Carnot, N.L.S.: Réflections sur la puissance motrice du feu et sur les machines propres à developer cette puissance. Annales Scientifiques de l’ Ecole Normale Supérieures, Sér 2, 393–457 (1872)Google Scholar
7. 7.
Carnot, N.S.L.: Reflections on the Motive Power of Heat. Transl: Thurston, Robert Henry (editor and translator). Wiley, New York (1890)Google Scholar
8. 8.
Carnot, N.L.S.: Betrachtungen über die bewegende Kraft des Feuers und die zur Entwicklung dieser Kraft geeigneten Maschinen (Übersetzer und Hrsg. Wilhelm Ostwald). Wilhelm Engelmann-Verlag (1892)Google Scholar
9. 9.
Clausius, R.: Über die bewegende Kraft der Wärme. Annalen der Physik 79, 368–397, 500–524 (1850)Google Scholar
10. 10.
Clausius, R.: Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheoriein. Annalen der Physik und Chemie 93(12), 481–506 (1854)
11. 11.
Clausius, R.: On a modified form of the second fundamental theorem in the mechanical theory of heat. Philos. Mag. 4 12(77), 81–98 (1856)Google Scholar
12. 12.
Clausius, R.: Über die Wärmeleitung gasförmiger Körper. Annalen der Physik 115, 1–57 (1862). doi:
13. 13.
Clausius, R.: Über verschiedene für die Anwendung bequeme Formen der Hauptgleichungen der mechanischen Wärmetheorie. Annalen der Physik 125, 353–400 (1865). doi:
14. 14.
Cropper, W.H.: The Road to Entropy Rudolf Clausius. Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking, pp. 93–105. Oxford University Press, Oxford (2004). ISBN 978-0-19-517324-6Google Scholar
15. 15.
Duhem, P., Wiener, P.P.: La Théorie Physique: Son Objet et sa Structure [The Aim and Structure of Physical Theory]. Jules Vuillemin. Princeton University Press, Princeton (1954). ISBN 978-0-691-02524-7Google Scholar
16. 16.
Einstein, A.: Investigations on the Theory of the Brownian Movement (1905). Edited with notes by R. Fürth. Dover Publications, New York (1956)Google Scholar
17. 17.
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Volume I: Mainly Mechanics, Radiation, and Heat, 2nd edn. Addison-Wesley, Reading (2005)Google Scholar
18. 18.
Gibbs, J.W.: Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics. New York: Dover Publications (1960) [1902]Google Scholar
19. 19.
Joule, J.P.: On the heat evolved by metallic conductors of electricity, and in the cells of a battery during electrolysis. Philos. Mag. 19, 260 (1841). doi: Google Scholar
20. 20.
Joule, J.P.: On the calorific effects of magneto-electricity, and on the mechanical value of heat. Philos. Mag. 3 23, 263, 347 & 435 (1843). doi:
21. 21.
Joule, J.P.: On the changes of temperature produced by the rarefaction and condensation of air. Philos. Mag. 3 26(174), 369–383 (1845). doi:
22. 22.
Joule, J.P.: ‘On the Mechanical Equivalent of Heat’. Brit. Assoc. Rep., trans. Chemical Sect, p. 31, read before the British Association at Cambridge, June (1845)Google Scholar
23. 23.
Joule, J.P.: On the existence of an equivalent relation between heat and the ordinary forms of mechanical power. Philos. Mag. 3 27(179), 205–207 (1845). doi:
24. 24.
Joule, J.P.: On the mechanical equivalent of heat. Philos. Trans. R. Soc. Lond. 140, 61–82 (1850). doi:
25. 25.
Lieb, E., Yngvarson, J.: The physics and mathematics of the second law of thermodynamics. de.arXiv.org> cond-mat> arXiv:cond-mat/9708200 (1997)
26. 26.
Longley, W.R., Van Name, R.G. (eds.): The collected works of J. Willard Gibbs. New York: Longmans, Green and Company, 2 volumes (1928) Yale University Press, New Haven (1948, 1957)Google Scholar
27. 27.
Maxwell, J.C.: A dynamical theory of the electromagnetic field. Philos. Trans. R. Soc. Lond. 155, 459–512 (1865)
28. 28.
Maxwell, J.C.: A Treatise on Electricity and Magnetism, vol. II. Clarendon Press, Oxford (1873)Google Scholar
29. 29.
Maxwell, J.C.: A Treatise on Electricity and Magnetism, vol. I. Clarendon Press, Oxford (1873)Google Scholar
30. 30.
Maxwell, J.C.: Van der Waals on the continuity of gaseous and liquid states. Nature 10(259), 477–480 (1874). doi:
31. 31.
Maxwell, J.C.: On the Stability of the Motion of Saturn’s RingsGoogle Scholar
32. 32.
Maxwell, J.C.: An Elementary Treatise on Electricity. Clarendon Press, Oxford (1881)Google Scholar
33. 33.
Maxwell, J.C.: Theory of Heat. Longmans Green Co., London (1908)Google Scholar
34. 34.
Maxwell, J.C.: The Scientific Papers of James Clerk Maxwell, vol. I. Dover Publication, New York (1890)Google Scholar
35. 35.
Maxwell, J.C.: The Scientific Papers of James Clerk Maxwell, vol. II. University Press, Cambridge (1890)Google Scholar
36. 36.
Mayer, R.: Bemerkungen über die Kräfte der unbelebten Natur. Annalen der Chemie und Pharmacie 43, 233 (1842) Engl. Translation: Mayer, J.R.: Remarks on the forces of inorganic nature. Philos. Mag. 4 24(162), 371–377 (1862)Google Scholar
37. 37.
Nernst, W.H.: Über die electromotorischen Kräfte, welche durch den Magnetismus in von einem Wärmestrom durchflossenen Metallplatten geweckt werden. Annalen der Physik 267, 760–789 (1887)
38. 38.
Nernst, W.H.: Über die elektromotorische Wirksamkeit der Jonen. Zeitschrift für Physik u. Chemie 4, 129 (1889)Google Scholar
39. 39.
Philibert, J.: One and a half century of diffusion: fick, Einstein, before and beyond. Diffus. Fundam. 4, 6.1–6.19 (2006)Google Scholar
40. 40.
Planck, M.: Treatise on Thermodynamics. Ogg, A. (transl.). London: Longmans, Green & Co. (1903)Google Scholar
41. 41.
Planck, M.: Über den zweiten Hauptsatz der mechanischen Wärmetheorie. Ackermann, München (1879)Google Scholar
42. 42.
Planck, M.: Das Prinzip von der Erhaltung der Energie. Leipzig (1887) nach: Hoffmann: Max Planck.München S. 32 (2008)Google Scholar
43. 43.
Planck, M.: Gegen die neue Energetik. Annalen der Physik 57, 72–78 (1896). doi:
44. 44.
Pogliani, L., Berberan-Santos, M.-N.: Constantin Carathéodory and the axiomatic thermodynamics. J. Math. Chem. 28, 1–3 (2000)Google Scholar
45. 45.
Truesdell, A.C., Muncaster, R.G.: Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics, 593 pp. Academic Press, New York (1980)Google Scholar
46. 46.
Van der Waals, J.D.: Over de Continuiteit van den Gasen Vloeistoftoestand (On the continuity of the gas and liquid state). Ph.D. thesis, University Leiden, The Netherlands (1873)Google Scholar
47. 47.
Wilson, E.B.: Vector Analysis. A Text-book for the Use of Students. Founded upon the Lectures of J.W. Gibbs. Yale University Press, New Haven (1901)Google Scholar