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What are the Scientific Roots of Sadi Carnot’s Cycle?

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Lazare and Sadi Carnot

Part of the book series: History of Mechanism and Machine Science ((HMMS,volume 19))

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Abstract

In this section we investigate the possible origin of the idea of the cycle in Sadi Carnot’s work , following the hypothesis of an analogy with the electric circuit in Alessandro Volta ’s battery . First we will present a comparison from the standpoint of the fundamental concepts between Sadi Carnot ’s theory of thermodynamics and the theory of electricity . Secondly we will propose an analogy between Carnot’s cycle and the cyclic path of the I current in Volta ’s battery , whose current (between two potentials ) corresponds to the heat flux which flows between the two thermostats of two reversible heat engines paired by Sadi Carnot. Additionally, we will report and comment on some analogies between electrostatic , electric phenomena and heat engines . In conclusion we present a global vision of every possible connection and will discuss its compatibility.

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Notes

  1. 1.

    Let us note, for example, the role played by artisans and practical science with respect to the birth of modern (and more mathematical) science; or generally speaking, the role played by mechanical science in engineers’ and architects’ designs during the Renaissance . (Pisano 2008).

  2. 2.

    Mach ([1896] 1986), p 314, line 12.

  3. 3.

    An overview of this chapter was published in: Pisano (2003), pp 327–348.

  4. 4.

    Mach ([1896] 1896), p 415, line 5. That is typically regarding the history of the foundations of physics or, the long–term comprehension of the development of scientific knowledge in historical epistemology (see, e.g., Chapters 6 and 9).

  5. 5.

    Count Alessandro Giuseppe Antonio Anastasio Volta ([1968] 1998). Alessandro Volta invented the battery when he was 54 years old and already one of the most famous European physicists. In 1778 he was appointed Regius Professor of Experimental Physics at Pavia University in Italy (Pancaldi). The physics department was named after him; idem for the unit of measurement of potential , which Volta called tension (later named the volt .) Nowadays more than 100 pieces of apparatus invented or used by Volta were conserved at Pavia department of physics and digitalized Le Opere di Alessandro Volta composed by 15 volumes for a national edition. See also the international and very important project European Cultural Heritage Online Project (ECHO) by Max Planck Institute for the History of Science in Berlin and other institutions. For details see: http://echo.mpiwg-berlin.mpg.de/home and http://echo.mpiwg-berlin.mpg.de/content/electricity .

  6. 6.

    Kuhn (1959), p 323, line 24.

  7. 7.

    Ivi, p 324, line 27. (Author’s quotation marks).

  8. 8.

    Volta ([1968] 1988), pp 526–527, line 36. (The translation is ours: RP). Cfr.: Volta (1796), (1800a, b), (1987).

  9. 9.

    In this chapter we will use the term “work” as Lazare and Sadi perceived it at that time. For our purposes, at times, such as a meta reflection in modern terms, will refer it as “quantity” and without explicit references Coriolis.

  10. 10.

    Let us also note the previous invention of the Leyda bottle by Peter Mussheenbroek (1692–1761) in 1745.

  11. 11.

    Volta (1816), p 245, line 1. (The translation is ours: RP).

  12. 12.

    Volta (1918–1929), IV, p 353, line 14. (The translation is ours: RP). He had quite a good knowledge of French and English experiments and studies as he frequently referenced them by names and descriptions (Volta 1782, pp 237–280; see also selected references in: Mottelay , pp 248–249).

  13. 13.

    Volta (1782), pp 278–279, line 28. (The translation is ours: RP).

  14. 14.

    Carnot (1786), pp iv–v, 11–12; see also Carnot (1778), §§ 27–79, (1780), § 102, §§ 133–141; Gillispie (1971), Appendix C, § 102, pp 301–303, §§ 133–141, pp 317–321. For the comparison and relationship between the two Carnots on that argument see below Chapter 11.

  15. 15.

    Black , I, pp 76–78, line 14. (Author’s quotations marks and italics).

  16. 16.

    The DNSs are discussed in previous Chapters 6 and 7. The DNSs that concern Sadi Carnot’s reasonings on equilibrium are: 8, 15, 31, 45 (Carnot 1978, pp 1–112) and they are also listed below in the Appendix. In addition, please see also: p 9, line 10; p. 10, line 7; p 10, line 10; p 12, line 3; p 14 line 2; p 14, line 15; p 16, line 17; p 17, line 1; p 23, line 5; p 26 ft 1, line 2.

  17. 17.

    DNSs 9, 31(=33 = 34), 32, 35 (=36), 37, 40, 41, 42, 43, 44, 45. (See below Appendix).

  18. 18.

    Galvani ([1841] 1988), p 201, line 27; see also Galvani (1794a). (Translation is ours: RP). On Galvani one can also consult: Galvani (1791, 1797).

  19. 19.

    In a modern performance of the Voltaic battery all of the electric potential differences which occur between every ionic pair that flow in the solution (before they reach the respective electrodes ) should be studied. However, assuming the exemplifying hypothesis that there are only two ionic species of opposing charges in the solution (and that, in the solution, they move methodically), we can consider a single constant electric potential difference (such as a hypothesis) for every couple (of the two species) of charges found in the solution. It is also necessary to hypothesize that in the acidulous solution, other disruptive phenomena such as those of overvoltage do not occur.

  20. 20.

    Mach ([1896] 1986), pp 310–311, line 20. (“ *” = Author’s footnote).

  21. 21.

    Another concise list might be (for our purpose): 1745: Grummert studies electric light in vacuo . 1745: Miles reads at The Royal Society (March 7) a paper concerning phosphorus , electricity and the role played by conducting bodies. Pivati writes Lettere della elettricità medica . 1753: Beccaria , scientific works on electricity are produced. 1756: Le Chevalier Jacques CF de la Perrierc de Roiffe write Mécanismes de l’électricité et de 1’univers . 1757; Wilcke studies the production of electricity by means of melting electrical substances (following Stephen Grey ’s studies). 1769: Volta addresses his de attractiva ignis electrici to Beccaria. 1775: Cavallo studies relationships between electricity and atmosphere and invents a small electroscope and a condenser of electricity. 1775: Volta produces quite important experiments on his inventions making them known by letters, e.g., the electrophorus , a sort of perpetual reservoir of electricity. 1759–1778: Benjamin produces important essays on electricity. 1781: Lavoisier proposes (see also Volta and Laplace ) that electricity is developed when solid or fluid bodies pass into the gaseous state . 1781: Kirwan, President of the Dublin Society and of the Royal Irish Academy produces quite important works on magnetism and electricity and receives from the English Royal Society its Gold Copley medal. 1790: Vassalli publishes his views concerning the electricity of bodies, electricity of water and ice. 1793: Fontana works on animal electricity. (Cfr.: Mottelay ).

  22. 22.

    Mach ([1896] 1986), p 308, line 10; see also pp 142–145.

  23. 23.

    For the sake of consistency, at letters W and V in the quotation from Mach we respectively substituted the letters Q and T.

  24. 24.

    Mach ([1896] 1986), pp 368–369, line 8. (Author’s quotation marks).

  25. 25.

    Let us note that the electric phenomena examined in this section are naturally different from the electrostatic phenomena presented in previous section.

  26. 26.

    In the Eqs. 8.8 and 8.9 we exchanged the letter “P” used by Fuchs with the letter “V”.

  27. 27.

    Callendar (1910), p 1. (Author’s quotation marks).

  28. 28.

    It should also be noted that energy , quantity of motion and angular motion also appear in mechanics ; but in this case only as convenient instruments for calculation, never as fundamental concepts; in fact in this theory the fundamental quantities are trajectory, velocity, mass and force ; where the quantity of motion is just another name to indicate the product of velocity times mass and energy as a certain constant of motion.

  29. 29.

    Schmid (1984), pp 794–795 (Author’s italics, numbers in running text and capital letters).

  30. 30.

    Schmid (1984), p 795.

  31. 31.

    Ibidem.

  32. 32.

    Ibidem, respectively formulas (3) and (4).

  33. 33.

    \( ^{33} \) Ibidem, line 6, formula (5).

  34. 34.

    In Schmid’s correct interpretation and calculus that term was not strictly necessary. Instead here we try to take into consideration what is interesting for us.

  35. 35.

    The manuscript Notes sur les mathématiques, la physique et autres sujets is also conserved at Archives of the Académie des Science–Institut de France, Paris. Thus, we used “Carnot S 1878a” to cite both of the two original manuscripts studied. The difference in the running text is presented by the titles of the two manuscripts. We let note that the manuscripts edited by Gauthier –Villars (Carnot 1878b) are not always integrally reproduced. For any complete consulting of the Sadi Carnot’s manuscripts, please see Fox (1986).

  36. 36.

    [also available in .pdf via: http://www.brera.unimi.it/sisfa/atti/index.html]

  37. 37.

    [available in .pdf via: International Galilean Bibliography , Istituto e Museo di Storia delle Scienze. Firenze: http://biblioteca.imss.fi.it/]

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  1. Department of History, Princeton University, Princeton, New Jersey, USA

    Charles Coulston Gillispie

  2. SCité University of Lille 1, Lille, France

    Raffaele Pisano

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Gillispie, C.C., Pisano, R. (2014). What are the Scientific Roots of Sadi Carnot’s Cycle?. In: Lazare and Sadi Carnot. History of Mechanism and Machine Science, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8011-7_8

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