Abstract
More than 100 years ago a Swedish schoolteacher Nils Engelbrektsson could theoretically derive the thermodynamic equation of state, which is universally valid. His colleague, a Swedish schoolteacher Karl Franzén had experimentally verified his inferences and could prove their validity. About hundred years of fierce struggle to persuade the colleagues do finally bring the desiderated victory to Nils and Karl: their trains of thoughts do deserve our careful looking at them. That is just the main idea behind the translation at hand [1. E. B. Starikov (2019) A Different Thermodynamics and Its True Heroes, Jenny Stanford Publishing, Singapore; 2. Entropy-Enthalpy Compensation: Finding a Methodological Common Denominator through Probability, Statistics, Physics, E. B. Starikov, Bengt Nordén, Shigenori Tanaka, Editors; Jenny Stanford Publishing, Singapore, 2020].
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11 November 2021
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Notes
Our note: In effect, this magnitude ought to be the chemical potential introduced by J. W. Gibbs.
Nota Bene:(A handwritten margin note by Nils Engelbrektsson on the page 32 of his original book, we translate): Strictly speaking, to insert a value for ρ into Eq. (35), we must recast Eq. (37a) as follows:\(\rho = - x\Delta \Phi_{1,0} + \Delta \Phi\)(37α), which ought to be both a partial differential equation and, at the same time, to satisfy the Pettersson’s formula \(\rho_{1,0} = \Delta c\) prior to all of our inferences—in contrast to (37a).
Given in its modified but strictly valid form (cf. Weinstein, Thermodynamik und Kinetik der Körper, 2nd volume, page 254).
Our note: The concept of constitutional supercooling is well-known in the modern metallurgy:
1. J. W. Rutter, B. Chalmers, A Prismatic Substructure Formed During Solidification of Metals, Canadian Journal of Physics, v. 31, pp. 15–39, 1953;
2. W. A. Tiller, K. A. Jackson, J. W. Rutter, B. Chalmers, The Redistribution of Solute Atoms During the Solidification of Metals, Acta Metallurgica, v. 1, pp. 428–437, 1953;
3. P. Pfann, Comment on paper by Tiller, Jackson, Rutter and Chalmers, Acta Metallurgica, v. 1, pp. 763–764, 1953;
4. Kenneth A. Jackson, Constitutional Supercooling Surface Roughening, Journal of Crystal Growth, v. 264, pp. 519–529, 2004.
That was but Nils Engelbrektsson who has introduced and analyzed it, just in its general sense of Phase Interface Stability. Indeed, Nils does treat the Entropy notion explicitly, so he could successfully derive the universally valid thermodynamic equation of state—to study Phase Interfaces, as well as their stability—both systematically and in general.
Appendix, §1.
cf. Appendix, §2.
cf. Appendix, § 16.
Our comment: Nils reverts here to Eq. (160b) without indicating what is the purpose of such a jump…
Appendix, § 12a.
Our comment: Throughout here, Nils does employ the noun ‘vikten’, i.e., ‘the weight’ in English. Nonetheless, to properly express the physical–chemical essence of the concept introduced, we would rather employ here the noun ‘the percentage’. As Nils’ work ought to be of the clear methodological significance, we prefer to stay by the Nils’ word choice further on. Howbeit, Nils’ work has a signature link to ‘Equilibrium of Heterogeneous Substances’ by J. W. Gibbs and shows hence the very direction to drive Gibbs’ train of thoughts to its further stations.
The function \({\mathcal{V}}^{\prime}\left( x \right)\) differs from the function \({\mathcal{V}}\left( x \right)\) only by an additive constant.
Appendix, §§2–16; As for the sublimating substances, there is no material to verify the isobar from the present viewpoint.
Appendix, §13.
Appendix, §5.
Disregarding conversion points in the restricted sense (cf. step 1).
Appendix, §5.
See the footnote12 on Page 83 here, which is relevant to Eq. (176e).
Appendix, §§ 10, 12a, 13, 15.
Appendix, §4.
Appendix, §8.
Our comment: It is the situation when liquid, gas and solid phases do co-exist at a given temperature.
Appendix §8.
Appendix, §9.
The decision as for the starting point on the temperature axis for solids ought to be rather immediate, according to Mr. Franzén’s statement. Cf. Appendix, Figs. XIV–XXI.
Appendix, §§ 11, 12b, 14.
E. B. Starikov (2019) A Different Thermodynamics and Its True Heroes, Pan Stanford Publishing, Singapore, Chapter 2.
Nikolai Semyonovich Kurnakov (Russian: Hикoлaй Ceмёнoвич Кypнaкoв, 1860–1941) was a Russian chemist internationally recognized as the originator of the physico-chemical analysis.
The work on the salts interchange had first been reported to the Egyptian Institute in Cairo in July 1799 (Messidor VII), and later published in the third volume of Mémoires de l’Institut National. At the same time it has been published as a separate book: “Recherches sur les lois de l'affinité”, par le citoyen Berthollet, an IX (1801); see the German translation in Ostwald’s Klassiker der exakten Wissenschaften (1896), No. 74, as well.
Berthollet’s data on the soda formation and nature have also been confirmed by Hilgard’s subsequent observations (Berichte der Deutschen Chemischen Gesellschaft, v. 25, p. 3226), see also works by Melikov (Journal of Russian Physical–Chemical Society, v. 28, p. 307, p. 551) and Tanatar (ibid.—v. 28, p. 327, p. 376).
In recent years, Annales de Chimie has again been published separately.
Dominique François Jean Arago (1786–1853): Œuvres complètes, t. II, p. 532.
P. Duhem: Revue philomathique de Bordeaux et du Sud-Ouest, Seconde année, Numéros 5–6 (1899).
Jean Victor Poncelet: Traité des propriétés projectives des figures, Paris: Librairie Bachelier, 1822.
Our comment: It is just here that Kurnakov approaches the work by Nils and Karl infinitesimally close. Still, he is dearly missing the proper definition of the Entropy Notion to correctly proceed with this train of thoughts…
Joseph Louis Proust (1754–1826) was a French chemist. He is best known for his 1794 discovery of the constant composition law stating that chemical compounds do always combine in constant proportions.
Our note: What Prof. Kurnakov calls for here has indeed emerged, it is actively developing (see the References below):
a) D. H. Rouvray, A Rationale for the Topological Approach to Chemistry; Journal of Molecular Structure. THEOCHEM, Volume 336, 101–114, 1995.
b) David Brown, Topology and Chemistry; Structural Chemistry, Volume 13, 339–355, 2002.
c) Michelle Francl, Stretching Topology; Nature Chemistry, Volume 1, 334–335, 2009.
Meanwhile, we deal with molecular topology as a part of mathematical chemistry representing the algebraic description of chemical compounds—to allow a unique and easy characterization of them, and the sound basis for this delivers the Quantum Chemistry, which is in turn a product of Quantum Physics, a valid physical theory treating the Entropy notion but implicitly, unlike Nils and Karl suggest. The actual problem would be reconciling the conceptual gap between implicit and explicit pictures of Entropy. What was—and is—the actual difficulty of solving such a problem, we will discuss later on in this Appendix.
In: Journal of the Russian Physicochemical Society, v. 30 (2), pp. 225–232.
Augustus Matthiessen (1831–1870) was a British chemist and physicist.
Hendrik Willem Bakhuis Roozeboom (1854–1907) was Dutch physical chemist studied phase behaviour in detail.
Pavel Petrovich Anosov (Пaвeл Пeтpoвич Aнocoв, 1796–1851) was a Russian mining engineer, a metallurgical scientist, a major organizer of the mining industry, a researcher of the Southern Ural’s nature, and a governor of Tomsk (in Siberia).
Dmitry Konstantinovich Chernov (Дмитpий Кoнcтaнтинoвич Чepнoв, 1839–1921) was a Russian metallurgist.
Floris Osmond (1849–1912) was an outstanding French metallurgist.
Henry Clifton Sorby (1826–1908) was an English microscopist and geologist.
M. Beliaiev: Les précurseurs de la métallographie. Réunion des membres français et beiges de l'Association Internationale pour l'essai des matériaux de construction. Section des métaux, 1912, p. 30;—Гopный Жypнaл, 1914, №3, 313.—Η. Я. Hecтepoвcкий. Maтepиaлы к биoгpaфии П. П. Aнocoвa, Пeтpoгpaд, 1919.
E. S. Shepherd, G. A. Rankin, F. E. Wright, Z. anorg. Chem., 71 (1911), 19; Rankin, Wright, ibid., 92 (1915), 213; Neues Jahrbuch für Mineralogie, 1916, II, 26.
Anders Richard Åkerman (1837–1922) was a Swedish metallurgist and namesake of the mineral Åkermanite.
Namely: Kirleut Lake (Perekop group) in the Crimea, the Black Sea, Kara-Bugaz-Gol and the Caspian Sea.
N. Kournikov and G. Zhemchuzhny have reported their results to the Department of Chemistry of the Russian Physico-Chemical Society on November 23, 1917 and published them in the Bulletin of the Institute of Physico-Chemical Analysis, vol. 1, pp. 185–244 (1919).
D’Ans, Zeitschrift “Kali”, 1915. The work has been carried out on behalf of the Union for the scientific study of German deposits of potassium salts.
Blasdale, J. Ind. Eng. Chemistry (1920), 164; J. Chem. Soc. Abstracts, 1920, 227.
Shiro Takegami, J. Tokyo Chem. Soc., v. 41, pp. 831–868 (1920); J. Chem. Soc. Abstracts, 1921, 30.
François Ernest Mallard (1833–1894) was an eminent French scholar in the fields of crystallography and mineralogy.
Evgraf Stepanovich Fedorov (Eвгpaф Cтeпaнoвич Фёдopoв, 1853–1919) was a Russian mathematician, crystallographer and mineralogist.
Vladimir Ivanovich Vernadsky (Bлaдимиp Ивaнoвич Bepнaдcкий, 1863–1945) was a Russian, Ukrainian and Soviet mineralogist and geochemist considered as one of the founders of geochemistry, biogeochemistry, and radiogeology.
Alexander Evgenʹevich Fersman (Aлeкcaндp Eвгeньeвич Фepcмaн, 1883–1945) was a prominent Russian and Soviet geochemist and mineralogist.
Heike Kamerlingh Onnes, (1853–1926) was an outstanding Dutch physicist and Nobel laureate.
Our immediate comment: …and Nils and Karl’s seminal results do firmly and formally prove this conclusion!
К. Пиpcoн, Гpaммaтикa нayки, cтp. 316. — B. Клиффopд, Здpaвый cмыcл тoчныx нayк, cтp. 236–258. Kurnakov has chosen to cite here the Russian translations of Pearson and Clifford’s monographs.
Karl Pearson (1857–1936) was an English mathematician and biostatistician.
Sir Francis Galton (1822–1911) was an English Victorian era statistician, polymath, sociologist, psychologist, anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, and psychometrician.
William Kingdon Clifford (1845–1879) was an English mathematician and philosopher.
Ernst Laas (1837–1885) was a German positivist philosopher.
Karl Robert Eduard von Hartmann (1842–1906) was a German philosopher, independent scholar and the author of Philosophy of the Unconscious (1869).
The Russian translation of Pearson's book is in general satisfactory. The ambivalence of translators affects some pieces in the equal translation of the same terms: e.g., the one conveys the term “mode” by the term “modus”, whereas the other, completely unsuccessfully, translates it by the “category”. To some extent, translators do abuse foreign terms—this does facilitate the translation work—but complicates the reading effort at the same time.
Leonid Evgenʹevich Gabrilovich (Galich) (1878–1953):
Milestones in life, career inside and outside the university:
1899–1901—assistant at Tomsk University; Professor of the St. Petersburg Pedagogical Academy; Since 1921—a journalist for the émigré Parisian newspaper Obshchee Delo; Permanent employee of the New Russian Word; Member of the Religious and Philosophical Society in St. Petersburg (1914); 1930–1939—Member of the Board of the Russian Scientific and Philosophical Society; Member of the Masonic Lodge “Jupiter” (1927–1930).
Research interests, scientific contributions:
During his years at the university, most of works by Gabrilovich are devoted to the metaphysics and the study of historical philosophy. In his early years, he wrote scientific articles on symbolism, criticizing its philosophical and idealistic orientation. His philosophic research relevant to Nils ‘ work: Arch. syst. Philos., XV, S. 40–52, 1909. Later on, he was engaged in practical engineering—and had gotten a patent in the multiple wireless telegraphy.
Über mathematisches Denken und den Begriff der aktuellen Form, von Dr. Leonid Gabrilovitsch, Privat-Dozent der Philosophie an der Universität St. Petersburg; Bibliothek für Philosophie—herausgegeben von Ludwig Stein, der 8. Band; Beilage zu Heft 4 des ‚Archivs für systematische Philosophie ‘, Band XXVI, 1914; Druck und Verlag von Leonhard Simion Nf., Berlin W 57, Bülowstr. 56.
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Nils Engelbrektsson (1875–1963) and Karl Franzén (1882–1967): Deceased.
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Engelbrektsson, N., Franzén, K. & Starikov, E.B. The basic features of thermodynamics. Monatsh Chem 152, 1437–1490 (2021). https://doi.org/10.1007/s00706-021-02837-0
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DOI: https://doi.org/10.1007/s00706-021-02837-0