On the Equilibrium of Heterogeneous Substances

On the Equilibrium of Heterogeneous Substances (highlighted)

In famous publications, “On the Equilibrium of Heterogeneous Substances” is a 300-page, 160,000-word, 700-equation treatise, published in parts between October 1875 and July 1878, by American mathematical engineer Willard Gibbs, which investigated the mathematical results derivable when one considers the energy ε and entropy η of any material system in the various states of which it is capable. [1]

In commentary on his Equilibrium paper, Gibbs stated that: [15]

“[I had no] sense of the value of time, of my own or others, when I wrote it.”

Gibbs' Equilibrium is generally considered to have laid out the main foundations for the science of chemical thermodynamics. Gibbs' Equilibrium, together with German physicist Rudolf Clausius' 1865 Mechanical Theory of Heat, upon which Gibbs' memoir was built, totaling 1,158-equations, went on to stimulate the founding of the various "schools of thermodynamics". Gibbs' Equilibrium (rank #89) has been described as one of the top 111 books that shaped western civilization. [14]

Hidden treasures
In 1891, Gibbs' Equilibrium was translated into German, by German chemist Wilhelm Ostwald, and in 1899 into French by French chemist Henry Le Chatelier. [7] It has frequently been mentioned that Ostwald undertook the task of translation because he believed there were hidden treasures in it. In the preface to his Thermodynamische Studien, von J. Willard Gibbs (1892), Ostwald states: [17]

“The material of the work is still of direct importance at the moment, and the interest in it is not historical. For only a small part of the almost immeasurable results which are contained and suggested here have as yet been realized. There are still hidden treasures of the greatest variety and importance here for the theoretical and most of all for the experimental worker.”

At the turn of the 19th century, French thermodynamicist Pierre Duhem, likewise, commented on how Johannes van der Waals, was the first to see its hidden power, to perceive the phase rule, “among the algebraic formulas where Gibbs had to some extent hidden it.” [18]

In 1989, thermodynamics historian Carlo Cercignani commented how “Gibbs succinct and abstract style and unwillingness to include examples and applications to particular experimental situations made his work very difficult to read. Famous scientists such as Helmholtz and Planck developed their own thermodynamic methods in an independent fashion and remained quite unaware of the treasures buried in the third volume of Transactions of the Connecticut Academy of Arts and Sciences.” [19] Likewise, in 2007, German thermodynamics historian Ingo Muller comments on this further: [20]

“Ostwald, the German translator of Gibbs, had said that he undertook the task because he believed in hidden treasures in Gibbs’ work. He was right, and le Chatelier and later Haber and Bergius were chemists who uncovered and lifted the treasures as did Roozeboom.”

The fruition of some of these treasures coming to bear is evidenced in the 1949 summary that "the work of Ostwald, of Haber, of [Carl] Bosch and [Friedrich] Bergius, each of whom received a Nobel prize, was based directly on the application of Gibbs' concepts; indeed, the very first Nobel prize in chemistry went to a follower (van't Hoff). [21]

As to the difficultly faced by Ostwald, or for that matter anyone in search of these so-called hidden treasures said to be found in Gibbs 700-equations, Ostwald expressed it best: [17]

“One cannot help deny that the study of these researches offers inner difficulties. Actuated by a wish for the greatest possible universality and plainness of expression, Gibbs has chosen a mode of presentation which calls for an unusual attentiveness and devotion on the part of the reader, owing to the abstractness of the form and the difficult presentation.”

One of the most obvious of these presentation difficulties is that Gibbs scripted his 700-equations using Greek symbols, a likely adoption of those used in 1869 by French engineer Francois Massieu, albeit difficult to follow.

The thermodynamical problem of the equilibrium of heterogeneous substances, according to James Maxwell, was first attacked by German physicist Gustav Kirchhoff in 1855, who studied the properties of mixtures of sulphuric acid with water, and the density of the vapor in equilibrium with the mixture. Kirchhoff’s method, according to Maxwell, was then employed by German mathematical physicist Carl Neumann in his 1875 Lectures on the Mechanical Theory of Heat. Neither, however, according to Maxwell, used the methods of both the intrinsic energy and the entropy of the substance, as did Gibbs. [22]

The beginnings of Gibbs' Equilibrium treatise trace to two 1873 papers in the Transactions of the Connecticut Academy on "Graphical Methods in the Thermodynamics of Fluids," and "Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces." [4] In December 1875, German physicist Rudolf Clausius had cited Gibbs use of the term "isentropic" in his Graphical Methods. [11]

Scottish physicist James Maxwell was one of the first to recognize the significance of the work and to promote it, beginning in 1873, in various publications at and around Cambridge. [6] In a 29 July 1876 letter to Peter Tait, for instance, Maxwell says: [16]

“Have you Willard Gibbs on Equilibrium of Heterogeneous Substances. If not read him. Refreshing after H. Spencer on the Instability of the Homogenous.”

In December of 1878, Gibbs published an 18-page abstract to the Equilibrium in the American Journal of Science. [8] In shortened overview, according to Gibbs’ biographer Lynde Wheeler, in the Equilibrium Gibbs starts with the first and second laws of thermodynamics as defined by Clausius, giving a rigorous derivation of the general mathematical conditions of equilibrium and stability to which they lead. He then proceeds to methodically discuss the necessary modifications of the prime equation (combined law of thermodynamics) and the particular forms the equilibrium conditions take on when there is brought into picture: [13]

(a) the presence of matter of different kinds of states.
(b) the presence of gravitational forces.
(c) the effects of a state of strain in the solids which may be present.
(d) the effects of surface tensions in the bounding surfaces between various portions.
(e) the effects of electrical forces.

The central feature gained from Gibbs’ treatises, according to Dutch physical chemist Johannes van der Waals, winner of the 1910 Nobel Prize for the development of an equation of state for gases and liquids, which Gibbs had sent him shortly after their publication, was the principle that: “for a given amount of substance, equilibrium sets in if the free energy is minimum for the temperature and pressure.” [2]

Gibbs' Equilibrium was later digested and disseminated in simpler format by those as Gilbert Lewis and Merle Randall in 1923, James Partington in 1924, and Edward Guggenheim in 1933. [9] According to Partington, for instance, who seems to be referring to Lewis and Randall: [12]

“It is particularly the countrymen of Willard Gibbs who have in recent years contributed most effectively to chemical thermodynamics.”

In particular, it was the Lewis school of thermodynamics that progressed the work of Gibbs to its fullest extent.

Gibbs's Equilibrium paper has been described as "the Principia of thermodynamics". [3] Similarly, according to 1973 views of American physicist Robert Lindsay: [5]

“In the hands of Willard Gibbs, thermodynamics became a powerful tool for the study of chemical reactions ... his famous memoir On the Equilibrium of Heterogeneous Substances formed a large part of the basis of physical chemistry and thus led to the establishment on a firm scientific basis of what has come to called chemical engineering.”

In modern commentary, Gibbs' Equilibrium is still considered one of the most important yet near-impenetrable works in core thermodynamics. In 1999, for instance, Japanese physicist David Bottomley commented that:

“Very few experts in thermodynamics have the ability to read this from cover-to-cover.”

and that "anyone who hopes to make advances in the fundamental theory or interpretation of thermodynamics (assuming, contrary to current dogma, that such advances can be made) needs to read the majority of this book”. [10]

See also
Gibbsian thermodynamics

1. Gibbs, Willard. (1876). "On the Equilibrium of Heterogeneous Substances", Transactions of the Connecticut Academy, III. pp. 108-248, Oct., 1875-May, 1876, and pp. 343-524, may, 1877-July, 1878.
2. Van der Walls, Johannes D. (1910). “The Equation of State for Gases and Liquids”, Nobel Lecture, NobelPrize.org.
3. Bryson, Bill (2003). A Short History of Nearly Everything. Broadway Books, 116-17,121.
4. (a) Gibbs, J. Willard. (1873). "Graphical Methods in the Thermodynamics of Fluids", Transactions of the Connecticut Academy, I. pp. 309-342, April-May.
(b) Gibbs, J. Willard. (1873). "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", Transactions of the Connecticut Academy, II. pp.382-404, Dec.
5. Lindsay, Robert B. (1973). The Role of Science in Civilization, (pg. 213-14). Westport: Greenwood Press.
6. Maxwell, James C. (editors: Elizabeth Garber, Stephen G. Brush, C. W. Francis Everitt) (1995). Maxwell on Heat and Statistical Mechanics: On "avoiding All Personal Enquiries" of Molecules (Document 37: Draft of “On the Equilibrium of Heterogeneous Substances”, pgs 255-57, Document 38: “On the Equilibrium of Heterogeneous Substances”, pgs 257-62, Document 39: Abstract of “On the Equilibrium of Heterogeneous Substances”, pgs 262-65). Lehigh University Press.
7. Josiah Willard Gibbs - Britannica (1911).
8. Willard, Gibbs. (1878). “On the Equilibrium of Heterogeneous Substances: Abstract by the Author”, American Journal of Science, 3 ser., Vol. XVI, pgs. 441-58, Dec.
9. (a) Lewis, Gilbert N. and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances, New York: McGraw-Hill Book Co., Inc.
(b) Guggenheim, Eduard, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs. London: Methuen & Co.
10. (a) Amazon book review, August 21, 1999.
(b) Bottomley, David J. (1997). “Views on Thermodynamics”, Jpn. J. Appl. Phys. Part 2, vol. 36, L1464.
11. Clausius, Rudolf. (1879). The Mechanical Theory of Heat (pg. 68). London: Macmillan & Co.
12. Partington, James R. (1924). Chemical Thermodynamics: An Introduction to General Thermodynamics and its Applications to Chemistry (pg. v). D. Van Nostrand.
13. Wheeler, Lynde, P. (1951). Josiah Willard Gibbs - the History of a Great Mind (pg. 75). Woodbridge, Connecticut: Ox Bow Press.
14. Downs, Robert B. (1961). Molders of the Modern Mind: 111 Books that Shaped Western Civilization (book 89: Josiah Willard Gibbs’ On the Equilibrium of Heterogeneous Substances, pg. 306). Barnes & Noble.
15. Cropper, William H. (2004). Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking, (section II: Thermodynamics, pgs. 41-134; ch. 9: “The Greatest Simplicity: Willard Gibbs”, pgs 106-23). Oxford University Press.
16. Maxwell, James. (1876). “Postcard to Peter Guthrie Tait”, 29 July, in The Scientific Letters and Papers of James Clerk Maxwell: 1874-1879 (pgs. 385), 1990, edited by Peter Harman. Cambridge University Press.
(a) Ostwald, Wilhelm. (1992). Thermodynamische Studien, von J. Willard Gibbs (preface, pg. #). Publisher.
(b) Rukeyser, Muriel. (1942). Willard Gibbs - American Genius (pg. 314). Garden City, New York: Doubleday, Doran & Co., Inc.
18. Caldi, D. G. and Mostow, George D. (1990). Proceedings of the Gibbs Symposium, May 15-17, 1989 (hidden treasures, pg. 10; section: Gibbs in economics, by Paul Samuelson, pgs. 255-68). American Mathematical Society.
19. Cercignani, Carlo. (1998). Ludwig Boltzmann - the Man Who Trusted Atoms (hidden treasures, pg. 139). Oxford: Oxford University Press.
20. Müller, Ingo. (2007). A History of Thermodynamics: the Doctrine of Energy and Entropy (pg. 128). New York: Springer.
21. Author. (1949). “Article” (pg. 15). Scientific American, 255.
22. Maxwell, James. (1876). “Review: On the Equilibrium of Heterogeneous Substance”, Proceedings of the Cambridge Philosophical Society, Vol. II.; in: Scientific Papers of James Clerk Maxwell (pgs. 488-). Cambridge University Press, 1890.

Further reading
● Maxwell, James. (1876). “On the Equilibrium of Heterogeneous Substances”, Proceedings of the Cambridge Philosophical Society, Vol 2, pgs. 427-30.
● Saurel, Paul. (1902). “On the Critical States of a Binary System” (pgs. 629-35). The Journal of Physical Chemistry, American Chemical Society.
● C.G.K. (1907). “The Scientific Word of Willard Gibbs” (pgs 361-62), Nature, 14 Feb.

External links
On the Equilibrium of Heterogeneous Substances – Wikipedia.
On the Equilibrium of Heterogeneous Substances – Britannica.

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