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Josiah Willard Gibbs (1839-1903)
JOSIAH WILLARD GIBBS (1839-1903) Robert J. Deltete This essay describes Gibbs’s transformation of thermodynamics and his applications of that novel theory to various problems in physical chemistry. The last section then considers the overall nature of his project in theoretical physics and its relevance to philosophy.
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BIOGRAPHY
Gibbs was the only son among five children of the distinguished philologist and professor of sacred literature at Yale College.1 The younger Gibbs grew up in New Haven and graduated from Yale in 1858, having won a string of scholarships and prizes in both Latin and mathematics. He continued at Yale as a student of engineering in the new graduate school, and in 1863 received one of the first Ph.D. degrees granted in the United States. After serving as a tutor for three years, giving elementary instruction in Latin and natural philosophy to undergraduates, Gibbs left New Haven for further study in Europe. He spent a year each in Paris, at the Collège de France and the Sorbonne, and at the universities of Berlin and Heidelberg, attending lectures in mathematics and physics and reading widely in both fields. He was never a student of any of the luminaries whose lectures he attended (the list includes Liouville and Kronecker in mathematics, and Kirchhoff and Helmholtz in physics), but these European studies, rather than his earlier education in engineering, provided the foundation for his subsequent research. (An important qualification is Gibbs’s fondness for “the niceties of geometrical reasoning” [Gibbs, 1974, 43], which is evident in his engineering thesis before it played a prominent role in his thermodynamic work.) Gibbs returned to New Haven in June 1869. He never again left America and rarely ever left New Haven except for his annual summer holidays in northern New England and a very occasional journey to lecture or attend a meeting. Gibbs never married and lived all his life in the house in which he had grown up, close to the college buildings, sharing it with two of his sisters and the family of one of them. In July 1871, two years before he published his first scientific paper, Gibbs was appointed professor of mathematical physics at Yale. He held that position without salary for the first nine years, living on inherited income. It was 1 For biographical material on Gibbs, I have relied on Klein (esp. [1972; 1989]) who, in turn, largely relies on [Wheeler, 1952].
Handbook of the Philosophy of Science. Volume 6: Philosophy of Chemistry. Volume editors: Robin Findlay Hendry, Paul Needham and Andrea I. Woody. General editors: Dov M. Gabbay, Paul Thagard and John Woods. c 2012 Elsevier BV. All rights reserved.
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during this time that he wrote the memoirs on thermodynamics that, in most estimations, constitute his greatest contribution to science. Gibbs was seriously tempted to leave Yale in 1880, when he was invited to join the faculty of the new Johns Hopkins University in Baltimore. Only then did his alma mater offer him a salary — only two thirds of what Hopkins would have paid; but the advantages of remaining in familiar surroundings, plus the high regard in which he was held by colleagues, convinced Gibbs to stay. He continued to teach at Yale until his death, after a brief illness, in the spring of 1903. Gibbs’s research interests evolved from engineering to mechanics, and then to thermodynamics, vector analysis and the electromagnetic theory of light, and statistical mechanics. Since his work in thermodynamics and its applications to physical chemistry is likely most relevant to readers of this volume, that work is the subject of my essay. Section II deals with Gibbs’s novel development of thermodynamics and Section III focuses on his application of that thermodynamic theory to various problems in physical chemistry. Section IV then steps back to consider the overall nature of his project and its relevance to philosophy. 2
THERMODYNAMICS
When Gibbs first turned his attention to thermodynamics in the early 1870’s, the subject had already achieved a certain level of maturity. The essential step had been taken in 1850 by Rudolf Clausius, when he argued that two laws are needed to reconcile Carnot’s principle about the motive power of heat with the law of energy transformation and conservation. Efforts to understand the second of the two laws finally led Clausius in 1865 to his most concise and ultimately most fruitful analytical formulation. In effect, two basic quantities, internal energy and entropy, are defined by the two laws of thermodynamics. The internal energy U is that function of the state of the system whose differential is given by the equation expressing the first law, (1) dU = đQ + đW, where đQ and đW are, respectively, the heat added to the system and the external work done on the system in an infinitesimal process.2 For a simple fluid, the work is given by the equation (2)
đW = −pdV,
where p is the pressure on the system and V is its volume. The entropy S is that state function (discussed by Clausius as early as 1854, but not given a name by him until 1865) whose differential is given by the equation (3) dS = đQ/T, 2 I have altered Clausius’ notation, and also Gibbs’s in what follows, to conform to contemporary usage. This includes the “bar” on the inexact differentials.
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applicable to reversible processes, where T is the absolute temperature. For irreversible processes, equation (3) must be replaced by the inequality (4) dS > đQ/T. Statements (3) and (4), taken together, express the second law in differential form. The power and importance of the entropy concept were not evident to Clausius’ contemporaries when he introduced it in 1865. Indeed, Clausius himself did not view entropy as the basic concept for understanding the second law. He preferred to express the physical meaning of that law in terms of the concept of disgregation, another word that he coined, which he interpreted in molecular and mechanical terms [Clausius, 1862]; see [Klein, 1969]. Clausius restricted his use of entropy to its convenient role as a summarizing concept. In the memoir where it was introduced, he kept the original thermodynamic concepts, heat and work, at the center of his thinking and derived the experimentally useful consequences of the two laws without using the entropy function — or even the internal energy function! Not so Gibbs. When he published his first scientific memoir on thermodynamics in the spring of 1873 [Gibbs, 1873a], Gibbs quietly transformed the subject.3 He began by listing the basic concepts to be used in describing a thermodynamic system, among them energy and entropy, and then immediately combined equations (1) to (3) above to obtain (5) dU = T dS − pdV, a relation that contains only the state variables of the system, the path-dependent heat and work having been eliminated [1906, I, 1-2]. Although it took some time for the transformation to be appreciated, it was profound. For Clausius and his contemporaries, thermodynamics was the study of the interplay between heat and work — which is not surprising, given the etymology of the word. For Gibbs, however, thermodynamics became the theory of the properties of matter at equilibrium. This transformation is not immediately evident in Gibbs’s writings. In his first memoir, his objectives were limited. Gibbs argued that an equation expressing the internal energy of a thermodynamic system in terms of its entropy and volume could appropriately be called its “fundamental equation,” since equation (5) would then allow one to determine the two equations of state expressing temperature and pressure as functions of those extensive parameters [1906, I, 4, 6, 86]. And then, as the title of the paper promises, he discussed various geometrical representations of thermodynamic relations in two dimensions, especially the volume-entropy diagram suggested by the fundamental equation. Among other things, Gibbs pointed out how well the latter diagram expressed the region of simultaneous co-existence of the vapor, liquid, and solid phases of a substance. This “triple point” corresponds to a unique set of values of pressure and temperature, but it occupies the interior of a triangle in the volume-entropy plane [1906, I, 20-28, esp. 24]. 3 For assistance with Gibbs’s science, I have consulted [Donnan and Haas, 1936; Donnan, 1925] and the essays of Martin Klein listed in the References.
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The title of a second memoir [Gibbs, 1873b], published a few months after the first, might suggest that Gibbs sought only to extend his geometrical methods from two dimensions to three; but one does not have to read very far to see that he was doing something quite different. Again beginning with the “fundamental equation” [1906, I, 33], Gibbs’s emphasis was now on the phenomena to be explained, rather than on the graphical methods for representing them. That is, his interests were more physical than strictly mathematical. The central physical problem was to give a general characterization of the equilibrium state of a material system — of any body that can be solid, liquid, gas, or some combination of these according to circumstances. This time Gibbs used only one way of representing the equilibrium states: the surface described by those states in the space whose coordinate axes are energy, volume, and entropy [1906, I, 33-34, 37-43]. This surface represents the fundamental thermodynamic equation of the body. He proceeded to establish the relationships between the geometry of the surface and the physical conditions for thermodynamic equilibrium and its stability. For example, Gibbs showed that for two phases of the same substance to be in equilibrium with each other, not only must they share the same temperature T and pressure p, but the energies, entropies, and volumes of the two phases (per unit mass) must satisfy the equation (6) U2 − U1 = T (S2 − S1 ) − p(V2 − V1 ),
where the subscripts refer to the two phases [1906, I, 48-49]. 3
PHYSICAL CHEMISTRY
There are many suggestions in Gibbs’s first two papers that his treatment of thermodynamics had chemical applications; but these suggestions were only worked out in a third “essay,” his book-length memoir “On the Equilibrium of Heterogeneous Substances,” which appeared in two parts in 1876 and 1878, and which surely ranks as one of the greatest works in the history of physical science. In this memoir, Gibbs vastly enlarged the domain encompassed by thermodynamics, treating chemical, elastic, surface, and electrochemical phenomena by a single, unified method. He described the fundamental idea underlying the whole work in a lengthy abstract, which began: It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not appear to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium. [1878; 1906, I, 354] Gibbs then stated the general conditions of equilibrium whose manifold consequences his memoir had developed. They may be given in two alternative ways,
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which he showed to be equivalent: “For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy [entropy], the variation of its entropy [energy] shall either vanish or be negative [positive]” [1906, I, 54, 354]. That is, (7) (δU )S ≥ 0 or (8) (δS)U ≤ 0. Importantly, expression (7) makes it clear that thermodynamic equilibrium is a generalization of mechanical equilibrium, both being characterized by minimum energy under appropriate conditions. The consequences of this criterion could then be worked out as soon as the energy of a system is given in terms of the proper variables. Gibbs’s first, and probably most significant, application of this approach was to the problem of chemical equilibrium. To do this, however, he had to modify equation (5) to include any change of internal energy due to a change in the mass of the chemical components. This he did for the simplest case of a homogeneous phase by writing (5) in the form (9) dU = T dS − pdV +
n X
µi dmi ,
i=1
where the dmi gives the change in mass of the ith chemical substance, Si , . . . , Sn , whose masses can be varied, and µi is what Gibbs called the “chemical potential” of the ith substance [1906, I, 62, 65, 86, 92-96]. The chemical potential of any substance, in turn, is related to the energy U of the system by the equation (10) µi = (∂ U/∂ mi )S,V,mj , where the subscripts indicate that µi represents the rate of change of energy with respect to the mass of the ith component of the phase, the masses of all the other components being held constant along with the entropy and volume [1906, I, 93]; cf. [Donnan and Haas, II, 21-22, 61]. Hence, the condition for equilibrium, under these circumstances, is that the chemical potential for each actually present component substance be constant throughout the whole of the system considered [1906, I, 65]. In a heterogeneous system composed of several homogeneous phases, the fundamental equilibrium condition leads to the requirement that temperature, pressure, and the chemical potential of each independent chemical component must have the same values throughout the system [1906, I, 94-95]. From these general conditions on the intensive parameters Gibbs derived the phase rule, which specifies the number of independent variations δ (or degrees of freedom, again analogous to the situation in mechanics) in a system of r coexistent phases having n independent chemical components:
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(11) δ = n + 2 − r. This rule later proved to be an invaluable guide to understanding a mass of experimental material, but incredibly (as it now seems) Gibbs did not single it out for special mention in his memoir [1906, I, 96-97]. Of special interest for this essay is the attention Gibbs paid to showing how to obtain the specific conditions for equilibrium when chemical reactions could take place in a system. Suppose, for example, that a reaction of the type (12)
X
aj Aj = 0
j
can take place. Here the aj s are integers (stoichiometric coefficients) and the Aj s stand for the chemical symbols of the reacting substances. (An example, from [Donnan and Haas, II, 23]; cf. [Gibbs, 1906, I, pp. 93-94], is the following reaction: H2 + Cl2 − 2HCl = 0, where a1 = 1, a2 = 1, a3 = −2, and the corresponding Aj are H2 , Cl2 , and HCl, respectively.) The equilibrium condition that Gibbs derived for such a reaction has the very simple form (13)
X
aj µj = 0,
j
obtained by replacing the chemical symbols Aj with the chemical potential µj of the corresponding substance in the reaction equation [1906, I, 94, 171]. Moreover, since the potentials could in principle be determined from experimental data (even if, at the time, this was possible only for a rather limited number of situations — see [Donnan, 1925, 464-466; Wheeler, 1952, 78]), the equilibrium conditions were established by equation (13). Gibbs’s great memoir showed how the general theory of thermodynamic equilibrium could be applied to phenomena as diverse as the dissolving of a crystal in a liquid [1906, I, 320-325], the temperature dependence of the electromotive force of an electrochemical cell [1906, I, 338-349], and the heat absorbed when the surface of discontinuity between two fluids is increased [1906, I, 229-231, 271272]. But even more important than the particular results he obtained was his introduction of the general method and concepts with which all the applications of thermodynamics, chemical included, could be carried out. “In this immortal work,” wrote the editors of an extensive commentary on Gibbs’s thermodynamic writings, “Gibbs . . . brought the science of generalized thermodynamics to the same degree of perfect and comprehensive generality that Lagrange and Hamilton had in an earlier era brought the science of generalized dynamics.” And they added: it contains “a complete and perfect system of chemical thermodynamics, i.e., a system of thermodynamics peculiarly well adapted to the most general and complete application to chemical problems” [Donnan and Haas, I, vii].
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PHILOSOPHY
Gibbs is not an easy read. He wrote in a terse, abstract style and provided few examples to illustrate his general conclusions. In addition, he would seldom tell his readers about the specific problems that led to the work on which he was reporting, much less inform them of any larger project he thought he results might further (see [Klein, 1980; Deltete, 1995a]). Pierre Duhem even concluded that “We must resign ourselves to ignorance about the philosophical ideas that no doubt presided over the birth of physical theories in Gibbs’s mind” [Duhem, 1907, 196]. Other contemporaries, however, thought that they had discerned the broader philosophical motivation for Gibbs’s scientific work. I consider two of them, the energeticists Georg Helm and Wilhelm Ostwald,4 both of whom profoundly admired the science but disagreed, equally profoundly, about the philosophical import of it. Helm was an energetic phenomenalist. His official position, even if not always the one he adhered to in practice, is contained in what I have elsewhere called the “Relations Thesis” [1995b, 137-138; 1999, 11-12]. For our purposes, two features of the Relations Thesis are important: first, it claims that we can only know phenomena and changes in phenomena, all of which are energetic in character; second, it claims, in consequence, that the goal of natural science is to describe and relate energy phenomena in the simplest and most unified manner possible. In his history of energetics, Helm counted Gibbs among the preeminent defenders of this view of the nature of science: Completely free of any bias in favor of the mechanics of atoms, establishing with complete impartiality the strict consequences of the two laws [of thermodynamics], without any longing glances at and yearning for mechanics — thus the work of Gibbs suddenly stands before our gaze . . . . What a work, in which chemical processes are treated without the traditional chemical apparatus of atoms, in which the theories of elasticity, of capillarity and crystallization, and of electromotive force, are set forth without all the usual devices of atomistic origin! Naked and pure, the true object of the theoretical knowledge of nature stands before us: the establishment of quantitative relationships between the parameters which determine the state of a material system during any changes subject to investigation. [Helm, 1898, 146; Deltete, 1999, 194] At best, Helm’s appraisal is misleading; at worst, it is simply mistaken. To be sure, Gibbs sought to keep separate the general principles of his thermodynamics, and the consequences that could be derived from them, from more special assumptions about the molecular constitution of bodies and molecular motions. And his reasons for doing so were largely the same as Clausius’: the desire to keep the thermodynamic presentation free of assumptions that could be attacked as inadequately founded or even gratuitous. But when he thought he could clarify 4 General discussions of energetics, and more detailed ones of both Helm and Ostwald, may be found in my essays listed in the References.
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his discussion by referring to molecular behavior, Gibbs did not hesitate to do so. These references are infrequent, but they do occur — in his treatment of the reaction carrying NO2 into N2 O4 [1906, I, 175-184], for example, and in his mention of the “sphere of molecular action” when he introduced his analysis of the thermodynamics of capillarity [1906, I, 219]. The discussion of the so-called “Gibbs paradox” having to do with the diffusion of gases [1906, I, 165-168] is perhaps the best known of the passages in “Heterogeneous Equilibrium” that is explicitly molecular, but there is an entire section of his great memoir devoted to “Certain Points relating to the Molecular Constitution of Bodies” [1906, I, 138-144] in which Gibbs freely spoke of “molecules of different sorts;” and he later wrote approvingly of Clausius’ concept of disgregation, praising him for his “remarkable insight” and his “very valuable contribution to molecular science” [1889, 264-265]; cf. [Klein, 1969]. I conclude that Gibbs was not a phenomenalist, energetic or otherwise, but believed in the molecular constitution of matter, even if the dynamics that served as a model for his thermodynamics said little about that constitution. Unlike Helm, Ostwald was an energetic realist. His official position, even if not the one he always followed, is perhaps best described by what I have elsewhere called the Composition Thesis [1995b, 139-140; 2008, 194-200]. On this view “material objects” (or “physical-chemical systems”) are nothing more than energy complexes, spatially co-present and coupled clusters of energy; and Ostwald found it, at least implicitly, in Gibbs: We . . . want to hazard the attempt to construct a world view exclusively from energetic material without using the concept of matter .... [This approach] has even been developed with the widest compass for the new chemistry in the fundamental work of W. Gibbs, without, of course, having been explicitly formulated. [1902, 165-166] Reminiscing in his autobiography, Ostwald was more emphatic: [Gibbs’s writings] had the greatest influence on my own development, for while he does not particularly emphasize it, Gibbs works exclusively with quantities of energy and their factors, and shuns entirely all kinetic hypotheses . . . . I could not help but notice that the more than 200 equations stated and treated in his major work were almost without exception equations between quantities of energy. This observation . . . became for me of the greatest importance, since it showed that his fundamental work could be characterized as a chemical energetics. [1926, II, 61-62, 63-64] Ostwald misunderstood Gibbs’s motivation. To begin with, Gibbs was evidently not trying to construct an energetics, or “theory of energy as such,” as Ostwald referred to his own project. For Gibbs, thermodynamics was not essentially a theory of energy, but rather the study of the equilibrium states of material systems and of the necessary and sufficient conditions of these states. As noted earlier, Gibbs introduced assumptions about the nature of matter only when needed, preferring
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instead an approach of the greatest possible generality. But there is no suggestion that he wished to reduce matter to a complex of energy factors in line with Ostwald’s Composition Thesis. This is not to say that energy did not play an important role in Gibbs’s development of thermodynamics. It did. But it enters as an especially important property of the material systems that were the primary subject of his interest. “The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it capable,” Gibbs wrote at the beginning of his memoir on heterogeneous equilibrium [1906, I, 55]. The reason, he explained, is that these properties of a material system allow one to understand the interactions of a system with its surroundings and its conditions of equilibrium. Gibbs said much the same thing in his letter accepting the Rumford Medal (equivalent at the time to a Nobel prize): “The leading idea which I followed in my paper on the Equilibrium of Heterogeneous Substances was to develop the roles of energy and entropy in the theory of thermo-dynamic equilibrium,” adding that his investigation had led him to “certain functions which play the principal part in determining the behavior of matter in respect to chemical equilibrium” [Gibbs, 1881; Donnan and Haas, 1936, I, 55; Wheeler, 1952, 89]. Unlike Ostwald, moreover, it is clear from these remarks that for Gibbs the concept of entropy was at least as important for understanding the behavior of thermodynamic systems (“such as all material systems actually are”) as the concept of energy. I conclude, therefore, that Gibbs was not an energetic realist. If it was not, as I claim, an energetic project, either phenomenalist or realist, that motivated Gibbs’s work in thermodynamics and its application to chemistry, the natural question is what did. One cannot be sure, but the answer, I suggest, was to develop his subject matter logically from a very simple and general point of view. This suggestion is confirmed by what seems to have been Gibbs’s only public comment on his intent. “One of the principal objects of theoretical research,” he wrote in his letter accepting the Rumford Medal, “is to find the point of view from which the subject appears in the greatest simplicity” (1881; in Donnan and Haas I, 54 and Wheeler, 89). Other aspects of Gibbs’s style indicate what that meant for him. The author of a commemorative essay on Gibbs’s father wrote the following of the elder Gibbs: “Mr. Gibbs loved system and was never satisfied until he had cast his material into the proper form. His essays on special topics are marked by the nicest logical arrangement” (Wheeler, 9). The same could equally have been said of Gibbs himself. He always sought to take a very general approach to the subjects that engaged him, to develop his ideas rigorously and systematically from clearly stated first principles, and to avoid whenever possible any special assumptions. In short, Paul Tannery’s evaluation of one of Duhem’s works could easily serve as a evaluation of any of Gibbs’s: “To draw all logical consequences from a very general principle, to show clearly what it contains and what it does not, and to specify the points where experiment must intervene to bring in something really new — such is the aim [Duhem] pursues, and undoubtedly he will thus contribute in large
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measure to the organization of current science” (quoted in [Jaki, 1984, 279-280]). This is a good summary of what Gibbs tried to do in his main study on thermodynamics. His memoir on heterogeneous equilibrium begins by stating very simple and general conditions for the equilibrium and stability of a material system, and then proceeds to work out, very carefully, the consequences of those conditions for diverse situations, beginning from relatively simple ones and gradually adding more complexity (heterogeneous composition, gravity, surface tension, strain in solids, and electrical forces, for example). He was aware that for practical purposes the consequences are often more useful than the general statements from which they are derived (the phase rule is an example); but he preferred to begin with the latter rather than the former, “believing that it would be useful to exhibit the conditions of equilibrium of thermodynamic systems in connection with those quantities [pressure, temperature, volume, energy and entropy] which are most simple and most general in their definitions, and which appear most important in the general theory of such systems” [1878; 1906, I, 355-56]. It therefore seems fair to say that Gibbs was motivated in this work, as in others, by the search for a simple, very general standpoint that would allow him to retrieve accepted results in a rigorous manner and to predict new ones. The reason for logical rigor, I conjecture, is that he valued it as the best means of “showing exactly what a principle contains and what it does not” in order “to specify the points where experiment must intervene to bring in something really new.” That theory — even simple and general theory — is constrained by experiment is something of which Gibbs was evidently aware (see, e.g., [1881; in Donnan and Haas I, 55]). A prescient example may be found in the Preface he wrote to his work on statistical mechanics [Gibbs, 1902]. Gibbs proposed his statistical theory as a “branch of rational mechanics” that did not “attempt to frame hypotheses concerning the constitution of material bodies.” Earlier, I argued that Gibbs was no defender of phenomenalism, that he presupposed the molecular structure of matter; but in his statistical mechanics, where one might otherwise expect him to do so, he declined to offer any theory of that structure. The reason is that Gibbs did not see how to formulate a general theory that was compatible with the available experimental findings. In fact, he said, “In the present state of science, it seems hardly possible” to construct such a theory and that, in consequence, one would be “building on an insecure foundation.” He therefore concluded: “Difficulties of this kind have deterred the author from attempting to explain the mysteries of nature” and have forced him to be content with a more modest aim [1902, vii-viii]. Given the revolution in physics, including matter theory, that would soon occur, Gibbs’s confession was not only honest but wise.
BIBLIOGRAPHY [Clausius, 1876] R. Clausius. Die mechanische Wärmetheorie, 2nd ed., Braunschweig: Vieweg, 1876. This volume conveniently collects the essays of 1850, 1854, 1862 and 1865 mentioned in the text.
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[Deltete, 1995a] R. J. Deltete. Gibbs and Ostwald: A Contrast in Scientific Style, Journal of Chemical Education 73: 289-295, 1995. [Deltete, 1995b] R. J. Deltete. Gibbs and the Energeticists, in A.J. Kox and D. Siegel (eds), No Truth Except in the Details: Essays in Honor of Martin J. Klein, Dordrecht: Kluwer, 135-169, 1995. [Deltete, 1999 ] R. J. Deltete. The Historical Development of Energetics, Dordrecht: Kluwer, 1999. Trans. of Georg Helm, Die geschichtlichen Entwicklung der Energetik. Leipzig: Veit & Comp., 1898. [Deltete, 2000] R. J. Deltete. Gibbs, Josiah Willard, in The MacMillan Encyclopedia of Energy, New York, Macmillan & Co., pp. 579-581. 2000. [Deltete, 2003] R. J. Deltete. Energetics, in: J.L. Heilbron (ed), The Oxford Companion to the History of Modern Science, New York: Oxford University Press, pp. 256-257, 2003. [Deltete, 2005] R. J. Deltete. Die Lehre von der Energie: Georg Helm’s Energetic Manifesto, Centaurus 47: 140-162, 2005. [Deltete, 2007a] R. J. Deltete. Wilhelm Ostwald’s Energetics 1: Origins and Motivations, Foundations of Chemistry 9: 3-56, 2007. [Deltete, 2007b] R. J. Deltete. Wilhelm Ostwald’s Energetics 2: Energetic Theory and Applications, Part I, Foundations of Chemistry 9: 265-316, 2007. [Deltete, 2008] R. J. Deltete. Wilhelm Ostwald’s Energetics 3: Energetic Theory and Applications, Part II, Foundations of Chemistry 10: 187-221, 2008. [Deltete, 2009] R. J. Deltete. Georg Helm’s Chemical Energetics, Centaurus (In Press). [Duhem, 1907] P. Duhem. Étude sur le caractère de l’oeuvre de Gibbs (Àpropos de The Scientific Papers of Willard Gibbs), Bulletin des Sciences Mathématiques 31 (1907): 181-211, 1907. [Donnan, 1925] F. G. Donnan. The Influence of J. Willard Gibbs on the Science of Physical Chemistry, Journal of the Franklin Institute 199: 457-483, 1925. [Donnan and Haas, 1936] F. G. Donnan and A. Haas. A Commentary on the Scientific Writings of J. Willard Gibbs, 2 vols., New Haven: Yale University Press, 1936. [Gibbs, 1873a] J. W. Gibbs. Graphical Methods in the Thermodynamics of Fluids, Transactions of the Connecticut Academy of Arts and Sciences 2: 309-342. Rpt. in Gibbs (1906), I, pp. 1-32, 1873. [Gibbs, 1873b] J. W. Gibbs. A Method of Geometrical Representation of the Thermodynamics Properties of Substances by Means of Surfaces, Transactions of the Connecticut Academy of Arts and Sciences 2: 382-404. Rpt. in Gibbs (1906), I, pp. 33-54, 1973. [Gibbs, 1876-1878] J. W. Gibbs. On the Equilibrium of Heterogeneous Substances, Transactions of the Connecticut Academy of Arts and Sciences 3: 108-248 (1876); 343-524 (1878). Rpt. in Gibbs (1906), I, pp. 55-353 1876–1878. [Gibbs, 1878] J. W. Gibbs. Abstract of ‘On the Equilibrium of Heterogeneous Substances’,” American Journal of Science 16: 441-458, 1878. Rpt. In Gibbs (1906), I, pp. 354-371. [Gibbs, 1881] J. W. Gibbs. To the American Academy of Arts and Sciences, January 10, 1881. Rpt. in Donnan and Haas (1936), I, pp. 54-55 and Wheeler (1952), pp. 88-89. [Gibbs, 1889] J. W. Gibbs. Rudolf Julius Emanuel Clausius, Proceedings of the American Academy of Arts and Sciences 16 (1889). Rpt. In Gibbs (1906), II, pp. 261-267, 1889. [Gibbs, 1902] J. W. Gibbs. Elementary Principles in Statistical Mechanics, Delevoped with Special Reference to the Rational Foundation of Thermodynamics, New York: Scribner’s, 1902. [Gibbs, 1906] J. W. Gibbs. The Scientific Papers of J. Willard Gibbs, 2 vols., H. A. Bumstead and R. G. Van Name (eds.), New York: Longmans, Green, and Co, 1906. [Gibbs, 1974] J. W. Gibbs. The Early Work of Willard Gibbs in Applied Mechanics, L. P. Wheller, E. O. Waters, and S. W. Dudley (eds.), New York, Schuman. [Jaki, 1984] S. L. Jaki. Uneasy Genius: The Life and Work of Pierre Duhem, Dordrecht: Martinus Nijhoff, 1984. [Klein, 1969] M. J. Klein. Gibbs on Clausius, Historical Studies in the Physical Sciences 1: 127-149, 1969. [Klein, 1972] M. J. Klein. Gibbs, Josiah Willard, in Dictionary of Scientific Biography, C. G. Gillispie (ed.), New York, Scribner’s, vol. 5, pp. 386-393, 1972.
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[Klein, 1977] M. J. Klein. The Early Papers of J. Willard Gibbs: A Transformation in Thermodynamics, in Human Implications of Scientific Advance. Proceedings of the XVth International Congress of the History of Science. Edinburgh, 10-15 August 1977, Edinburgh, 1978, pp. 330-341, 1977. [Klein, 1980] M. J. Klein. The Scientific Style of Josiah Willard Gibbs, in Springs of Scientific Creativity: Essays on the Founders of Modern Science, R. Aris, H. T. Davis, and R. H. Stuewer (eds.), Minneapolis, University of Minnesota Press, 1983, pp. 142-162, 1980. [Klein, 1989] M. J. Klein. The Physics of J. Willard Gibbs in His Time, in Proceedings of the Gibbs Symposium. Yale University, May 15-17, 1989, D. G. Caldi and G. D. Mostow (eds.), New York, American Mathematical Society, pp. 1-21, 1989. [Klein, 1990] M. J. Klein. The Physics of J. Willard Gibbs in His Time, Physics Today (September, 1990): 40-48, 1990. [Wilhelm, 1902] O. Wilhelm. Vorlesungen über Naturphilosophie, gehalten im Sommer 1901 an der Universität Leipzig, Leipzig: Veit & Co, 1902. [Wilhelm, 1926] O. Wilhelm. Lebenslinien: Eine Selbstbiographie, 3 vols., Berlin: Klasing & Co., 1926-1927. [Wheeler, 1952] L. P. Wheeler. Josiah Willard Gibbs. The History of a Great Mind, 2nd ed., New Haven: Yale University Press, 1952.
1
BIOGRAPHY
Gibbs was the only son among five children of the distinguished philologist and professor of sacred literature at Yale College.1 The younger Gibbs grew up in New Haven and graduated from Yale in 1858, having won a string of scholarships and prizes in both Latin and mathematics. He continued at Yale as a student of engineering in the new graduate school, and in 1863 received one of the first Ph.D. degrees granted in the United States. After serving as a tutor for three years, giving elementary instruction in Latin and natural philosophy to undergraduates, Gibbs left New Haven for further study in Europe. He spent a year each in Paris, at the Collège de France and the Sorbonne, and at the universities of Berlin and Heidelberg, attending lectures in mathematics and physics and reading widely in both fields. He was never a student of any of the luminaries whose lectures he attended (the list includes Liouville and Kronecker in mathematics, and Kirchhoff and Helmholtz in physics), but these European studies, rather than his earlier education in engineering, provided the foundation for his subsequent research. (An important qualification is Gibbs’s fondness for “the niceties of geometrical reasoning” [Gibbs, 1974, 43], which is evident in his engineering thesis before it played a prominent role in his thermodynamic work.) Gibbs returned to New Haven in June 1869. He never again left America and rarely ever left New Haven except for his annual summer holidays in northern New England and a very occasional journey to lecture or attend a meeting. Gibbs never married and lived all his life in the house in which he had grown up, close to the college buildings, sharing it with two of his sisters and the family of one of them. In July 1871, two years before he published his first scientific paper, Gibbs was appointed professor of mathematical physics at Yale. He held that position without salary for the first nine years, living on inherited income. It was 1 For biographical material on Gibbs, I have relied on Klein (esp. [1972; 1989]) who, in turn, largely relies on [Wheeler, 1952].
Handbook of the Philosophy of Science. Volume 6: Philosophy of Chemistry. Volume editors: Robin Findlay Hendry, Paul Needham and Andrea I. Woody. General editors: Dov M. Gabbay, Paul Thagard and John Woods. c 2012 Elsevier BV. All rights reserved.
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during this time that he wrote the memoirs on thermodynamics that, in most estimations, constitute his greatest contribution to science. Gibbs was seriously tempted to leave Yale in 1880, when he was invited to join the faculty of the new Johns Hopkins University in Baltimore. Only then did his alma mater offer him a salary — only two thirds of what Hopkins would have paid; but the advantages of remaining in familiar surroundings, plus the high regard in which he was held by colleagues, convinced Gibbs to stay. He continued to teach at Yale until his death, after a brief illness, in the spring of 1903. Gibbs’s research interests evolved from engineering to mechanics, and then to thermodynamics, vector analysis and the electromagnetic theory of light, and statistical mechanics. Since his work in thermodynamics and its applications to physical chemistry is likely most relevant to readers of this volume, that work is the subject of my essay. Section II deals with Gibbs’s novel development of thermodynamics and Section III focuses on his application of that thermodynamic theory to various problems in physical chemistry. Section IV then steps back to consider the overall nature of his project and its relevance to philosophy. 2
THERMODYNAMICS
When Gibbs first turned his attention to thermodynamics in the early 1870’s, the subject had already achieved a certain level of maturity. The essential step had been taken in 1850 by Rudolf Clausius, when he argued that two laws are needed to reconcile Carnot’s principle about the motive power of heat with the law of energy transformation and conservation. Efforts to understand the second of the two laws finally led Clausius in 1865 to his most concise and ultimately most fruitful analytical formulation. In effect, two basic quantities, internal energy and entropy, are defined by the two laws of thermodynamics. The internal energy U is that function of the state of the system whose differential is given by the equation expressing the first law, (1) dU = đQ + đW, where đQ and đW are, respectively, the heat added to the system and the external work done on the system in an infinitesimal process.2 For a simple fluid, the work is given by the equation (2)
đW = −pdV,
where p is the pressure on the system and V is its volume. The entropy S is that state function (discussed by Clausius as early as 1854, but not given a name by him until 1865) whose differential is given by the equation (3) dS = đQ/T, 2 I have altered Clausius’ notation, and also Gibbs’s in what follows, to conform to contemporary usage. This includes the “bar” on the inexact differentials.
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applicable to reversible processes, where T is the absolute temperature. For irreversible processes, equation (3) must be replaced by the inequality (4) dS > đQ/T. Statements (3) and (4), taken together, express the second law in differential form. The power and importance of the entropy concept were not evident to Clausius’ contemporaries when he introduced it in 1865. Indeed, Clausius himself did not view entropy as the basic concept for understanding the second law. He preferred to express the physical meaning of that law in terms of the concept of disgregation, another word that he coined, which he interpreted in molecular and mechanical terms [Clausius, 1862]; see [Klein, 1969]. Clausius restricted his use of entropy to its convenient role as a summarizing concept. In the memoir where it was introduced, he kept the original thermodynamic concepts, heat and work, at the center of his thinking and derived the experimentally useful consequences of the two laws without using the entropy function — or even the internal energy function! Not so Gibbs. When he published his first scientific memoir on thermodynamics in the spring of 1873 [Gibbs, 1873a], Gibbs quietly transformed the subject.3 He began by listing the basic concepts to be used in describing a thermodynamic system, among them energy and entropy, and then immediately combined equations (1) to (3) above to obtain (5) dU = T dS − pdV, a relation that contains only the state variables of the system, the path-dependent heat and work having been eliminated [1906, I, 1-2]. Although it took some time for the transformation to be appreciated, it was profound. For Clausius and his contemporaries, thermodynamics was the study of the interplay between heat and work — which is not surprising, given the etymology of the word. For Gibbs, however, thermodynamics became the theory of the properties of matter at equilibrium. This transformation is not immediately evident in Gibbs’s writings. In his first memoir, his objectives were limited. Gibbs argued that an equation expressing the internal energy of a thermodynamic system in terms of its entropy and volume could appropriately be called its “fundamental equation,” since equation (5) would then allow one to determine the two equations of state expressing temperature and pressure as functions of those extensive parameters [1906, I, 4, 6, 86]. And then, as the title of the paper promises, he discussed various geometrical representations of thermodynamic relations in two dimensions, especially the volume-entropy diagram suggested by the fundamental equation. Among other things, Gibbs pointed out how well the latter diagram expressed the region of simultaneous co-existence of the vapor, liquid, and solid phases of a substance. This “triple point” corresponds to a unique set of values of pressure and temperature, but it occupies the interior of a triangle in the volume-entropy plane [1906, I, 20-28, esp. 24]. 3 For assistance with Gibbs’s science, I have consulted [Donnan and Haas, 1936; Donnan, 1925] and the essays of Martin Klein listed in the References.
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The title of a second memoir [Gibbs, 1873b], published a few months after the first, might suggest that Gibbs sought only to extend his geometrical methods from two dimensions to three; but one does not have to read very far to see that he was doing something quite different. Again beginning with the “fundamental equation” [1906, I, 33], Gibbs’s emphasis was now on the phenomena to be explained, rather than on the graphical methods for representing them. That is, his interests were more physical than strictly mathematical. The central physical problem was to give a general characterization of the equilibrium state of a material system — of any body that can be solid, liquid, gas, or some combination of these according to circumstances. This time Gibbs used only one way of representing the equilibrium states: the surface described by those states in the space whose coordinate axes are energy, volume, and entropy [1906, I, 33-34, 37-43]. This surface represents the fundamental thermodynamic equation of the body. He proceeded to establish the relationships between the geometry of the surface and the physical conditions for thermodynamic equilibrium and its stability. For example, Gibbs showed that for two phases of the same substance to be in equilibrium with each other, not only must they share the same temperature T and pressure p, but the energies, entropies, and volumes of the two phases (per unit mass) must satisfy the equation (6) U2 − U1 = T (S2 − S1 ) − p(V2 − V1 ),
where the subscripts refer to the two phases [1906, I, 48-49]. 3
PHYSICAL CHEMISTRY
There are many suggestions in Gibbs’s first two papers that his treatment of thermodynamics had chemical applications; but these suggestions were only worked out in a third “essay,” his book-length memoir “On the Equilibrium of Heterogeneous Substances,” which appeared in two parts in 1876 and 1878, and which surely ranks as one of the greatest works in the history of physical science. In this memoir, Gibbs vastly enlarged the domain encompassed by thermodynamics, treating chemical, elastic, surface, and electrochemical phenomena by a single, unified method. He described the fundamental idea underlying the whole work in a lengthy abstract, which began: It is an inference naturally suggested by the general increase of entropy which accompanies the changes occurring in any isolated material system that when the entropy of the system has reached a maximum, the system will be in a state of equilibrium. Although this principle has by no means escaped the attention of physicists, its importance does not appear to have been duly appreciated. Little has been done to develop the principle as a foundation for the general theory of thermodynamic equilibrium. [1878; 1906, I, 354] Gibbs then stated the general conditions of equilibrium whose manifold consequences his memoir had developed. They may be given in two alternative ways,
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which he showed to be equivalent: “For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy [entropy], the variation of its entropy [energy] shall either vanish or be negative [positive]” [1906, I, 54, 354]. That is, (7) (δU )S ≥ 0 or (8) (δS)U ≤ 0. Importantly, expression (7) makes it clear that thermodynamic equilibrium is a generalization of mechanical equilibrium, both being characterized by minimum energy under appropriate conditions. The consequences of this criterion could then be worked out as soon as the energy of a system is given in terms of the proper variables. Gibbs’s first, and probably most significant, application of this approach was to the problem of chemical equilibrium. To do this, however, he had to modify equation (5) to include any change of internal energy due to a change in the mass of the chemical components. This he did for the simplest case of a homogeneous phase by writing (5) in the form (9) dU = T dS − pdV +
n X
µi dmi ,
i=1
where the dmi gives the change in mass of the ith chemical substance, Si , . . . , Sn , whose masses can be varied, and µi is what Gibbs called the “chemical potential” of the ith substance [1906, I, 62, 65, 86, 92-96]. The chemical potential of any substance, in turn, is related to the energy U of the system by the equation (10) µi = (∂ U/∂ mi )S,V,mj , where the subscripts indicate that µi represents the rate of change of energy with respect to the mass of the ith component of the phase, the masses of all the other components being held constant along with the entropy and volume [1906, I, 93]; cf. [Donnan and Haas, II, 21-22, 61]. Hence, the condition for equilibrium, under these circumstances, is that the chemical potential for each actually present component substance be constant throughout the whole of the system considered [1906, I, 65]. In a heterogeneous system composed of several homogeneous phases, the fundamental equilibrium condition leads to the requirement that temperature, pressure, and the chemical potential of each independent chemical component must have the same values throughout the system [1906, I, 94-95]. From these general conditions on the intensive parameters Gibbs derived the phase rule, which specifies the number of independent variations δ (or degrees of freedom, again analogous to the situation in mechanics) in a system of r coexistent phases having n independent chemical components:
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(11) δ = n + 2 − r. This rule later proved to be an invaluable guide to understanding a mass of experimental material, but incredibly (as it now seems) Gibbs did not single it out for special mention in his memoir [1906, I, 96-97]. Of special interest for this essay is the attention Gibbs paid to showing how to obtain the specific conditions for equilibrium when chemical reactions could take place in a system. Suppose, for example, that a reaction of the type (12)
X
aj Aj = 0
j
can take place. Here the aj s are integers (stoichiometric coefficients) and the Aj s stand for the chemical symbols of the reacting substances. (An example, from [Donnan and Haas, II, 23]; cf. [Gibbs, 1906, I, pp. 93-94], is the following reaction: H2 + Cl2 − 2HCl = 0, where a1 = 1, a2 = 1, a3 = −2, and the corresponding Aj are H2 , Cl2 , and HCl, respectively.) The equilibrium condition that Gibbs derived for such a reaction has the very simple form (13)
X
aj µj = 0,
j
obtained by replacing the chemical symbols Aj with the chemical potential µj of the corresponding substance in the reaction equation [1906, I, 94, 171]. Moreover, since the potentials could in principle be determined from experimental data (even if, at the time, this was possible only for a rather limited number of situations — see [Donnan, 1925, 464-466; Wheeler, 1952, 78]), the equilibrium conditions were established by equation (13). Gibbs’s great memoir showed how the general theory of thermodynamic equilibrium could be applied to phenomena as diverse as the dissolving of a crystal in a liquid [1906, I, 320-325], the temperature dependence of the electromotive force of an electrochemical cell [1906, I, 338-349], and the heat absorbed when the surface of discontinuity between two fluids is increased [1906, I, 229-231, 271272]. But even more important than the particular results he obtained was his introduction of the general method and concepts with which all the applications of thermodynamics, chemical included, could be carried out. “In this immortal work,” wrote the editors of an extensive commentary on Gibbs’s thermodynamic writings, “Gibbs . . . brought the science of generalized thermodynamics to the same degree of perfect and comprehensive generality that Lagrange and Hamilton had in an earlier era brought the science of generalized dynamics.” And they added: it contains “a complete and perfect system of chemical thermodynamics, i.e., a system of thermodynamics peculiarly well adapted to the most general and complete application to chemical problems” [Donnan and Haas, I, vii].
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PHILOSOPHY
Gibbs is not an easy read. He wrote in a terse, abstract style and provided few examples to illustrate his general conclusions. In addition, he would seldom tell his readers about the specific problems that led to the work on which he was reporting, much less inform them of any larger project he thought he results might further (see [Klein, 1980; Deltete, 1995a]). Pierre Duhem even concluded that “We must resign ourselves to ignorance about the philosophical ideas that no doubt presided over the birth of physical theories in Gibbs’s mind” [Duhem, 1907, 196]. Other contemporaries, however, thought that they had discerned the broader philosophical motivation for Gibbs’s scientific work. I consider two of them, the energeticists Georg Helm and Wilhelm Ostwald,4 both of whom profoundly admired the science but disagreed, equally profoundly, about the philosophical import of it. Helm was an energetic phenomenalist. His official position, even if not always the one he adhered to in practice, is contained in what I have elsewhere called the “Relations Thesis” [1995b, 137-138; 1999, 11-12]. For our purposes, two features of the Relations Thesis are important: first, it claims that we can only know phenomena and changes in phenomena, all of which are energetic in character; second, it claims, in consequence, that the goal of natural science is to describe and relate energy phenomena in the simplest and most unified manner possible. In his history of energetics, Helm counted Gibbs among the preeminent defenders of this view of the nature of science: Completely free of any bias in favor of the mechanics of atoms, establishing with complete impartiality the strict consequences of the two laws [of thermodynamics], without any longing glances at and yearning for mechanics — thus the work of Gibbs suddenly stands before our gaze . . . . What a work, in which chemical processes are treated without the traditional chemical apparatus of atoms, in which the theories of elasticity, of capillarity and crystallization, and of electromotive force, are set forth without all the usual devices of atomistic origin! Naked and pure, the true object of the theoretical knowledge of nature stands before us: the establishment of quantitative relationships between the parameters which determine the state of a material system during any changes subject to investigation. [Helm, 1898, 146; Deltete, 1999, 194] At best, Helm’s appraisal is misleading; at worst, it is simply mistaken. To be sure, Gibbs sought to keep separate the general principles of his thermodynamics, and the consequences that could be derived from them, from more special assumptions about the molecular constitution of bodies and molecular motions. And his reasons for doing so were largely the same as Clausius’: the desire to keep the thermodynamic presentation free of assumptions that could be attacked as inadequately founded or even gratuitous. But when he thought he could clarify 4 General discussions of energetics, and more detailed ones of both Helm and Ostwald, may be found in my essays listed in the References.
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his discussion by referring to molecular behavior, Gibbs did not hesitate to do so. These references are infrequent, but they do occur — in his treatment of the reaction carrying NO2 into N2 O4 [1906, I, 175-184], for example, and in his mention of the “sphere of molecular action” when he introduced his analysis of the thermodynamics of capillarity [1906, I, 219]. The discussion of the so-called “Gibbs paradox” having to do with the diffusion of gases [1906, I, 165-168] is perhaps the best known of the passages in “Heterogeneous Equilibrium” that is explicitly molecular, but there is an entire section of his great memoir devoted to “Certain Points relating to the Molecular Constitution of Bodies” [1906, I, 138-144] in which Gibbs freely spoke of “molecules of different sorts;” and he later wrote approvingly of Clausius’ concept of disgregation, praising him for his “remarkable insight” and his “very valuable contribution to molecular science” [1889, 264-265]; cf. [Klein, 1969]. I conclude that Gibbs was not a phenomenalist, energetic or otherwise, but believed in the molecular constitution of matter, even if the dynamics that served as a model for his thermodynamics said little about that constitution. Unlike Helm, Ostwald was an energetic realist. His official position, even if not the one he always followed, is perhaps best described by what I have elsewhere called the Composition Thesis [1995b, 139-140; 2008, 194-200]. On this view “material objects” (or “physical-chemical systems”) are nothing more than energy complexes, spatially co-present and coupled clusters of energy; and Ostwald found it, at least implicitly, in Gibbs: We . . . want to hazard the attempt to construct a world view exclusively from energetic material without using the concept of matter .... [This approach] has even been developed with the widest compass for the new chemistry in the fundamental work of W. Gibbs, without, of course, having been explicitly formulated. [1902, 165-166] Reminiscing in his autobiography, Ostwald was more emphatic: [Gibbs’s writings] had the greatest influence on my own development, for while he does not particularly emphasize it, Gibbs works exclusively with quantities of energy and their factors, and shuns entirely all kinetic hypotheses . . . . I could not help but notice that the more than 200 equations stated and treated in his major work were almost without exception equations between quantities of energy. This observation . . . became for me of the greatest importance, since it showed that his fundamental work could be characterized as a chemical energetics. [1926, II, 61-62, 63-64] Ostwald misunderstood Gibbs’s motivation. To begin with, Gibbs was evidently not trying to construct an energetics, or “theory of energy as such,” as Ostwald referred to his own project. For Gibbs, thermodynamics was not essentially a theory of energy, but rather the study of the equilibrium states of material systems and of the necessary and sufficient conditions of these states. As noted earlier, Gibbs introduced assumptions about the nature of matter only when needed, preferring
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instead an approach of the greatest possible generality. But there is no suggestion that he wished to reduce matter to a complex of energy factors in line with Ostwald’s Composition Thesis. This is not to say that energy did not play an important role in Gibbs’s development of thermodynamics. It did. But it enters as an especially important property of the material systems that were the primary subject of his interest. “The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it capable,” Gibbs wrote at the beginning of his memoir on heterogeneous equilibrium [1906, I, 55]. The reason, he explained, is that these properties of a material system allow one to understand the interactions of a system with its surroundings and its conditions of equilibrium. Gibbs said much the same thing in his letter accepting the Rumford Medal (equivalent at the time to a Nobel prize): “The leading idea which I followed in my paper on the Equilibrium of Heterogeneous Substances was to develop the roles of energy and entropy in the theory of thermo-dynamic equilibrium,” adding that his investigation had led him to “certain functions which play the principal part in determining the behavior of matter in respect to chemical equilibrium” [Gibbs, 1881; Donnan and Haas, 1936, I, 55; Wheeler, 1952, 89]. Unlike Ostwald, moreover, it is clear from these remarks that for Gibbs the concept of entropy was at least as important for understanding the behavior of thermodynamic systems (“such as all material systems actually are”) as the concept of energy. I conclude, therefore, that Gibbs was not an energetic realist. If it was not, as I claim, an energetic project, either phenomenalist or realist, that motivated Gibbs’s work in thermodynamics and its application to chemistry, the natural question is what did. One cannot be sure, but the answer, I suggest, was to develop his subject matter logically from a very simple and general point of view. This suggestion is confirmed by what seems to have been Gibbs’s only public comment on his intent. “One of the principal objects of theoretical research,” he wrote in his letter accepting the Rumford Medal, “is to find the point of view from which the subject appears in the greatest simplicity” (1881; in Donnan and Haas I, 54 and Wheeler, 89). Other aspects of Gibbs’s style indicate what that meant for him. The author of a commemorative essay on Gibbs’s father wrote the following of the elder Gibbs: “Mr. Gibbs loved system and was never satisfied until he had cast his material into the proper form. His essays on special topics are marked by the nicest logical arrangement” (Wheeler, 9). The same could equally have been said of Gibbs himself. He always sought to take a very general approach to the subjects that engaged him, to develop his ideas rigorously and systematically from clearly stated first principles, and to avoid whenever possible any special assumptions. In short, Paul Tannery’s evaluation of one of Duhem’s works could easily serve as a evaluation of any of Gibbs’s: “To draw all logical consequences from a very general principle, to show clearly what it contains and what it does not, and to specify the points where experiment must intervene to bring in something really new — such is the aim [Duhem] pursues, and undoubtedly he will thus contribute in large
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measure to the organization of current science” (quoted in [Jaki, 1984, 279-280]). This is a good summary of what Gibbs tried to do in his main study on thermodynamics. His memoir on heterogeneous equilibrium begins by stating very simple and general conditions for the equilibrium and stability of a material system, and then proceeds to work out, very carefully, the consequences of those conditions for diverse situations, beginning from relatively simple ones and gradually adding more complexity (heterogeneous composition, gravity, surface tension, strain in solids, and electrical forces, for example). He was aware that for practical purposes the consequences are often more useful than the general statements from which they are derived (the phase rule is an example); but he preferred to begin with the latter rather than the former, “believing that it would be useful to exhibit the conditions of equilibrium of thermodynamic systems in connection with those quantities [pressure, temperature, volume, energy and entropy] which are most simple and most general in their definitions, and which appear most important in the general theory of such systems” [1878; 1906, I, 355-56]. It therefore seems fair to say that Gibbs was motivated in this work, as in others, by the search for a simple, very general standpoint that would allow him to retrieve accepted results in a rigorous manner and to predict new ones. The reason for logical rigor, I conjecture, is that he valued it as the best means of “showing exactly what a principle contains and what it does not” in order “to specify the points where experiment must intervene to bring in something really new.” That theory — even simple and general theory — is constrained by experiment is something of which Gibbs was evidently aware (see, e.g., [1881; in Donnan and Haas I, 55]). A prescient example may be found in the Preface he wrote to his work on statistical mechanics [Gibbs, 1902]. Gibbs proposed his statistical theory as a “branch of rational mechanics” that did not “attempt to frame hypotheses concerning the constitution of material bodies.” Earlier, I argued that Gibbs was no defender of phenomenalism, that he presupposed the molecular structure of matter; but in his statistical mechanics, where one might otherwise expect him to do so, he declined to offer any theory of that structure. The reason is that Gibbs did not see how to formulate a general theory that was compatible with the available experimental findings. In fact, he said, “In the present state of science, it seems hardly possible” to construct such a theory and that, in consequence, one would be “building on an insecure foundation.” He therefore concluded: “Difficulties of this kind have deterred the author from attempting to explain the mysteries of nature” and have forced him to be content with a more modest aim [1902, vii-viii]. Given the revolution in physics, including matter theory, that would soon occur, Gibbs’s confession was not only honest but wise.
BIBLIOGRAPHY [Clausius, 1876] R. Clausius. Die mechanische Wärmetheorie, 2nd ed., Braunschweig: Vieweg, 1876. This volume conveniently collects the essays of 1850, 1854, 1862 and 1865 mentioned in the text.
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[Deltete, 1995a] R. J. Deltete. Gibbs and Ostwald: A Contrast in Scientific Style, Journal of Chemical Education 73: 289-295, 1995. [Deltete, 1995b] R. J. Deltete. Gibbs and the Energeticists, in A.J. Kox and D. Siegel (eds), No Truth Except in the Details: Essays in Honor of Martin J. Klein, Dordrecht: Kluwer, 135-169, 1995. [Deltete, 1999 ] R. J. Deltete. The Historical Development of Energetics, Dordrecht: Kluwer, 1999. Trans. of Georg Helm, Die geschichtlichen Entwicklung der Energetik. Leipzig: Veit & Comp., 1898. [Deltete, 2000] R. J. Deltete. Gibbs, Josiah Willard, in The MacMillan Encyclopedia of Energy, New York, Macmillan & Co., pp. 579-581. 2000. [Deltete, 2003] R. J. Deltete. Energetics, in: J.L. Heilbron (ed), The Oxford Companion to the History of Modern Science, New York: Oxford University Press, pp. 256-257, 2003. [Deltete, 2005] R. J. Deltete. Die Lehre von der Energie: Georg Helm’s Energetic Manifesto, Centaurus 47: 140-162, 2005. [Deltete, 2007a] R. J. Deltete. Wilhelm Ostwald’s Energetics 1: Origins and Motivations, Foundations of Chemistry 9: 3-56, 2007. [Deltete, 2007b] R. J. Deltete. Wilhelm Ostwald’s Energetics 2: Energetic Theory and Applications, Part I, Foundations of Chemistry 9: 265-316, 2007. [Deltete, 2008] R. J. Deltete. Wilhelm Ostwald’s Energetics 3: Energetic Theory and Applications, Part II, Foundations of Chemistry 10: 187-221, 2008. [Deltete, 2009] R. J. Deltete. Georg Helm’s Chemical Energetics, Centaurus (In Press). [Duhem, 1907] P. Duhem. Étude sur le caractère de l’oeuvre de Gibbs (Àpropos de The Scientific Papers of Willard Gibbs), Bulletin des Sciences Mathématiques 31 (1907): 181-211, 1907. [Donnan, 1925] F. G. Donnan. The Influence of J. Willard Gibbs on the Science of Physical Chemistry, Journal of the Franklin Institute 199: 457-483, 1925. [Donnan and Haas, 1936] F. G. Donnan and A. Haas. A Commentary on the Scientific Writings of J. Willard Gibbs, 2 vols., New Haven: Yale University Press, 1936. [Gibbs, 1873a] J. W. Gibbs. Graphical Methods in the Thermodynamics of Fluids, Transactions of the Connecticut Academy of Arts and Sciences 2: 309-342. Rpt. in Gibbs (1906), I, pp. 1-32, 1873. [Gibbs, 1873b] J. W. Gibbs. A Method of Geometrical Representation of the Thermodynamics Properties of Substances by Means of Surfaces, Transactions of the Connecticut Academy of Arts and Sciences 2: 382-404. Rpt. in Gibbs (1906), I, pp. 33-54, 1973. [Gibbs, 1876-1878] J. W. Gibbs. On the Equilibrium of Heterogeneous Substances, Transactions of the Connecticut Academy of Arts and Sciences 3: 108-248 (1876); 343-524 (1878). Rpt. in Gibbs (1906), I, pp. 55-353 1876–1878. [Gibbs, 1878] J. W. Gibbs. Abstract of ‘On the Equilibrium of Heterogeneous Substances’,” American Journal of Science 16: 441-458, 1878. Rpt. In Gibbs (1906), I, pp. 354-371. [Gibbs, 1881] J. W. Gibbs. To the American Academy of Arts and Sciences, January 10, 1881. Rpt. in Donnan and Haas (1936), I, pp. 54-55 and Wheeler (1952), pp. 88-89. [Gibbs, 1889] J. W. Gibbs. Rudolf Julius Emanuel Clausius, Proceedings of the American Academy of Arts and Sciences 16 (1889). Rpt. In Gibbs (1906), II, pp. 261-267, 1889. [Gibbs, 1902] J. W. Gibbs. Elementary Principles in Statistical Mechanics, Delevoped with Special Reference to the Rational Foundation of Thermodynamics, New York: Scribner’s, 1902. [Gibbs, 1906] J. W. Gibbs. The Scientific Papers of J. Willard Gibbs, 2 vols., H. A. Bumstead and R. G. Van Name (eds.), New York: Longmans, Green, and Co, 1906. [Gibbs, 1974] J. W. Gibbs. The Early Work of Willard Gibbs in Applied Mechanics, L. P. Wheller, E. O. Waters, and S. W. Dudley (eds.), New York, Schuman. [Jaki, 1984] S. L. Jaki. Uneasy Genius: The Life and Work of Pierre Duhem, Dordrecht: Martinus Nijhoff, 1984. [Klein, 1969] M. J. Klein. Gibbs on Clausius, Historical Studies in the Physical Sciences 1: 127-149, 1969. [Klein, 1972] M. J. Klein. Gibbs, Josiah Willard, in Dictionary of Scientific Biography, C. G. Gillispie (ed.), New York, Scribner’s, vol. 5, pp. 386-393, 1972.
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[Klein, 1977] M. J. Klein. The Early Papers of J. Willard Gibbs: A Transformation in Thermodynamics, in Human Implications of Scientific Advance. Proceedings of the XVth International Congress of the History of Science. Edinburgh, 10-15 August 1977, Edinburgh, 1978, pp. 330-341, 1977. [Klein, 1980] M. J. Klein. The Scientific Style of Josiah Willard Gibbs, in Springs of Scientific Creativity: Essays on the Founders of Modern Science, R. Aris, H. T. Davis, and R. H. Stuewer (eds.), Minneapolis, University of Minnesota Press, 1983, pp. 142-162, 1980. [Klein, 1989] M. J. Klein. The Physics of J. Willard Gibbs in His Time, in Proceedings of the Gibbs Symposium. Yale University, May 15-17, 1989, D. G. Caldi and G. D. Mostow (eds.), New York, American Mathematical Society, pp. 1-21, 1989. [Klein, 1990] M. J. Klein. The Physics of J. Willard Gibbs in His Time, Physics Today (September, 1990): 40-48, 1990. [Wilhelm, 1902] O. Wilhelm. Vorlesungen über Naturphilosophie, gehalten im Sommer 1901 an der Universität Leipzig, Leipzig: Veit & Co, 1902. [Wilhelm, 1926] O. Wilhelm. Lebenslinien: Eine Selbstbiographie, 3 vols., Berlin: Klasing & Co., 1926-1927. [Wheeler, 1952] L. P. Wheeler. Josiah Willard Gibbs. The History of a Great Mind, 2nd ed., New Haven: Yale University Press, 1952.