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| In the [[history of thermodynamics]], '''''On the Equilibrium of Heterogeneous Substances''''' is a 300-page paper written by American mathematical-engineer [[Willard Gibbs]]. It is one of the founding papers in [[thermodynamics]], along with German physicist [[Hermann von Helmholtz]]'s 1882 paper "''[[Thermodynamik chemischer Vorgänge]].''" Together they form the foundation of [[chemical thermodynamics]] as well as a large part of [[physical chemistry]].<ref>{{cite book | last = Ott | first = Bevan J. | coauthors = Boerio-Goates, Juliana | title = Chemical Thermodynamics – Principles and Applications | publisher = Academic Press | year = 2000 | isbn = 0-12-530990-2}}</ref><ref name="Servos">{{cite book | last = Servos | first = John, W. | title = Physical Chemistry from Ostwald to Pauling | publisher = Princeton University Press | year = 1990 | isbn = 0-691-08566-8}}</ref>
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| Gibbs's ''Equilibrium'' marked the beginning of chemical thermodynamics by integrating [[chemical]], physical, [[electrical]], and [[Electromagnetism|electromagnetic]] phenomena into a coherent system. It introduced concepts such as [[chemical potential]], [[phase rule]], and others, which form the basis for modern physical chemistry. American writer [[Bill Bryson]] describes Gibbs's ''Equilibrium'' paper as "the ''[[Philosophiae Naturalis Principia Mathematica|Principia]]'' of [[thermodynamics]]".<ref>{{cite book | last = Bryson | first = Bill | title = A Short History of Nearly Everything | pages = 116–17,121 | publisher = Broadway Books | year = 2003 | isbn = 0-7679-0818-X}}</ref>
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| ''On the Equilibrium of Heterogeneous Substances'', was originally published in a relatively obscure American journal, the ''Transactions of the Connecticut Academy of Arts and Sciences'', in several parts, during the years 1875 to 1878 (although most cite "1876" as the key year).<ref>Gibbs, Willard, J. (1876). ''Transactions of the Connecticut Academy of Arts and Sciences'', III, pp. 108-248, Oct. 1875-May 1876, and pp. 343-524, May 1877-July 1878.</ref> It remained largely unknown until translated into German by [[Wilhelm Ostwald]] and into French by [[Henry Louis Le Chatelier]].
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| ==Overview==
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| Gibbs first contributed to mathematical physics with two papers published in 1873 in the Transactions of the Connecticut Academy on "[[graphical methods|Graphical Methods]] in the [[Thermodynamics]] of [[Fluids]]," and "Method of Geometrical Representation of the Thermodynamic Properties of Substances by means of Surfaces." His subsequent and most important publication was "On the Equilibrium of Heterogeneous Substances" (in two parts, 1876 and 1878). In this monumental, densely woven, 300-page treatise, the [[first law of thermodynamics]], the [[second law of thermodynamics]], the [[fundamental thermodynamic relation]], are applied to the predication and quantification of [[thermodynamics|thermodynamic]] [[Spontaneous process|reaction tendencies]] in any [[thermodynamic system]] in a visual, three-dimensional [[graphical]] language of [[Lagrangian]] calculus and [[phase transition]]s, among others.<ref name="Gibbs">{{cite book | last = Gibbs | first = J. Willard | title = The Scientific Papers of J. Willard Gibbs - Volume One Thermodynamics | publisher = Ox Bow Press | year = 1993 | isbn = 0-918024-77-3 | url=http://books.google.com/books?id=-neYVEbAm4oC&dq=scientific+papers+of+j+willard+gibbs}}</ref> As stated by [[Henri Louis Le Chatelier]], it "founded a new department of chemical science that is becoming comparable in importance to that created by [[Lavoisier]]." This work was translated into German by W. Ostwald (who styled its author the "founder of [[chemical energetics]]") in 1891 and into French by H. le Chatelier in 1899.<ref>[http://www.1911encyclopedia.org/Josiah_Willard_Gibbs Josiah Willard Gibbs] - Britannica (1911).</ref>
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| Gibbs's "Equilibrium" paper is considered one of the greatest achievements in physical science in the 19th century and one of the foundations of the science of [[physical chemistry]].<ref name="Servos" /> In these papers Gibbs applied [[thermodynamics]] to the interpretation of physicochemical phenomena and showed the explanation and interrelationship of what had been known only as isolated, inexplicable facts.
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| Gibbs' papers on heterogeneous equilibria included:
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| * Some [[chemical potential]] concepts
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| * Some [[Thermodynamic free energy|free energy]] concepts
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| * A [[statistical ensemble|Gibbsian ensemble]] ideal (basis of the [[statistical mechanics]] field)
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| * A ''[[Gibbs phase rule|phase rule]]''
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| ==Opening section==
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| <div style="font-size:115%"> | |
| {{cquote|Die Energie der Welt ist konstant.}}</div>
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| <center>(The [[energy]] of the [[world]] is constant).</center><br>
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| <div style="font-size:115%">
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| {{cquote|Die Entropie der Welt strebt einem Maximum zu.}}</div>
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| <center>(The [[entropy]] of the world tends to a maximum)</center>
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| :::::::::::::::::::::::[[Rudolf Clausius|Clausius]]<ref>Clausius, R. (1865). ''The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies.'' London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.</ref>
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| 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 is capable. As the difference of the values of the energy for any two states represents the combined amount of [[Work (thermodynamics)|work]] and [[thermodynamic work|heat]] received or yielded by the [[thermodynamic system|system]] when it is brought from one [[thermodynamic state|state]] to the other, and the difference of entropy is the limit of all possible values of the integral:
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| :<math>\int \frac{\delta Q}{T}</math>
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| in which ''dQ'' denotes the element of heat received from external sources, and ''T'' is the temperature of the part of the system receiving it, the varying values of energy and entropy characterize in all that is essential the effect producible by the system in passing from one state to another. For by mechanical and thermodynamic contrivances, supposedly theoretically perfect, any supply of work and heat may be transformed into any other which does not differ from it either in the amount of work and heat taken together or in the value of the integral:
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| :<math>\int \frac{\delta Q}{T}</math>
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| But it is not only in respect to the external relations of a system that its energy and entropy are of predominant importance. As in the case of simple mechanical systems, such as are discussed in theoretical mechanics, which are capable of only one kind of action upon external systems, namely the performance of mechanical work, the function which expresses the capability of the system of this kind of action also plays the leading part in the theory of equilibrium, the condition of equilibrium being that the variation of this function shall vanish, so in a thermodynamic system, such as all material systems are, which is capable of two different kinds of action upon external systems, the two functions which express the twofold capabilities of the system afford an almost equally simple criterion for equilibrium.
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| ==References==
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| {{reflist}}
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| ==External links==
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| * Gibbs's paper "[http://web.mit.edu/jwk/www/docs/Gibbs1875-1878-Equilibrium_of_Heterogeneous_Substances.pdf On the Equilibrium of Heterogeneous Substances]"
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| * At the Internet Archive, [http://archive.org/details/Onequilibriumhe00Gibb Part 1] and [http://archive.org/details/Onequilibriumhe00GibbA Part 2] in various file formats.
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| [[Category:Thermodynamics literature]]
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| [[Category:1870s in science]]
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| [[Category:1876 in science]]
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| [[Category:Physics books]]
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| [[Category:Works originally published in American magazines]]
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| [[Category:1876 works]]
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| [[Category:Works originally published in science and technology magazines]]
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