In the

history of thermodynamics The history of thermodynamics is a fundamental strand in the history of physics, the history of chemistry, and the history of science in general. Owing to the relevance of thermodynamics in much of science and technology, its history is finely wo ...

, ''On the Equilibrium of Heterogeneous Substances'' is a 300-page paper written by American chemical physicist

Willard Gibbs Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...

. It is one of the founding papers in

thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

, along with German physicist

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

's 1882 paper "'' Thermodynamik chemischer Vorgänge.''" Together they form the foundation of

chemical thermodynamics Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurement ...

as well as a large part of

physical chemistry Physical chemistry is the study of macroscopic and microscopic phenomena in chemical systems in terms of the principles, practices, and concepts of physics such as motion, energy, force, time, thermodynamics, quantum chemistry, statistical mecha ...

. Gibbs's ''Equilibrium'' marked the beginning of chemical thermodynamics by integrating

chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...

, physical,

electrical Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...

, and

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

phenomena into a coherent system. It introduced concepts such as

chemical potential In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...

phase rule In thermodynamics, the phase rule is a general principle governing "pVT" systems, whose thermodynamic states are completely described by the variables pressure (), volume () and temperature (), in thermodynamic equilibrium. If is the number of ...

, and others, which form the basis for modern physical chemistry. American writer

Bill Bryson William McGuire Bryson (; born 8 December 1951) is an American–British journalist and author. Bryson has written a number of nonfiction books on topics including travel, the English language, and science. Born in the United States, he has b ...

describes Gibbs's ''Equilibrium'' paper as "the '' Principia'' of

". ''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 Transaction or transactional may refer to: Commerce * Financial transaction, an agreement, communication, or movement carried out between a buyer and a seller to exchange an asset for payment *Debits and credits in a Double-entry bookkeeping sys ...

'', in several parts, during the years 1875 to 1878 (although most cite "1876" as the key year). It remained largely unknown until translated into German by

Wilhelm Ostwald Friedrich Wilhelm Ostwald (; 4 April 1932) was a Baltic German chemist and German philosophy, philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst, ...

and into French by

Henry Louis Le Châtelier Henry Louis Le Chatelier (; 8 October 1850 – 17 September 1936) was a French chemist of the late 19th and early 20th centuries. He devised Le Chatelier's principle, used by chemists and chemical engineers to predict the effect a changing conditi ...

Overview

Gibbs first contributed to mathematical physics with two papers published in 1873 in the ''Transactions of the

Connecticut Academy of Arts and Sciences The Connecticut Academy of Arts and Sciences is a learned society founded in 1799 in New Haven, Connecticut "to cultivate every art and science which may tend to advance the interest and happiness of a free and virtuous people." Its purpose is the ...

'' on "

Graphical Methods A chart (sometimes known as a graph) is a graphical representation for data visualization, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart". A chart can represent ta ...

in the

Thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...

Fluids In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...

," 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 first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...

, the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and Energy transformation, energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects ( ...

, the

fundamental thermodynamic relation In thermodynamics, the fundamental thermodynamic relation are four fundamental equations which demonstrate how four important thermodynamic quantities depend on variables that can be controlled and measured experimentally. Thus, they are essentiall ...

, are applied to the predication and quantification of

thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...

reaction tendencies in any

thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surroundings may include other thermodynamic systems, or physical systems that are ...

in a visual, three-dimensional

graphical Graphics () are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain. In contemporary usage, it includes a pictorial representation of data, as in design and manufacture, ...

language of

Lagrangian Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...

calculus and

phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...

s, among others. As stated by

Henri Louis Le Chatelier Henry Louis Le Chatelier (; 8 October 1850 – 17 September 1936) was a French chemist of the late 19th and early 20th centuries. He devised Le Chatelier's principle, used by chemists and chemical engineers to predict the effect a changing conditi ...

, it "founded a new department of chemical science that is becoming comparable in importance to that created by

Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

chemical energetics") in 1891 and into French by H. le Chatelier in 1899. 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

. In these papers Gibbs applied

to the interpretation of physicochemical phenomena and showed the explanation and interrelationship of what had been known only as isolated, inexplicable facts. Gibbs' papers on heterogeneous equilibria included: * Some

concepts * Some free energy concepts * A Gibbsian ensemble ideal (basis of the

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

field) * A ''

Opening section

:::::::::::::::::::::::

Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...

The comprehension of the laws which govern any material system is greatly facilitated by considering the

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

and

entropy Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

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 Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal tr ...

and

heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...

received or yielded by the

system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment (systems), environment, is described by its boundaries, ...

when it is brought from one

state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * ''Our S ...

to the other, and the difference of entropy is the limit of all possible values of the integral: :

\int \frac

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: :

\int \frac

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.

References

External links

{{Wikisource, Scientific Papers of Josiah Willard Gibbs, Volume 1/Chapter IIIa, On the Equilibrium of Heterogeneous Substances * At the Internet Archive
Part 1
an
Part 2
in various file formats. Thermodynamics literature 1870s in science 1876 in science Physics books Works originally published in American magazines 1876 non-fiction books Works originally published in science and technology magazines