Great scientists. Josiah Willard Gibbs. Josiah Willard Gibbs - biography Josiah Flint - real and true

Gibbs I (Gibbs)

James (December 23, 1682, Footdismere, near Aberdeen, - August 5, 1754, London), English architect. He studied in Holland and Italy (in 1700-09 with C. Fontana (See Fontana)), collaborated with C. Ren. Representative of classicism. G.'s buildings are distinguished by their impressive simplicity and integrity of composition, elegance of details (the churches of St. Mary-le-Strand, 1714-1717, and St. Martin-in-the-Fields, 1722-1726, in London; the Radcliffe Library in Oxford, 1737 -49).

Lit.: Summerson J., Architecture in Britain. 1530-1830, Harmondsworth, 1958.

II (Gibbs)

Josiah Willard (11.2.1839, New Haven, - 28.4.1903, ibid.), American theoretical physicist, one of the founders of thermodynamics and statistical mechanics. Graduated from Yale University (1858). In 1863 he received a Doctor of Philosophy degree from Yale University, and from 1871 he became a professor there. G. systematized thermodynamics and statistical mechanics, completing their theoretical construction. Already in his first articles, G. developed graphical methods for studying thermodynamic systems, introduced three-dimensional diagrams, and obtained relationships between the volume, energy, and entropy of matter. In 1874-78, in the treatise “On the Equilibrium of Heterogeneous Substances”, he developed the theory of thermodynamic potentials (See Thermodynamic potentials), proved the phase rule (the general condition for the equilibrium of heterogeneous systems), created the thermodynamics of surface phenomena and electrochemical processes; G. generalized the principle of entropy, applying the second law of thermodynamics to a wide range of processes, and derived fundamental equations that make it possible to determine the direction of reactions and equilibrium conditions for mixtures of any complexity. The theory of heterogeneous equilibrium, one of the most abstract theoretical contributions of G. to science, has found wide practical application.

In 1902, “Basic principles of statistical mechanics, set forth with special application to the rational basis of thermodynamics” were published, which was the completion of classical statistical physics, the fundamental principles of which were laid in the works of J. TO. Maxwell and L. Boltzmann. The statistical research method developed by G. makes it possible to obtain thermodynamic functions that characterize the state of matter. G. gave a general theory of fluctuations of the values of these functions from equilibrium values determined by formal thermodynamics, and an adequate description of the irreversibility of physical phenomena. G. is also one of the creators of vector calculus in its modern form (“Elements of vector analysis”, 1881-1884).

G.'s works showed remarkably precise logic and thoroughness in finishing the results. Not a single error has yet been discovered in G.'s works; all his ideas have been preserved in modern science.

Works: The collected works, v. 1-2, N. Y. - L., 1928; The scientific papers, v. 1-2, N.Y., 1906; in Russian lane - Basic principles of statistical mechanics, M. - L., 1946; Thermodynamic works, M., 1950.

Lit.: Semenchenko V.K., D.W. Gibbs and his main works on thermodynamics and statistical mechanics (To the 50th anniversary of his death), “Advances in Chemistry”, 1953, vol. 22, century. 10; Frankfurt W. I., Frank A. M., Josiah Willard Gibbs, M., 1964.

O. V. Kuznetsova.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Gibbs" is in other dictionaries:

- (English Gibbs, sometimes Gibbes) English surname. Gibbs, Josiah Willard American physicist, mathematician and chemist, one of the founders of the theories of phenomenological and statistical thermodynamics, vector analysis, statistical ... ... Wikipedia

- (Gibbs) Josiah Willard (1839 1903), American physicist. One of the creators of statistical mechanics. Developed the general theory of thermodynamic equilibrium (including limited systems), the theory of thermodynamic potentials, derived the main... ... Modern encyclopedia

- (Gibbs) Joshua Willard (1839 1903), American theoretical scientist in the field of physics and chemistry. Professor at Yale University. He devoted his life to developing the fundamentals of physical chemistry. The application of THERMODYNAMICS in relation to physical processes has led... ... Scientific and technical encyclopedic dictionary

Gibbs- Gibbs, a: Gibbs distribution... Russian spelling dictionary

Gibbs D.W.- GIBBS Josiah Willard (18391903), Amer. theoretical physicist, one of the creators of thermodynamics and statistics. mechanics. Developed the theory of thermodynamics. potentials, discovered the general condition for the equilibrium of heterogeneous systems phase rule, derived the equation... ... Biographical Dictionary

- ... Wikipedia

Books

Woodworking Practical course, Gibbs N.. Wood is a magnificent material. Many masters have special feelings for it not because of its beauty and strength, but rather because of the desire to tame this malleable and at the same time...

Biography

early years

Gibbs was born on February 11, 1839 in New Haven, Connecticut. His father, a professor of spiritual literature at Yale Divinity School (later affiliated with Yale University), was famous for his involvement in a lawsuit called Amistad. Although the father's name was also Josiah Willard, "Junior" was never used with the son's name; in addition, five other members of the family bore the same name. His maternal grandfather was also a graduate of Yale University in literature. After attending Hopkins School, at the age of 15, Gibbs entered Yale College. In 1858, he graduated from college at the top of his class and was awarded for his success in mathematics and Latin.

Years of maturity

In 1863, by decision of the Sheffield School of Science at Yale, Gibbs was awarded the first US degree of Doctor of Philosophy (PhD) in technical sciences for his dissertation “On the shape of the teeth of gear wheels.” In subsequent years, he taught at Yale: for two years he taught Latin and for another year - what was later called natural philosophy and is comparable to the modern concept of “natural sciences”. In 1866 he went to Europe to continue his studies, spending one year each in Paris, Berlin and then Heidelberg, where he met Kirchhoff and Helmholtz. At that time, German scientists were leading authorities in chemistry, thermodynamics and basic natural sciences. These three years, in fact, constitute that part of the scientist’s life that he spent outside of New Haven.

In 1869 he returned to Yale, where in 1871 he was appointed professor of mathematical physics, the first such position in the United States, a post he held for the rest of his life.

The professorship was initially unpaid, a situation typical of the time (especially in Germany), and Gibbs was required to publish his papers. In 1876-1878 he writes a number of articles on the analysis of multiphase chemical systems using the graphical method. They were later published in the monograph “On the Equilibrium of Heterogeneous Substances,” his best known work. This work by Gibbs is considered one of the greatest scientific achievements of the 19th century and one of the fundamental works in physical chemistry. In his articles, Gibbs used thermodynamics to explain physicochemical phenomena, connecting what had previously been a set of individual facts.

“It is generally accepted that the publication of this monograph was an event of paramount importance in the history of chemical science. However, it took several years before its significance was fully realized; the delay was mainly due to the fact that the mathematical form used and the strict deductive techniques make reading difficult for anyone, and especially for students in the field of experimental chemistry, with whom it was most relevant ... "

Important sections covered in his other papers on heterogeneous equilibria include:

Chemical potential and free energy concepts

Gibbs ensemble model, the basis of statistical mechanics

Gibbs phase rule

Gibbs also published works on theoretical thermodynamics. In 1873, his article on the geometric representation of thermodynamic quantities was published. This work inspired Maxwell to make a plastic model (called Maxwell's thermodynamic surface) to illustrate Gibbs's construct. The model was subsequently sent to Gibbs and is currently kept at Yale University.

Later years

In 1880, the newly opened Johns Hopkins University in Baltimore, Maryland, offered Gibbs a position for $3,000, to which Yale responded by increasing the salary to $2,000. But Gibbs didn't leave New Haven. From 1880 to 1884, he combined the ideas of two mathematicians: the "quaternion" of William Hamilton and the "external algebra" of Hermann Grassmann, and created (independently from the British physicist and engineer Oliver Heaviside) vector analysis. In 1882-89. Gibbs makes improvements to it, writes works on optics, and develops a new electric theory of light. He deliberately avoids theorizing about the structure of matter, which was a wise decision in view of the subsequent revolutionary events in subatomic particle physics and quantum mechanics. His chemical thermodynamics was more universal than any other chemical theory existing at that time.

After 1889, he continued his work on statistical thermodynamics, “equipping quantum mechanics and Maxwell’s theories with a mathematical framework.” He wrote the classic textbooks on statistical thermodynamics, which were published in 1902. Gibbs also made contributions to crystallography and applied his vector method to the calculation of planetary and cometary orbits.

Little is known about the names and careers of his students. Gibbs never married and lived his entire life in his father's house with his sister and brother-in-law, a librarian at Yale. He was so focused on science that he was generally inaccessible to personal interests. His protégé E.W. Wilson said: “I saw very little of him outside the classroom. He had a habit of going for a walk in the afternoon along the streets between his office in the old laboratory and home - a little exercise in the break between work and lunch - and then you could sometimes meet him." Gibbs died in New Haven and is buried in Grove Street Cemetery.

Scientific recognition

Recognition did not come to the scientist immediately, in particular because Gibbs mainly published in “Transactions of the Connecticut Academy of Sciences”- a magazine published under the editorship of his librarian son-in-law, little read in the United States and even less in Europe. At first, only a few European theoretical physicists and chemists (including, for example, the Scottish physicist James Clerk Maxwell) paid attention to his work. It was only after Gibbs's articles were translated into German (by Wilhelm Ostwald in 1892) and French (Henri Louis le Chatelier in 1899) that his ideas became widespread in Europe. His theory of the phase rule was experimentally confirmed in the works of H.V. Bahuis Rosebohm, who demonstrated its applicability in various aspects.

On his home continent, Gibbs was rated even less. Nevertheless, he was recognized, and in 1880 the American Academy of Arts and Sciences awarded him the Rumford Prize for his work on thermodynamics. And in 1910, in memory of the scientist, the American Chemical Society, on the initiative of William Converse, established the Willard Gibbs Medal.

American schools and colleges of the time emphasized traditional subjects rather than science, and students showed little interest in his lectures at Yale. Gibbs' acquaintances described his work at Yale this way:

“In his last years he remained a tall, distinguished gentleman with a healthy gait and a healthy complexion, managing his duties at home, approachable and responsive to students. Gibbs was highly regarded by his friends, but American science was too concerned with practical issues to apply his solid theoretical work during his lifetime. He lived out his quiet life at Yale and deeply admired several bright students, without making a first impression on American scholars comparable to his talent.” (Crowther, 1969)

It should not be thought that Gibbs was little known in his day. For example, the mathematician Jayen-Carlo Rota, looking through the shelves of mathematics literature in the Sterling Library (at Yale University), came across a mailing list handwritten by Gibbs and attached to some notes. The list included over two hundred notable mathematicians of the time, including Poincaré, Hilbert, Boltzmann and Mach. One can come to the conclusion that among the luminaries of science, Gibbs's works were better known than the printed material indicates. Gibbs' achievements, however, were finally recognized only with the appearance in 1923 of the publication of Gilbert Newton Lewis and Merle Randall “Thermodynamics and the Free Energy of Chemical Substances”, which introduced Gibbs' methods to chemists from various universities. These same methods formed, for the most part, the basis of chemical technology.

The list of academies and societies of which he was a member includes the Connecticut Academy of Arts and Sciences, the National Academy of Sciences, the American Philosophical Society, the Dutch Scientific Society, Haarlem; Royal Scientific Society, Göttingen; The Royal Institution of Great Britain, the Cambridge Philosophical Society, the Mathematical Society of London, the Manchester Literary and Philosophical Society, the Royal Academy of Amsterdam, the Royal Society of London, the Royal Prussian Academy in Berlin, the French Institute, the Physical Society of London, and the Bavarian Academy of Sciences.

According to the American Mathematical Society, which established the so-called Gibbs Lectures in 1923 to promote general competence in mathematical approaches and applications, Gibbs was the greatest scientist ever born on American soil.

In 1873, when he was 34 years old, Gibbs showed extraordinary research abilities in the field of mathematical physics. This year two articles appeared in the Connecticut Academy Bulletin. The first was entitled “Graphical methods in the thermodynamics of fluids”, and the second – “Method of geometric representation of the thermodynamic properties of substances using surfaces”

These were followed in 1876 and 1878 by two parts of a much more fundamental paper, "On Equilibrium in Heterogeneous Systems", which summarize his contributions to physical science, and are undoubtedly among the most significant and distinguished literary monuments of the scientific activity of the nineteenth century.

When discussing chemically homogeneous media in the first two papers, Gibbs often used the principle that a substance is in equilibrium if its entropy cannot be increased at constant energy. In the epigraph of the third article, he quoted the famous expression of Clausius “Die Energie der Welt ist constant. Die Entropio der Welt strebt einem Maximum zu,” which means “The energy of the world is constant. The entropy of the world tends to maximum.” He showed that the above-mentioned equilibrium condition, derived from the two laws of thermodynamics, has universal application, neatly removing one constraint after another, most notably that the substance must be chemically homogeneous. An important step was the introduction of the masses of the components that make up a heterogeneous system as variables in fundamental differential equations. It is shown that in this case the differential coefficients at energies with respect to these masses enter into equilibrium in the same way as intensive parameters, pressure and temperature. He called these coefficients potentials. Analogies with homogeneous systems are constantly used, and mathematical operations are similar to those used in the case of extending the geometry of three-dimensional space to n-dimensional space.

It is widely accepted that the publication of these papers was of particular importance for the history of chemistry. In fact, this marked the formation of a new branch of chemical science, which, according to M. Le Chatelier, was comparable in importance to the works of Lavoisier. However, it took several years before the value of these works became generally recognized. This delay was mainly due to the fact that reading the articles was quite difficult, especially for students involved in experimental chemistry, due to the extraordinary mathematics and scrupulous conclusions. At the end of the 19th century, there were very few chemists with sufficient knowledge of mathematics to read even the simplest parts of the papers. Thus, some of the most important laws, first described in these articles, were subsequently proven by other scientists either theoretically or, more often, experimentally. Nowadays, however, the value of Gibbs's methods and the results obtained are recognized by all students of physical chemistry.

In 1891, Gibbs's works were translated into German by Professor Ostwald, and in 1899 into French thanks to the efforts of G. Roy and A. Le Chatelier. Despite the fact that many years have passed since publication, in both cases the translators noted not so much the historical aspect of the memoirs, but rather the many important issues that were discussed in these articles and which had not yet been confirmed experimentally. Many theorems have already served as starting points or guidelines for experimenters, others, such as the phase rule, helped to classify and explain logically complex experimental facts. In turn, using the theory of catalysis, solid solutions, and osmotic pressure, it was shown that many facts that previously seemed incomprehensible and could hardly be explained are, in fact, easy to understand and are consequences of the fundamental laws of thermodynamics. When discussing multicomponent systems where some components are present in very small quantities (dilute solutions), the theory goes as far as it can go based on the initial considerations. At the time of publication of the article, the lack of experimental facts did not allow the formulation of the fundamental law that Van't Hoff later discovered. This law was originally a consequence of Henry's law for a mixture of gases, but upon further examination it turned out that it has a much wider application.

Professor Gibbs, like many other physicists of those years, realized the need to use vector algebra, through which quite complex spatial relationships associated with different areas of physics can be easily and accessiblely expressed. Gibbs always preferred the clarity and elegance of the mathematics he used, so he was particularly keen to use vector algebra. However, in Hamilton's quaternion system he did not find a tool that would satisfy all his requirements. In this regard, he shared the views of many researchers who wanted to reject quaternion analysis, despite its logical validity, in favor of a simpler and more direct descriptive apparatus - vector algebra. With the help of his students, in 1881 and 1884, Professor Gibbs secretly published a detailed monograph on vector analysis, a mathematical apparatus that he had developed. The book quickly spread among his fellow scientists. While working on his book, Gibbs relied mainly on Grassmann's Ausdplinungslehre and the algebra of multiple relations. The mentioned studies were of particular interest to the professor, and, as he later noted, gave him the greatest aesthetic pleasure among all his activities. Many of his papers, in which he rejected the quaterinion theory of Grassmann, considered the founder of modern algebra, appeared in the pages of the journal Nature.

When the utility of vector algebra as a mathematical system was confirmed over the next 20 years by himself and his students, Gibbs agreed, albeit reluctantly, to publish a more detailed work on vector analysis. Since at that time he was completely absorbed in another topic, the preparation of the manuscript for publication was entrusted to one of his students, Dr. E.B. Wilson (E. B. Wilson), who coped with this task admirably and deserved the gratitude of all his contemporaries interested in the subject.

In addition, Professor Gibbs was extremely interested in the application of vector analysis to the solution of astronomical problems and gave many similar examples in the paper “On the Determination of Elliptical Orbits from Three Complete Observations.” The methods developed in this work were subsequently used by Professors W. Beebe and A. W. Phillips to calculate the orbit of Comet Swift (1880) from three observations, which became a serious test of the method. They found that the Gibbs method had significant advantages over the Gauss and Oppolzer methods, the convergence of suitable approximations was faster, and much less effort was expended in finding the fundamental equations for the solution. These two articles were translated by Buchholz and included in the second edition of Klinkerfues's Theoretische Astronomie.

From 1882 to 1889, five articles appeared in the American Journal of Science on selected topics in the electromagnetic theory of light and its connections with various theories of elasticity. It is interesting that special hypotheses about the relationship between space and matter were completely absent. The only assumptions made about the structure of matter are that it consists of particles that are quite small relative to the wavelength of light, but not infinitesimal, and that it somehow interacts with electric fields in space. Using methods whose simplicity and clarity were reminiscent of his studies in thermodynamics, Gibbs showed that in the case of completely transparent media the theory not only explained the dispersion of color (including the dispersion of optical axes in a birefringent medium), but also led to Fresnel's laws of double reflection for any wavelength, taking into account low energies that determine color dispersion. He noted that circular and elliptical polarization can be explained if we consider the energy of light of even higher orders, which, in turn, does not refute the interpretation of many other known phenomena. Gibbs carefully derived general equations for monochromatic light in a medium with varying degrees of transparency, arriving at expressions different from those obtained by Maxwell, which did not explicitly contain the dielectric constant of the medium and conductivity.

Some experiments of Professor C. S. Hastings in 1888 (which showed that birefringence in Iceland spar is in exact accordance with Huygens' law) again forced Professor Gibbs to take up the theory of optics and write new articles in which, in a fairly simple form, from elementary reasoning he showed that the dispersion of light strictly corresponds to the electrical theory, while none of the theories of elasticity proposed at that time could be reconciled with the experimental data obtained.

In his latest work, "Fundamental Principles of Statistical Mechanics," Professor Gibbs returned to a topic closely related to the subject of his earlier publications. In them he was engaged in the development of consequences of the laws of thermodynamics, which are accepted as data based on experiment. In this empirical form of science, heat and mechanical energy were regarded as two different phenomena, of course mutually transforming into each other with certain limitations, but fundamentally different in many important parameters. In accordance with the popular tendency to unify phenomena, many attempts have been made to reduce these two concepts into one category, to show, in fact, that heat is nothing more than the mechanical energy of small particles, and that the extradynamic laws of heat are the consequence of a huge number of independent mechanical systems in any body - numbers so large that it is difficult for a person with his limited imagination to even imagine. And yet, despite the confident assertions in many books and popular exhibitions that “heat is the mode of molecular motion,” they were not entirely convincing, and this failure was regarded by Lord Kelvin as a blight on the history of nineteenth-century science. Such studies must deal with the mechanics of systems with a huge number of degrees of freedom, and it would be possible to compare the results of calculations with observation; these processes must be statistical in nature. Maxwell more than once pointed out the difficulties of such processes, and also said (and this was often quoted by Professor Gibbs) that in such matters serious mistakes were made even by people whose competence in other areas of mathematics was not in doubt.

Impact on subsequent work

Gibbs's works attracted a lot of attention and influenced the activities of scientists, some of them became Nobel laureates:

In 1910, the Dutchman Jan Diederik van der Waals was awarded the Nobel Prize in Physics. In his Nobel lecture, he noted the influence of Gibbs's equations of state on his work.

In 1918, Max Planck received the Nobel Prize in Physics for his work in the field of quantum mechanics, in particular for the publication in 1900 of his quantum theory. His theory was based substantially on the thermodynamics of Rudolf Clausius, J. Willard Gibbs and Ludwig Boltzmann. Planck said this about Gibbs: “his name not only in America, but throughout the world will be ranked among the most famous theoretical physicists of all time...”.

At the beginning of the 20th century, Gilbert N. Lewis and Merle Randall used and expanded Gibbs' theory of chemical thermodynamics. They presented their research in 1923 in a book called “Thermodynamics and the Free Energy of Chemical Substances” and was one of the fundamental textbooks on chemical thermodynamics. In the 1910s William Gioc attended the College of Chemistry at Berkeley University and received a bachelor's degree in chemistry in 1920. At first he wanted to become a chemical engineer, but under the influence of Lewis he became interested in chemical research. In 1934 he became a full professor of chemistry at Berkeley, and in 1949 he received the Nobel Prize for his cryochemical research using the third law of thermodynamics.

Gibbs's work had a significant influence on the formation of the views of Irving Fisher, an economist who had a PhD from Yale.

Personal qualities

Professor Gibbs was a man of honest character and innate modesty. In addition to his successful academic career, he was busy with New Haven's Hopkins High School, where he provided custodial services and served as fund treasurer for many years. As befits a man primarily engaged in intellectual activity, Mr. Gibbs never sought or desired to have a wide circle of acquaintances. However, he was not an asocial person, but, on the contrary, he was always extremely friendly and open, able to support any topic, and always calm and inviting. Expansiveness was alien to his nature, as was insincerity. He could laugh easily and had a lively sense of humor. Although he rarely talked about himself, he sometimes liked to give examples from his personal experience. No quality of Professor Gibbs impressed his colleagues and students more than his modesty and complete unawareness of his limitless intellectual resources. A typical example is a phrase he uttered in the company of a close friend regarding his mathematical abilities. With absolute sincerity he said: “If I were successful in mathematical physics, I think it was because I was lucky enough to avoid mathematical difficulties.”

Perpetuation of the name

In 1945, Yale University, in honor of J. Willard Gibbs, introduced the title of Professor of Theoretical Chemistry, which was retained until 1973 by Lars Onsager (Nobel Prize winner in Chemistry). A laboratory at Yale University and a position as senior lecturer in mathematics were also named in Gibbs' honor. On February 28, 2003, a symposium was held at Yale to mark the 100th anniversary of his death.

Rutgers University (New Jersey) has a professorship. J. Willard Gibbs in thermomechanics, currently held by Bernard D. Coleman.

In 1950, a bust of Gibbs was placed in the Hall of Fame for Great Americans.

On May 4, 2005, the United States Postal Service issued a series of postage stamps featuring portraits of Gibbs, John von Neumann, Barbara McClintock, and Richard Feynman.

The US Navy oceanographic expedition vessel USNS Josiah Willard Gibbs (T-AGOR-1), which operated from 1958-71, was named after Gibbs.

Works, publications

Graphical methods in the thermodynamics of fluids. Trans. Connecticut Acad. Arts and Sciences, Vol. II, 1873, pp. 309-342.
A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. Trans. Connecticut Acad. Arts and Sciences, Vol. II, 1873, pp. 382-404.
On the equilibrium of heterogeneous substances. Trans. Connecticut Acad. Arts and Sciences, Vol. Ill, 1875-1878, pp. 108-248; pp. 343-524. Abstract: American Journal. Sci., 3d ser., Vol. XVI, pp. 441-458.
Elements of vector analysis arranged for the use of students in physics. New Haven, 8°, pp. 1-86 in 1881, and pp. 37-83 in 1884. (Not published.)
Notes on the electromagnetic theory of light. 1. On double refraction and the dispersion of colors in perfectly transparent media. American Journal. Sci., 3d ser., Vol. XXIII, 1882, pp. 262-275. II.
On double refraction in perfectly transparent media which exhibit the phenomena of circular polarization. American Journal. Sci., 3d ser., Vol. XXIII, 1882, pp. 400-476. III. On the general equations of monochromatic light in media of every degree of transparency. American Journal. Sci., 3d ser., Vol. XXV, 1883, pp. 107-118.
On the fundamental formula of statistical mechanics, with applications to astronomy and thermodynamics. (Abstract.) Proc. American Assoc. Adv. Sci., Vol. XXXIII, 1884, pp. 57 and 58.
On the velocity of light as determined by Foucault's revolving mirror. Nature, Vol. XXXIII, 1886, p. 582.
A comparison of the elastic and electrical theories of light, with respect to the law of double refraction and the dispersion of colors. American Journal. Sci., 3d ser., Vol. XXXV, 1888, pp. 467-475.
A comparison of the electrical theory of light with Sir William Thomson's theory of a quasi-labile ether. American Journ. Sci., 3d ser., Vol. XXXVTI, 1880, pp. 120-144. Reprint: Philos. Mag. , 5th ser., Vol. XXVII, 1889, pp. 238-253.
On the determination of elliptic orbits from three complete observations. Mem. Nat. Acad. Sci., Vol. IV, 1889, pp. 79-104. On the role of quaternions in the algebra of vectors. Nature, Vol. XLIII, 1891, pp. 511-514. Quaternions and the Ausdehnungslehre. Nature, Vol. XLIV, 1891, pp. 79-82. Quaternions and the algebra of vectors. Nature, Vol. XLVII, 1898, pp. 463-464. Quaternions and vector analysis. Nature, Vol. XLVIII, 1893, pp. 364-367.
Vector analysis: A text-book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs, by E. B. Wilson. Yale Bicentennial Publications, pp. XVIII -f 436. G. Scrilmer's Sons, 1901.
Elementary principles in statistical mechanics, developed with especial reference to the rational foundation of thermodynamics. Yale Bicentennial Publications, pp. XVIII + 207. S. Scribner's Sons, 1902
On the use of vector methods in the determination of orbits. Letter to Dr. Hugo Buchholz, editor of Klinkerfues's Theoretisehe Astronomie. Scientific Papers, Vol. II, 1906, pp. 149-154.
The scientific papers, v. 1-2, N. Y., 1906 (in Russian translation - “Basic principles of statistical mechanics”, M. - L., 1946;
Gibbs J.W. Thermodynamic works, M., 1950.

GIBBS (Gibbs) Josiah Willard (11.2.1839, New Haven - 28.4.1903, ibid.), American theoretical physicist, member of the US National Academy of Sciences (1879), the Royal London (1897) and other scientific societies. Graduated from Yale University (1858; Ph.D., 1863).

In 1863-66 he taught there. He improved his education (1866-69) at the universities of Paris, Berlin and Heidelberg. Since 1871 - professor of mathematical physics at Yale University.

Gibbs is the creator of statistical physics. In 1902 he published the work “Basic principles of statistical mechanics...”, which was the completion of classical statistical physics. The statistical research method developed by Gibbs makes it possible to obtain all thermodynamic functions that characterize the state of a macroscopic system based on the properties of its constituent microparticles. Established laws that determine the probability of a given microscopic state of a system (see Gibbs distribution). He developed a general theory of fluctuations of the values of these functions from equilibrium values determined by thermodynamics. The Gibbs method of statistical ensembles is used in both classical and quantum physics.

In his first articles (1873), Gibbs developed the method of entropy diagrams, which made it possible to graphically represent all the thermodynamic properties of matter, introduced three-dimensional diagrams and established a connection between the volume, energy and entropy of a system. With his work “On the Equilibrium of Heterogeneous Substances” (1876-1878), Gibbs completed the construction of theoretical thermodynamics and laid the foundations of chemical thermodynamics. In this work, he outlined the general theory of thermodynamic equilibrium and the method of thermodynamic potentials, introduced the concept of “chemical potential”; derived an equation that allows one to determine the direction of chemical reactions and equilibrium conditions for heterogeneous systems; formulated the general condition for equilibrium in a multiphase heterogeneous system (see Gibbs phase rule). These results play a fundamental role in physical chemistry. Gibbs built a general theory of the thermodynamics of surface phenomena (developed the theory of capillary processes, formulated the laws of osmosis, laid the foundations of the thermodynamics of adsorption and proposed an equation for a quantitative description of adsorption - the Gibbs adsorption equation) and electrochemical processes; proposed graphical methods for depicting physicochemical equilibrium in three-component systems (Gibbs triangle). Gibbs published his works on thermodynamics in the small-circulation publication Transactions of the Connecticut Academy of Arts and Sciences, so the results of his research in Europe were almost unknown until 1892.

Developing the ideas of G. Grassmann, in the 1880s Gibbs created vector calculus in its modern form. Gibbs also worked on problems of optics, the electromagnetic theory of light, etc., and he owned a number of technical inventions.

G. Copley Medal of the Royal Society of London (1901). In 1950, a bust of Gibbs was placed in the Gallery of Fame for Great Americans.

Works: The scientific papers. N.Y., 1906. Vol. 1-2; The collected works. N. Y.; L., 1928. Vol. 1-2; Basic principles of statistical mechanics. M.; L., 1946; Thermodynamics. Statistical mechanics. M., 1982.

Lit.: A commentary on the scientific writings of J. W. Gibbs. New Haven, 1936. Vol. 1-2; Semenchenko V. K. D. V. Gibbs and his main works on thermodynamics and statistical mechanics. (To the 50th anniversary of his death) // Advances in Chemistry. 1953. T. 22. Issue. 10; Frankfurt W. I., Frank A. M. D. W. Gibbs. M., 1964.

Josiah Willard Gibbs Alma mater

Yale College[d]
Heidelberg University
Yale School of Engineering & Applied Science [d]

Gibbs triangle

In 1901, Gibbs was awarded the highest honor of the international scientific community at the time (awarded to only one scientist each year), the Copley Medal of the Royal Society of London, for becoming "the first to apply the second law of thermodynamics to a comprehensive consideration of the relationship between chemical, electrical and thermal energy and the ability to do work" .

Biography

early years

Years of maturity

In 1863, by decision of the Sheffield Scientific School (English) At Yale, Gibbs was awarded the first Doctor of Philosophy (PhD) degree in engineering in the United States for his dissertation “On the Shape of the Teeth of Gear Wheels.” In subsequent years, he taught at Yale: for two years he taught Latin and for another year - what was later called natural philosophy and is comparable to the modern concept of “natural sciences”. In 1866 he went to Europe to continue his studies, spending one year each in Paris, Berlin and then Heidelberg, where he met Kirchhoff and Helmholtz. At that time, German scientists were leading authorities in chemistry, thermodynamics and basic natural sciences. These three years, in fact, constitute that part of the scientist’s life that he spent outside of New Haven.

In 1869 he returned to Yale, where in 1871 he was appointed professor of mathematical physics (the first such position in the United States) and held this post for the rest of his life.

The professor's position was at first unpaid, a situation typical of the time (especially in Germany), and Gibbs was required to publish his papers. In 1876-1878 he writes a number of articles on the analysis of multiphase chemical systems using the graphical method. They were later published in a monograph "On the equilibrium of heterogeneous substances" (On the Equilibrium of Heterogeneous Substances), his best known work. This work by Gibbs is considered one of the greatest scientific achievements of the 19th century and one of the fundamental works in physical chemistry. In his articles, Gibbs used thermodynamics to explain physicochemical phenomena, connecting what had previously been a set of individual facts.

“It is generally accepted that the publication of this monograph was an event of paramount importance in the history of chemical science. However, it took several years before its significance was fully realized; the delay was mainly due to the fact that the mathematical form used and the strict deductive techniques make reading difficult for anyone, and especially for students in the field of experimental chemistry, with whom it was most relevant ... "

Important sections covered in his other papers on heterogeneous equilibria include:

Chemical potential and free energy concepts

Gibbs ensemble model, the basis of statistical mechanics

Gibbs phase rule

Later years

In 1884-89. Gibbs makes improvements to vector analysis, writes works on optics, and develops a new electrical theory of light. He deliberately avoids theorizing about the structure of matter, which was a wise decision in view of the subsequent revolutionary events in subatomic particle physics and quantum mechanics. His chemical thermodynamics was more universal than any other chemical theory existing at that time.

Little is known about the names and careers of his students. Gibbs never married and lived his entire life in his father's house with his sister and brother-in-law, a librarian at Yale. He was so focused on science that he was generally inaccessible to personal interests. American mathematician Edwin Bidwell Wilson (English) said: “Outside the walls of the classroom, I saw him very little. He had a habit of going for a walk in the afternoon along the streets between his office in the old laboratory and home - a little exercise in the break between work and lunch - and then you could sometimes meet him." Gibbs died in New Haven and is buried in Grove Street Cemetery.

Scientific recognition

Recognition did not come to the scientist immediately (in particular, because Gibbs mainly published in "Transactions of the Connecticut Academy of Sciences"- a magazine published under the editorship of his librarian son-in-law, little read in the United States and even less in Europe). At first, only a few European theoretical physicists and chemists (including, for example, the Scottish physicist James Clerk Maxwell) paid attention to his work. It was only after Gibbs's articles were translated into German (by Wilhelm Ostwald in 1892) and French (Henri Louis le Chatelier in 1899) that his ideas became widespread in Europe. His theory of the phase rule was experimentally confirmed in the works of H. W. Backhuis Rosebohm, who demonstrated its applicability in various aspects.

“Throughout his last years he remained a tall, distinguished gentleman with a healthy gait and a healthy complexion, coping with his duties at home, approachable and responsive to students. Gibbs was highly regarded by his friends, but American science was too concerned with practical issues to apply his solid theoretical work during his lifetime. He lived his quiet life at Yale and deeply admired several bright students, without making a first impression on American scholars comparable to his talent." (Crowther, 1969)

One should not think that Gibbs was little known during his lifetime. For example, mathematician Gian-Carlo Rota (English), while looking through the shelves of mathematics literature in the Sterling Library (at Yale University), I came across a mailing list handwritten by Gibbs and attached to some notes. The list included over two hundred notable mathematicians of the time, including Poincaré, Hilbert, Boltzmann and Mach. One can come to the conclusion that among the luminaries of science, Gibbs's works were better known than the printed material indicates.

Gibbs' achievements, however, were finally recognized only with the appearance in 1923 of the publication of Gilbert Newton Lewis and Merle Randall (English) , which introduced Gibbs' methods to chemists from various universities. These same methods formed, for the most part, the basis of chemical technology.

Chemical thermodynamics

Gibbs' major works relate to chemical thermodynamics and statistical mechanics, of which he is one of the founders. Gibbs developed the so-called entropy diagrams, which play a large role in technical thermodynamics, and showed (1871-1873) that three-dimensional diagrams make it possible to represent all the thermodynamic properties of matter.

In 1873, when he was 34 years old, Gibbs showed extraordinary research abilities in the field of mathematical physics. This year two articles appeared in the Connecticut Academy Bulletin. The first one was entitled “Graphical methods in the thermodynamics of fluids”, and the second - “Method of geometric representation of the thermodynamic properties of substances using surfaces”. With these works Gibbs laid the foundation geometric thermodynamics .

These were followed in 1876 and 1878 by two parts of a much more fundamental article, “On Equilibrium in Heterogeneous Systems,” which summarize his contributions to physical science, and are undoubtedly among the most significant and distinguished literary monuments of the scientific activity of the 19th century. Thus, Gibbs in 1873-1878. laid the foundations of chemical thermodynamics, in particular, developed the general theory of thermodynamic equilibrium and the method of thermodynamic potentials, formulated (1875) the phase rule, constructed a general theory of surface phenomena, and obtained an equation establishing the connection between the internal energy of a thermodynamic system and thermodynamic potentials.

When discussing chemically homogeneous media in the first two papers, Gibbs often used the principle that a substance is in equilibrium if its entropy cannot be increased at constant energy. In the epigraph of the third article he cited the famous expression of Clausius “Die Energie der Welt ist constant.” Die Entropie der Welt strebt einem Maximum zu", which means “The energy of the world is constant. The entropy of the world tends to maximum.” He showed that the above-mentioned equilibrium condition, derived from the two laws of thermodynamics, has universal application, neatly removing one constraint after another, most notably that the substance must be chemically homogeneous. An important step was the introduction of the masses of the components that make up a heterogeneous system as variables in fundamental differential equations. It is shown that in this case the differential coefficients at energies with respect to these masses enter into equilibrium in the same way as intensive parameters, pressure and temperature. He called these coefficients potentials. Analogies with homogeneous systems are constantly used, and mathematical operations are similar to those used in the case of expanding the geometry of three-dimensional space to n-dimensional space.

It is widely accepted that the publication of these papers was of particular importance for the history of chemistry. In fact, this marked the formation of a new branch of chemical science, which, according to M. Le Chatelier ( M. Le Chetelier) [ ], was compared in importance to the works of Lavoisier. However, it took several years before the value of these works became generally recognized. This delay was mainly caused by the fact that reading the articles was quite difficult (especially for students involved in experimental chemistry) due to extraordinary mathematical calculations and scrupulous conclusions. At the end of the 19th century there were very few chemists with sufficient knowledge of mathematics to read even the simplest parts of the papers; Thus, some of the most important laws, first described in these articles, were subsequently proven by other scientists either theoretically or, more often, experimentally. Nowadays, however, the value of Gibbs's methods and the results obtained are recognized by all students of physical chemistry.

Theoretical mechanics

Gibbs's scientific contribution to theoretical mechanics was also noticeable. In 1879, in relation to holonomic mechanical systems, he derived the equations of their motion from Gauss's principle of least constraint. In 1899, essentially the same equations as Gibbs’s were independently obtained by the French mechanic P. E. Appel, who pointed out that they describe the motion of both holonomic and nonholonomic systems (it is in problems of nonholonomic mechanics that the data now find their main application equations, usually called Appel's equations, and sometimes - Gibbs-Appel equations). They are usually regarded as the most general equations of motion of mechanical systems.

Vector calculus

Gibbs, like many other physicists of those years, realized the need to use vector algebra, through which quite complex spatial relationships associated with different areas of physics can be easily and accessiblely expressed. Gibbs always preferred the clarity and elegance of the mathematics he used, so he was particularly keen to use vector algebra. However, in Hamilton's quaternion theory he did not find a tool that satisfied all his requirements. In this regard, he shared the views of many researchers who wanted to reject quaternion analysis, despite its logical validity, in favor of a simpler and more direct descriptive apparatus - vector algebra. With the help of his students, in 1881 and 1884, Professor Gibbs secretly published a detailed monograph on vector analysis, the mathematical apparatus of which he had developed. The book quickly spread among his fellow scientists.

While working on his book, Gibbs relied mainly on labor "Ausdehnungslehre" Grassmann and the algebra of multiple relations. The mentioned studies were of particular interest to Gibbs, and, as he later noted, gave him the greatest aesthetic pleasure among all his activities. Many works in which he rejected Hamilton's theory of quaternions appeared in the pages of the journal Nature.

When the utility of vector algebra as a mathematical system was confirmed over the next 20 years by himself and his students, Gibbs agreed, albeit reluctantly, to publish a more detailed work on vector analysis. As he was at that time entirely absorbed in another subject, the preparation of the manuscript for publication was entrusted to one of his students, Dr. E. B. Wilson, who coped with the task. Now Gibbs is deservedly considered one of the creators of vector calculus in its modern form.

In addition, Professor Gibbs was extremely interested in the application of vector analysis to solving astronomical problems and gave many similar examples in the article “On the Determination of Elliptical Orbits from Three Complete Observations.” The methods developed in this work were subsequently used by Professors V. Beebe ( W Beebe) and A. W. Phillips ( A. W. Phillips) to calculate the orbit of Comet Swift based on three observations, which became a serious test of the method. They found that the Gibbs method had significant advantages over the Gauss and Oppolzer methods, the convergence of suitable approximations was faster, and much less effort was expended in finding the fundamental equations for the solution. These two articles were translated into German by Buchholz (German: Hugo Buchholz) and included in the second edition Theoretische Astronomie Klinkerfus.

Electromagnetism and optics

From 1882 to 1889 in the American Journal of Science ( American Journal of Science) five articles appeared on separate topics in the electromagnetic theory of light and its connections with various theories of elasticity. It is interesting that special hypotheses about the relationship between space and matter were completely absent. The only assumptions made about the structure of matter are that it consists of particles that are quite small relative to the wavelength of light, but not infinitesimal, and that it somehow interacts with electric fields in space. Using methods whose simplicity and clarity were reminiscent of his studies in thermodynamics, Gibbs showed that in the case of completely transparent media the theory not only explained the dispersion of color (including the dispersion of optical axes in a birefringent medium), but also led to Fresnel's laws of double reflection for any wavelengths taking into account low energies that determine color dispersion. He noted that circular and elliptical polarization can be explained if we consider the energy of light of even higher orders, which, in turn, does not refute the interpretation of many other known phenomena. Gibbs carefully derived general equations for monochromatic light in a medium with varying degrees of transparency, arriving at expressions different from those obtained by Maxwell, which did not explicitly contain the dielectric constant of the medium and conductivity.

Some experiments of Professor Hastings ( C. S. Hastings) 1888 (which showed that birefringence in Iceland spar is in exact accordance with Huygens' law) again forced Professor Gibbs to take up the theory of optics and write new articles in which, in a fairly simple form from elementary reasoning, he showed that the dispersion of light is strictly corresponds to the electrical theory, while none of the theories of elasticity proposed at that time could be reconciled with the experimental data obtained.

Statistical mechanics

In his latest work "Basic principles of statistical mechanics" Gibbs returned to a topic closely related to the subject of his earlier publications. In them he was engaged in the development of consequences of the laws of thermodynamics, which are accepted as data based on experiment. In this empirical form of science, heat and mechanical energy were regarded as two different phenomena - of course, mutually transforming into each other with certain limitations, but fundamentally different in many important parameters. In accordance with the popular tendency to unify phenomena, many attempts have been made to reduce these two concepts into one category, to show in fact that heat is nothing more than the mechanical energy of small particles, and that the extradynamic laws of heat are the consequence of a huge number of independent mechanical systems in any body - numbers so large that it is difficult for a person with his limited imagination to even imagine. Yet, despite the confident assertions in many books and popular exhibitions that “heat is the mode of molecular motion,” they were not entirely convincing, and this failure was regarded by Lord Kelvin as a blight on the history of 19th-century science. Such studies must deal with the mechanics of systems with a huge number of degrees of freedom, and it would be possible to compare the results of calculations with observation; these processes must be statistical in nature. Maxwell more than once pointed out the difficulties of such processes, and also said (and this was often quoted by Gibbs) that in such matters serious mistakes were made even by people whose competence in other areas of mathematics was not questioned.

Impact on subsequent work

Gibbs's works attracted a lot of attention and influenced the activities of many scientists, some of whom became Nobel laureates:

In 1910, the Dutchman J. D. Van der Waals was awarded the Nobel Prize in Physics. In his Nobel lecture, he noted the influence of Gibbs's equations of state on his work.

In 1918, Max Planck received the Nobel Prize in Physics for his work in the field of quantum mechanics, in particular for the publication in 1900 of his quantum theory. His theory was essentially based on the thermodynamics of R. Clausius, J. W. Gibbs and L. Boltzmann. Planck said this about Gibbs: “his name not only in America, but throughout the world will be ranked among the most famous theoretical physicists of all time...”.

Early 20th century Gilbert N. Lewis and Merle Randall (English) used and expanded the theory of chemical thermodynamics developed by Gibbs. They presented their research in 1923 in a book called "Thermodynamics and the Free Energy of Chemical Substances" and was one of the fundamental textbooks on chemical thermodynamics. In the 1910s William Gioc attended the College of Chemistry at Berkeley University and received a bachelor's degree in chemistry in 1920. At first he wanted to become a chemical engineer, but under the influence of Lewis he became interested in chemical research. In 1934 he became a full professor of chemistry at Berkeley, and in 1949 he received the Nobel Prize for his cryochemical research using the third law of thermodynamics.

Gibbs's work had a significant influence on the formation of the views of Irving Fisher, an economist who had a PhD from Yale.

Personal qualities

No quality of Professor Gibbs impressed his colleagues and students more than his modesty and complete unawareness of his limitless intellectual resources. A typical example is a phrase he uttered in the company of a close friend regarding his mathematical abilities. With absolute sincerity he said: “If I were successful in mathematical physics, I think it was because I was lucky enough to avoid mathematical difficulties.”

Perpetuation of the name

In 1950, a bust of Gibbs was placed in the Hall of Fame for Great Americans.

On May 4, 2005, the United States Postal Service issued a series of postage stamps featuring portraits of Gibbs, John von Neumann, Barbara McClintock, and Richard Feynman.

The US Navy oceanographic expedition vessel USNS Josiah Willard Gibbs (T-AGOR-1), which operated from 1958-71, was named after Gibbs.

] Translation from English edited by V.K. Semenchenko.
(Moscow - Leningrad: Gostekhizdat, 1950. - Classics of natural science)
Scan: AAW, processing, Djv format: mor, 2010

CONTENT:
Editor's Foreword (5).
Josiah Willard Gibbs, his life and main scientific works. VC. Semenchenko (11).
Works by J.W. Gibbs (list) (24).
J.W. Gibbs
THERMODYNAMIC WORK
I. GRAPHICAL METHODS IN THE THERMODYNAMICS OF LIQUIDS
Values and ratios that will be presented in diagrams (29).
The main idea and general properties of diagrams (31).
Entropy-temperature diagrams compared with diagrams commonly used (39).
The case of an ideal gas (42).
The case of condensing vapors (45).
Diagrams in which isometric, isopiestic, isothermal, isodynamic and isentropic lines of an ideal gas are simultaneously straight lines (48).
Volume-entropy diagram (53).
Location of isometric, isopiestic, isothermal and isentropic lines around point (63).
II. METHOD OF GEOMETRICAL REPRESENTATION OF THERMODYNAMIC PROPERTIES OF SUBSTANCES USING SURFACES
Depiction of volume, entropy, energy, pressure and temperature (69).
The nature of that part of the surface that represents states that are not homogeneous (70).
Surface properties related to the stability of thermodynamic equilibrium (75).
Main features of the thermodynamic surface for substances in solid, liquid and vapor states (81).
Problems related to the dissipated energy surface (89).
III. ON THE EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES
A preliminary note on the role of energy and entropy in the theory of thermodynamic systems (95).
CRITERIA FOR EQUILIBRIUM AND STABILITY
Suggested criteria (96).
Meaning of the term possible changes (98).
Passive resistances (98).
Legitimacy of criteria (99).
CONDITIONS FOR EQUILIBRIUM OF CONTACTING HETEROGENEOUS MASSES NOT SUBJECT TO. THE INFLUENCE OF GRAVITY, ELECTRIC FIELD, CHANGES IN THE SHAPE OF SOLID MASSES OR SURFACE TENSION
Statement of the problem (103).
Conditions of equilibrium between the initially existing homogeneous parts of a given mass (104).
Meaning of the term homogeneous (104).
Selection of substances considered as components. Actual and possible components (105).
Derivation of particular equilibrium conditions when all parts of the system have the same components (106).
Determination of potentials for the constituent parts of various homogeneous masses (107).
The case where some substances are only possible components in part of the system (107).
A type of particular equilibrium conditions when there are convertibility relations between substances that are considered as components of different masses (109).
Conditions relating to the possible formation of masses other than those originally present (112).
Very small masses cannot be treated in the same way as large masses (118).
The sense in which formula (52) can be considered as expressing the found conditions (119).
Condition (53) is always sufficient for equilibrium, but not always necessary (120).
A mass for which this condition is not satisfied is at least practically unstable (123).
(This condition is discussed later in the chapter “Stability”, see page 148)
Effect of solidification of any part of a given mass (124).
Influence of additional equations of imposed conditions (127).
Influence of the diaphragm (balance of osmotic forces) (128).
FUNDAMENTAL EQUATIONS
Definition and properties of fundamental equations (131).
About the quantities φ, y, e (135).
Expression of the equilibrium criterion through quantity (136).
Expressions of the equilibrium criterion in known cases using quantity (138).
POTENTIALS
The value of the potential for a substance of a given mass is independent of other substances that may be chosen to represent the composition of that mass (139).
The definition of potential that makes this property obvious (140).
We can distinguish in the same homogeneous mass the potentials for an indefinite number of substances, each of which has a very specific value. For the potentials of different substances of the same homogeneous mass, the equation is really the same as for units of these substances (140).
The potential values depend on arbitrary constants, which are determined by the determination of the energy and entropy of each elementary substance (143).
ABOUT THE EXISTING PHASES OF MATTER
Determination of phases and coexisting phases (143).
The number of independent changes possible in a system of coexisting phases (144).
Case of n + 1 coexisting phases (144).
The case when the number of coexisting phases is less than n + 1 (146).
INTERNAL STABILITY OF HOMOGENEOUS LIQUIDS ACCORDING TO FUNDAMENTAL EQUATIONS
General condition for absolute stability (148).
Other forms of this condition (152).
Stability with respect to continuous phase changes (154).
Conditions characterizing the boundaries of stability in this regard (163).
GEOMETRIC ILLUSTRATIONS
Surfaces on which the composition of the depicted bodies is constant (166).
Surfaces and curves for which the composition of the depicted body changes, but its temperature and pressure are constant (169).
CRITICAL PHASES
Definition (182).
The number of independent changes that the critical phase is capable of while remaining so (183).
Analytical expression of conditions characterizing critical phases. Position of critical phases relative to stability boundaries (183).
Changes that are possible under different circumstances for a mass that was originally a critical phase (185).
About the values of potentials when the amount of one of the components is very small (189).
ON SOME QUESTIONS RELATING TO THE MOLECULAR STRUCTURE OF BODIES
Proximate and primary components (192).
Phases of dissipated energy (195).
Catalysis is a perfect catalytic agent (196).
The fundamental equation for the phases of dissipated energy can be derived from a more general form of the fundamental equation (196).
Dissipated energy phases may sometimes be the only phases whose existence can be determined experimentally (197).
EQUILIBRIUM CONDITIONS FOR HETEROGENEOUS MASSES UNDER THE INFLUENCE OF GRAVITY
This problem is treated in two different ways:
The volume element is treated as variable (199).
The volume element is treated as fixed (203).
FUNDAMENTAL EQUATIONS OF IDEAL GASES AND GAS MIXTURES
Ideal gas (206).
Ideal gas mixture. Dalton's Law (210).
Some conclusions relating to the potentials of liquids and solids (223).
Considerations regarding the increase in entropy caused by diffusion when mixing gases (225).
Phases of dissipated energy of an ideal gas mixture, the components of which chemically interact with each other (228).
Gas mixtures with converting components (232).
The case of nitrous peroxide (236).
Fundamental equations for equilibrium phases (244).
SOLIDS
Conditions of internal and external equilibrium for solids in contact with liquids, in relation to all possible states of deformation of solids (247).
Deformations are expressed by nine derivatives (248).
Energy change in a solid element (248).
Derivation of equilibrium conditions (250).
Discussion of the condition relating to the dissolution of a solid (258).
Fundamental equations for solids (267).
Solids absorbing liquids (283).
CAPILLARITY THEORY
Surfaces of discontinuity between liquid masses
Preliminary remarks. Fracture surfaces. Separating surface (288).
Discussion of the problem. Particular equilibrium conditions for adjacent masses related to temperature and potentials, obtained earlier, do not lose their significance under the influence of the discontinuity surface. Surface energy and entropy. Surface densities of constituent substances. General expression for variation of energy surfaces. Equilibrium condition relating to pressures in adjacent masses (289).
Fundamental equations for discontinuity surfaces between liquid masses (300).
On the experimental determination of fundamental equations for discontinuity surfaces between liquid masses (303).
Fundamental equations for flat surfaces of discontinuity between liquid masses (305).
On the stability of discontinuity surfaces:
1) in relation to changes in the nature of the surface (310).
2) in relation to changes in which the shape of the surface changes (316).
On the possibility of the formation of a liquid of a different phase inside a homogeneous liquid (328).
On the possibility of formation at the surface where two different homogeneous liquids come into contact, a new liquid phase different from them (335).
Replacing potentials with pressures in the fundamental equations of surfaces (342).
Thermal and mechanical relationships related to the tensile strength of the fracture surface (348).
Impermeable films (354).
Internal equilibrium conditions for a system of heterogeneous liquid masses, taking into account the influence of discontinuity surfaces and gravitational force (356).
Conditions for stability (367).
On the possibility of the formation of a new discontinuity surface in the place where several discontinuity surfaces meet (369).
Conditions for stability of liquids with respect to the formation of a new phase at the line where three discontinuity surfaces meet (372).
Conditions for stability of liquids with respect to the formation of a new phase at the point where “the vertices of four different masses meet (381).
Liquid films (385).
Film element definition (385).
Each element can generally be considered as being in a state of equilibrium. The properties of an element in this state and thick enough that its interior has the properties of a substance in bulk. Conditions under which stretching the film will not cause an increase in tension. If the film has more than one component that does not belong to adjacent masses, then stretching will, generally speaking, cause an increase in tension. The value of film elasticity derived from the fundamental equations of surfaces and masses. Observable elasticity (385).
The elasticity of the film does not vanish at the boundary at which its inner part loses the properties of a substance in the mass, but a certain kind of instability appears (390).
Application of equilibrium conditions already derived for a system subject to the influence of gravity (pp. 361-363) to the case of a liquid film (391).
Regarding the formation of liquid films and processes leading to their destruction. Black spots in films of soapy water (393).
TERMINAL SURFACES BETWEEN SOLIDS AND LIQUIDS
Preliminary remarks (400).
Equilibrium conditions for isotropic solids (403).
The influence of gravity (407).
Equilibrium conditions in the case of crystals (408).
The influence of gravity (411).
Restrictions (413).
Equilibrium conditions for a line in which three different masses occur, one of which is solid (414).
General relations (418).
Different method and different notation (418).
ELECTROMOTIVE FORCE
Change of equilibrium conditions under the influence of electromotive force (422).
Flow equation. Ions. Electrochemical equivalents (422).
Equilibrium conditions (423).
Four cases (425).
Lippmann electrometer (428).
Limitations caused by passive resistance (429).
General properties of a perfect electrochemical device (430).
Reversibility as a test of ideality. Determination of electromotive force from changes that occur in the cell. Modification of the formula for the case of a non-ideal device (430).
When the cell temperature is considered constant, the change in entropy caused by the absorption or release of heat cannot be neglected; proof of this for a Grove gas battery charged with hydrogen and nitrogen, by currents caused by differences in the concentrations of the electrolyte, and for electrodes of zinc and mercury in a solution of zinc sulfate (431).
That the same is true when chemical processes take place in certain respects, is shown by reasoning a priori, based on the phenomenon occurring in the direct combination of the elements of water or the elements of hydrochloric acid and in the absorption of heat, which Favre has many times observed in galvanic or electrolytic cells (434).
The different physical states in which the ion is deposited do not affect the magnitude of the electromotive force if the phases are coexisting. Raoult's experiments (441).
Other formulas for electromotive force (446).
Editor's Notes (447).

From the editor's preface: The main thermodynamic works of Gibbs, the translation of which is given in this book, appeared in 1873-1878, but getting to know them is of not only historical interest for the modern reader...