Josiah Willard Gibbs

American physical scientist

• Born: February 11, 1839
• Birthplace: New Haven, Connecticut
• Died: April 28, 1903
• Place of death: New Haven, Connecticut

Gibbs established the theoretical basis for modern physical chemistry by quantifying the second law of thermodynamics and developing heterogeneous thermodynamics. This and other work earned for him recognition as the greatest American scientist of the nineteenth century.

Early Life

Josiah Willard Gibbs, later known usually as J. Willard Gibbs—to distinguish him from his father, who bore the same name—was the fourth child and son among five children of J. W. Gibbs, a professor of sacred literature at Yale College Theological Seminary, and Mary Anna Van Cleve Gibbs. Born in New Haven, Connecticut, Gibbs would live all of his life in that city, leaving only to take one trip abroad, and dying in the same house in which he grew up.

Well educated in private schools, Gibbs was graduated from Yale College in 1858, receiving prizes in Latin and mathematics. In 1863, he took his doctoral degree in engineering at Yale—one of the first such degrees in the United States; his dissertation was entitled On the Form of the Teeth of Wheels in Spur Gearing. For the next three years he tutored at Yale in Latin and natural philosophy, working on several practical inventions and obtaining a patent for one of them, an improved railway brake. The foregoing points to a not inconsiderable practical element in the chiefly theoretical scientist that Gibbs would become.

In 1866, Gibbs embarked on a journey to Europe, where he attended lectures by the best-known mathematicians and physicists of that era, spending a year each at the Universities of Paris, Berlin, and Heidelberg. What he learned at these schools would form the basis for his later theoretical work. His parents having died, and two of his sisters as well, he traveled with his remaining sisters, Anna and Julia, the latter returning home early to marry Addison Van Name, later librarian of Connecticut Academy, in 1867.

Upon his return to New Haven in 1869, Gibbs began work at once on his great theoretical undertaking, which he would not complete until 1878. He lived in the Van Name household, as did his sister Anna; neither he nor she was ever married. In 1871, he was appointed professor of mathematical physics at Yale—the first such chair in the United States—but without salary. He was obliged to live for nine years on his not very considerable inherited income. When The Johns Hopkins University, aware of the significance of his work, offered him a position at a good salary, Yale decided to offer Gibbs two-thirds of what Johns Hopkins would pay; it was enough for Gibbs.

In 1873, he published his first paper, “Graphical Methods in the Thermodynamics of Fluids,” which clarified the concept of entropy, introduced in 1850 by Rudolf Clausius. The genius of this insight was immediately recognized by James Clerk Maxwell in England, to whom Gibbs had sent a copy of the paper. The work was published, however, in a relatively obscure journal, The Transactions of the Connecticut Academy of Arts and Sciences, where almost all of Gibbs’s subsequent writings would appear. In addition, his style was so terse, austere, and condensed as to be unreadable to all but a few readers who were already well acquainted with his underlying assumptions. Consequently, for most of his life Gibbs would remain largely unknown, especially in the United States, except among a small circle of his scientific colleagues.

This undeserved obscurity never seemed to trouble Gibbs. By all accounts, he was a genuinely unassuming and unpretentious man, tolerant, kind, approachable, and seemingly unconscious of his intellectual eminence. He was by no means gregarious and probably more than a little aloof; he had few really close friends, though he kept up a large correspondence. He attended church regularly. Physically, he was of slight build and owed a certain frailty in health to a severe case of scarlet fever in childhood. However, he was strong enough to ride and was known as a good horseman. Photographs of him reveal a handsome but somewhat stern man with a well-trimmed, short beard. The photographic image leaves an apt impression of what he was in life: a gentleman, a professor, and a scientist of unimpeachable integrity.

Life’s Work

Gibbs published yet another paper in 1873, “A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces.” In 1876, the first 140 pages of his major work appeared (again in Transactions), the final 180 pages finally being published by that journal in 1878; both parts bore the title “On the Equilibrium of Heterogeneous Substances.” This work, of the utmost importance to science, never appeared in book form in English in Gibbs’s lifetime. Its significance was appreciated by Maxwell, who incorporated some of its findings into his own books, but he died in 1879.

Continental Europeans perceived the general importance of Gibbs’s discoveries, but had real difficulty reading Gibbs’s text. (Gibbs himself rejected all suggestions that he rewrite his treatise as a readable book.) Hermann Helmholtz and Max Planck both duplicated some of Gibbs’s work, simply because they did not know of it. A German translation of it, by the great scientist Wilhelm Ostwald, appeared only in 1892. French translations of various sections of the treatise were published in 1899 and 1903. Meanwhile, scientists came to perceive—in the words of physics professor Paul Epstein—that a

young investigator, having discovered an entirely new branch of science, gave in a single contribution an exhaustive treatment of it which foreshadowed the development of theoretical chemistry for a quarter of a century.

Gibbs’s was thus an achievement almost unparalleled in the history of science. Ostwald predicted that the result of Gibbs’s work would determine the form and content of chemistry for a century to come—and he was right. A French scientist compared Gibbs, in his importance to chemistry, with Antoine Lavoisier. It should be mentioned that the editors of The Transactions of the Connecticut Academy of Arts and Sciences published Gibbs’s work on faith alone as they were not able to understand it completely; they obtained the money for publishing the long treatise through private subscription.

Of special importance in Gibbs’s work is its sophisticated mathematics. It is therefore not possible to summarize his discoveries in a brief article. There are two features, however, that must be noted. First, Gibbs succeeded in precisely formulating the second law of thermodynamics , which states that the spontaneous flow of heat from hot to cold bodies is reversible only with the expenditure of mechanical or other nonthermal energy. Consequently, entropy (S), equal to heat (Q) divided by temperature change (T), must continually be increasing. Prior to Gibbs, thermodynamics simply did not exist as a science.

Second, Gibbs derived from his more complex heterogeneous thermodynamics the “phase rule,” which shows the relationship between the degrees of freedom (F) of a thermodynamic system and the number of components (C) and the number of phases (P), so that F = C + 2 - P. He showed how these relationships could be expressed graphically, in three dimensions. Often phase-rule diagrams proved to be the only practical key to the solution of hitherto insoluble problems concerning the mixing of components so that they would remain in equilibrium and not separate out and destroy the mixture. The phase rule helped make it possible to calculate in advance the temperature, pressure, and concentration required for stability—thus eliminating months and possibly years of tedious trial-and-error experiments. This would have important application in industry as well as in the laboratory.

Interestingly, after Gibbs’s one major treatise on thermodynamics, he never wrote another important paper on the subject. He had said the last word, and he knew it. He did not, however, remain idle. Between 1883 and 1889, he published five papers on the electromagnetic theory of light. This work, too, was well received.

Meanwhile, he had begun to receive a certain amount of more or less perfunctory recognition at home: He was elected to the National Academy of Sciences in 1879 and to the American Academy of Arts and Sciences in 1880; in 1880 he received the Rumford Medal from the latter; in 1885 he was elected a vice president of the American Association for the Advancement of Science.

In the period between 1889 and 1902, Gibbs lectured on the subject of statistical mechanics but published almost nothing on the topic except for a brief abstract. This would be his major work during the final portion of his life; it would require about the same gestation period as did his investigation of thermodynamics. Simultaneously, however, he was lecturing and publishing papers on vector analysis and multiple algebra; the theory of dyadics that appeared in these works is regarded as his most important published contribution to pure mathematics. A book based on his lectures, Gibbs’ Vector Analysis , was edited and published by a student, E. B. Wilson, in 1901.

During that same year, Gibbs was awarded the Copley Medal by the Royal Society of London for being the first to apply the second law of thermodynamics to the exhaustive discussion of the relation between chemical, electrical, and thermal energy and the capacity for external work. This was the highest honor for scientists prior to the founding of the Nobel Prize.

In 1902, Gibbs’s final important work was published under the title Elementary Principles in Statistical Mechanics Developed with Special Reference to the Rational Foundation of Thermodynamics . In this brilliant study, Gibbs was as far ahead of his time as he had been with his first major treatise. The later work has been called “a monument in the history of physics which marks the separation between the nineteenth and twentieth centuries.” Gibbs’s perception of the role played by probability in physical events made his last work a true precursor to quantum mechanics, which did not develop fully until the 1920’s.

During the year following the publication of his final gift to the world, Gibbs suffered from several minor ailments. One of these resulted in a sudden and acute attack from an intestinal obstruction, which led to Gibbs’s untimely death on April 28, 1903.

Significance

Gibbs’s contribution to American society occurred chiefly after his death. It is regrettable that few Americans had the capacity to recognize his achievements while he was alive, but it seems pointless to try to fix the blame for this. On the one hand, he himself declined to make his papers more accessible by revising them for a wider readership. On the other, physical chemistry was only beginning to develop in the United States. Few professors of either chemistry or physics had the background that would have enabled them to understand Gibbs’s work; there were no grand figures such as Rudolf Clausius, James Clerk Maxwell, William Thomson (Baron Kelvin), or Wilhelm Ostwald in the United States to welcome the new young genius personally.

In addition, the chemical industry in the United States was conservative in the matter of adopting new methods derived chiefly from theory, while at the same time it was caught up in the chaos of a greatly expanding industrialism. There was virtually no one available to examine the implications for the chemical industry of Gibbs’s new phase rule. Gradually, however, as the industry turned more and more to synthesizing new compounds and developing metal alloys, there came a demand for precisely the sort of tool that Gibbs long before had provided. The phase rule had an early application in alloys of iron and carbon to produce different types of steel. Another application involved the industrial synthesis of ammonia from nitrogen and hydrogen, and of nitric acid from ammonia. Although most of these applications were first worked out in Europe, American industry finally learned how to reap the benefits of bringing theory to bear on practical processes. It finally came to recognize what it owed to Gibbs.

The United States thus reaped the practical benefits of Gibbs’s work; it also had the honor of claiming as its own one of the world’s greatest theoretical scientists.

Bibliography

Bumstead, H. A. “Josiah Willard Gibbs.” In The Collected Works of J. Willard Gibbs, edited by H. A. Bumstead. 2 vols. New Haven, Conn.: Yale University Press, 1948. Reprinted, with some additions, from the American Journal of Science 4 (September, 1903). Also in a previous edition of The Collected Works, edited by W. R. Longley and R. G. Van Name. New York: Longmans, Green, 1928. Written by a former student who knew Gibbs well, this basic source for all other biographies includes a useful list of Gibbs’s publications in chronological order.

Caldi, D. G., and G. D. Mostow, eds. Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989. Providence, R.I.: American Mathematical Society, 1990. Collection of papers delivered at a professional conference commemorating Gibbs. Includes three articles providing a perspective of Gibbs, the man, and his place in the history of science.

Crowther, J. G. “Josiah Willard Gibbs.” In Famous American Men of Science, edited by J. G. Crowther. Freeport, N.Y.: Books for Libraries Press, 1969. Reprinted with minor changes from first edition. New York: W. W. Norton, 1937. Excellent psychological speculation about Gibbs’s family and his social and academic life. Two portraits, brief bibliography.

Jaffe, Bernard. “J. Willard Gibbs (1839-1903): America in the New World of Chemistry.” In Men of Science in America: The Role of Science in the Growth of Our Country. New York: Simon & Schuster, 1944. Excellent discussion of American reception (or lack of it) of Gibbs, and the consequences for American society. Good explanation of phase rule and its application in industry.

James, Ioan. Remarkable Physicists: From Galileo to Yukawa. New York: Cambridge University Press, 2004. This collection of brief biographies of prominent physicists includes a five-page overview of Gibbs’s life and scientific contributions.

Kraus, Charles A. “Josiah Willard Gibbs.” In Great Chemists, edited by Eduard Farber. New York: Interscience, 1961. Good discussion of experimental work and of phase rule.

Rukeyser, Muriel. Willard Gibbs. Garden City, N.Y.: Doubleday, Doran, 1942. Long text, reads almost like a novel, but offers good background detail that places Gibbs squarely within the context of the American culture of his time.

Seeger, Raymond John. J. Willard Gibbs: American Mathematical Physicist Par Excellence. Elmsford, N.Y.: Pergamon Press, 1974. Places greatest emphasis on details of mathematics and science. Includes useful chronology of life and work with a short bibliography.

Wheeler, Lynde Phelps. Josiah Willard Gibbs: The History of a Great Mind. Reprint. Woodbridge, Conn.: Oxbow Press, 1998. The authorized biography. Wheeler was a student of Gibbs during the 1890’s, and his account is comprehensive but rather genteel.