Josiah Willard Gibbs

J. Willard Gibbs
(1839-1903)
Born	February 11, 1839 New Haven, Connecticut, USA
Died	April 28, 1903 New Haven, Connecticut, USA
Residence	USA
Nationality	USA
Field	Physicist
Institutions	Yale University
Alma mater	Yale University
Academic advisor	Gustav Kirchhoff Hermann von Helmholtz
Notable students	Edwin Bidwell Wilson
Known for	Gibbs free energy Gibbs entropy Vector analysis Gibbs-Helmholtz equation Gibbs algorithm Gibbs distribution Gibbs state Gibbs phenomenon
Notable prizes	Copley Medal (1901)

Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was a preeminent American mathematical-engineer, theoretical physicist, and chemist noted for his famed 1876 publication of On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, which laid the foundation for the science of physical chemistry. He also enunciated the "phase rule" governing the number of components of a mixture and the various states that it can manifest at a given temperature and pressure.

Biography

Early years

Gibbs in his youth.

Josiah Willard Gibbs was born the fourth of five children, the others all being women, of Josiah Willard Gibbs, a professor of sacred literature at the Yale Divinity School, and Mary Anna Van Cleve Gibbs, the daughter of a Yale graduate. His father, is now most remembered for his involvement in the Amistad trial. Although the father was also named Josiah Willard, the son is never referred to as "Jr." His mother was the daughter of a Yale graduate in literature.

After attending the Hopkins School, Gibbs matriculated at Yale College at the age of 15. He graduated in 1858 near the top of his class, and was awarded prizes in mathematics and Latin.

Founder of chemical thermodynamics.

Middle years

In 1863, Gibbs was awarded the first Ph.D. degree in engineering in the USA from the Sheffield Scientific School at Yale. His dissertation was on "The form of the teeth of wheels in spur gearing," a problem that he reduced to one of planar geometry. He then tutored at Yale, two years in Latin and one year in what was then called natural philosophy, now comparable to the natural sciences, particularly physics. In 1866 he went to Europe, accompanied by two of his sisters, to study, spending a year each at Paris, Berlin, and Heidelberg, where he was influenced by Kirchhoff and Helmholtz. At the time, German academics were the leading authorities in chemistry, thermodynamics, and theoretical natural science in general. These three years account for nearly all of his life spent outside New Haven.

In 1869, he returned to Yale, and was but marginally employed. He tutored engineering students in French and worked on improvements to the governor of the Watt steam engine. In 1871, he was appointed Professor of Mathematical Physics, the first such professorship in the United States and a position he held for the rest of his life. The appointment was unpaid at first, a situation common in Germany and otherwise not unusual at the time, because the chair had not yet been endowed. In 1873, he published a paper on the geometric representation of thermodynamic quantities. The purpose of this paper was to demonstrate that one could as clearly represent the physical laws associated with thermodynamics through a graphical presentation as by analytical formulae. These papers came to the attention of Scottish physicist Maxwell, who included and expanded upon Gibbs's presentation in his own work on heat. Maxwell was inspired to make a plaster model illustrating Gibbs's construct applied to water, which he then sent to Gibbs. It is now in the possession of Yale University.

Between 1876 and 1878 Gibbs wrote a series of papers collectively titled On the Equilibrium of Heterogeneous Substances, now deemed one of the greatest scientific achievements of the 19th century and one of the foundations of physical chemistry. In these papers Gibbs applied thermodynamics to interpret physicochemical phenomena, successfully explaining and interrelating what had previously been a mass of isolated facts.

Gibbs's extremely economical style bordered on understatement, preventing all but the best minds to recognize the impact of his works. Some important topics covered in his other papers on heterogeneous equilibria include:

• The concepts of chemical potential and free energy (available energy);
• A Gibbsian ensemble ideal, a foundation of statistical mechanics;
• The Gibbs phase rule.

Willard Gibbs’ 1873 available energy (free energy) graph, which shows a plane perpendicular to the axis of v (volume) and passing through point A, which represents the initial state of the body. MN is the section of the surface of dissipated energy. Q_ε and Q_η are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε (internal energy) and η (entropy) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy (Gibbs free energy) and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

Gibbs also wrote on theoretical thermodynamics.

Later years

In 1880, the new Johns Hopkins University in Baltimore, Maryland offered Gibbs a position paying $3000. Yale responded by raising his salary to $2000, and he did not leave New Haven.

From 1880 to 1884, Gibbs combined the ideas of two mathematicians, the quaternions of William Rowan Hamilton and the exterior algebra of Hermann Grassmann to obtain vector analysis (independently formulated by the British mathematical physicist and engineer Oliver Heaviside). Gibbs designed vector analysis to clarify and advance mathematical physics.

In 1881, Gibbs distributed a pamphlet containing material he wrote on vector analysis. Gibbs found the system of quaternions, developed by Hamilton and popularized to some extent by William Tait, awkward, as it introduces a scalar quantity that has no geometric counterpart. Gibbs retained some of the quaternion notation in the form of the unit vectors i, j, and k, and introduced some of his own notation, such as using "X" as the multiplication symbol for the cross product of two vectors. In 1884, he distributed additional material that expresses the relationship beween the differential and integral calculus and vectors. In the same year, Gibbs delivered an address to the American Association for the Advancement of Science in which he coins the word "statistical mechanics." to mean, not just the theory of colliding molecules in gases, but any assemblage of bodies treated by the methods of the calculus of probabilities.

From 1885 to 1889, Gibbs refined his vector analysis, wrote on optics, and developed a new electrical theory of light. He deliberately avoided theorizing about the structure of matter, developing instead a theory that did not depend on a particular concept of the construction of matter.

After 1889, he worked on statistical mechanics, the application of the mathematics of probability to the kinetic theory of gases, laying a foundation and "providing a mathematical framework for quantum theory and for Maxwell's theories" He wrote classic textbooks on statistical mechanics, which Yale published in 1902. Gibbs applied his vector methods to the determination of planetary orbits in a paper entitled On the determination of elliptic orbits from three complete observations, a problem that many of the great physicists, from Isaac Newton down, had addressed. In this work, Gibbs sought to demonstrate the power of vector analysis "by showing that these notations so simplify the subject, that it is easy to construct a method for the complete solution of the problem." <<Crowe, Michael J. 1967. A history of vector analysis. Notre Dame: University of Notre Dame Press. 160.>> Gibbs's new method was quickly soon applied by others to establish the orbit of Swift's comet.

Information about the names and careers of Gibbs's students is not readily available, yet one of his protegés was Edwin Bidwell Wilson, who in turn passed his Gibbsian knowledge onto Paul Samuelson. He is known to have strongly influenced the education of the economist Irving Fisher, who completed a Yale Ph.D. in 1896.

Gibbs never married, living all his life in his childhood home with a sister and his brother-in-law, the Yale librarian. His focus on science was such that he was generally unavailable personally. His protégé E.B. Wilson explains: "Except in the classroom I saw very little of Gibbs. He had a way, toward the end of the afternoon, of taking a stroll about the streets between his study in the old Sloane Laboratory and his home — a little exercise between work and dinner — and one might occasionally come across him at that time." Gibbs died in New Haven and is buried in Grove Street Cemetery.

In 1901, Gibbs was awarded the Copley medal of 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 capacity for external work.” This summarizes Gibbs's most fruitful contribution to science. On February 28, 2003, Yale held a 100th anniversary symposium in his honor. According to the American Mathematical Society, which established the Josiah Willard Gibbs Lectureship in 1923 to increase public awareness of the aspects of mathematics and its applications, Gibbs is one of the greatest scientists America has ever produced. Nobelist Paul Samuelson describes Gibbs as "Yale's great physicist".

Scientific recognition

Recognition was slow in coming, in part because Gibbs published mainly in the Transactions of the Connecticut Academy of Sciences, a journal edited by his librarian brother-in-law, little read in the USA and even less so in Europe. At first, only a few European theoretical physicists and chemists, such as the Scot James Clerk Maxwell, paid any attention to his work. Only when Gibbs's papers were translated into German (then the leading language for chemistry) by Wilhelm Ostwald in 1892, and into French by Henri Louis le Chatelier in 1899, did his ideas receive wide currency in Europe. His theory of the phase rule was experimentally validated by the works of H. W. Bakhuis Roozeboom, who showed how to apply it in a variety of situations, thereby assuring it of widespread use.

Gibbs was even less appreciated in his native America. During his lifetime, American secondary schools and colleges emphasized classics rather than science, and students took little interest in his Yale lectures. (That scientific teaching and research are a fundamental part of the modern university emerged in Germany during the 19th century and only gradually spread from there to the USA.) Gibbs's position at Yale and in American science generally has been described as follows:

"In his later years he was a tall, dignified gentleman, with a healthy stride and ruddy complexion, performing his share of household chores, approachable and kind (if unintelligible) to students. Gibbs was highly esteemed by his friends, but American science was too preoccupied with practical questions to make much use of his profound theoretical work during his lifetime. He lived out his quiet life at Yale, deeply admired by a few able students but making no immediate impress on American science commensurate with his genius." (Crowther 1969: nnn)

Not to say that Gibbs was unknown in his day. The mathematician Gian-Carlo Rota, while casually browsing the mathematical stacks of Sterling Library, stumbled upon a handwritten mailing list attached to Gibbs' course notes. It listed over two hundred of the most notable scientists of Gibb’s time, including Poincaré, Hilbert, Boltzmann, and Mach. One must infer that Gibbs' work was somewhat better known among the scientific elite of his day than public material suggests.

In 1945, Yale University created the J. Willard Gibbs Professorship in Theoretical Chemistry, held until 1973 by Lars Onsager, who won the 1968 Nobel Prize in chemistry. This appointment was a very fitting one, as Onsager, like Gibbs, was primarily involved in the application of new mathematical ideas to problems in physical chemistry, especially statistical mechanics. There is also a J. Willard Gibbs Professorship of Thermomechanics presently held by Bernard D. Coleman at Rutgers University.

J. W. Gibbs Laboratory at Yale and The J. Willard Gibbs Assistant Professorship in Mathematics at Yale were also named in his honor.

On May 4, 2005 the United States Postal Service issued the American Scientists commemorative postage stamp series, depicting Gibbs, John von Neumann, Barbara McClintock and Richard Feynman.

Nobelists derived from the works of Gibbs

In 1901, Gibbs was awarded the Copley Medal of the Royal Society of the United Kingdom, illustrating worldwide recognition of his work among contemporary theoreticians. This medal, awarded to only one scientist each year, was the highest possible honor granted by the international scientific community of his day.

Whether or not Gibbs might have won a Nobel Prize, had it existed in the 1890s, is entirely speculative. His work was sufficiently innovative and important. One can safely say, however, that the field was crowded in 1901 when the Nobel Prizes were instituted, and that Gibbs' primary achievements came roughly a decade before the work of the early Nobel recipients. Gibbs contributions, however, were not fully recognized until well after the 1923 publication of Gilbert N. Lewis and Merle Randall’s 1923 Thermodynamics and the Free Energy of Chemical Substances, which introduced the methods of Gibbs to chemists world-wide, and upon which the science of chemical engineering is largely founded. Many have suggested that Lewis should have won a Nobel Prize, hence it is not unlikely that Gibbs would have won one as well, had the prize been in use decades earlier. To elaborate on this, the following outline lists the number of individuals who won a Nobel Prize through the works of Gibbs:

• Dutch scientist Johann van der Waals won the 1910 Nobel prize in physics, which, as he states in his Nobel Lecture, is due in part to the works of Gibbs and his equations of state.

• The work of German physicist Max Planck, winner of 1918 Nobel prize in physics, in quantum mechanics, particularly his 1900 quantum theory paper, is largely based on thermodynamics of Rudolf Clausius, Willard Gibbs, and Ludwig Boltzmann. Planck stated this about Gibbs: "…whose name not only in America but in the whole world will ever be reckoned among the most renowned theoretical physicists of all times…."

• At the turn of the 20th century, Gilbert Lewis worked in coordination with Merle Randall on the use of Gibbs chemical thermodynamic theories and published their results in the 1923 textbook Thermodynamics and the Free Energy of Chemical Substances, one of the two founding books in chemical thermodynamics. In the 1910s, William Giauque entered the College of Chemistry at Berkeley, where he received a bachelor of science degree in chemistry, with honors, in 1920. Although he entered university with an interest in becoming a chemical engineer, he soon developed an interest in research under the influence of Professor Gilbert Lewis. Due to his outstanding performance as a student, he became an Instructor of Chemistry at Berkeley in 1922 and after passing through the various grades of professorship, he became full Professor of Chemistry in 1934. In 1949, he won the Nobel Prize in Chemistry for his studies in the properties of matter at temperatures close to absolute zero in relation to the third law of thermodynamics.

• In 1947, American economist Paul Samuelson published his book Foundations of Economic Analysis, from his doctoral dissertation at Harvard University, his magnum opus, is based on the classical thermodynamic methods Gibbs. and in 1947 and was sole recipient of the Nobel Prize in Economics in 1970, the second year of the Prize.

Tributes

“

…who founded a new department of chemical science which is becoming comparable in importance with that created by Lavoisier.

”

– Henri Louis Le Chatelier, 1885 formulated Le Chatelier's principle

Quotations

• "Mathematics is a language." (reportedly spoken by Gibbs at a Yale faculty meeting)
• "A mathematician may say anything he pleases, but a physicist must be at least partially sane."
• "It has been said that 'the human mind has never invented a labor-saving machine equal to algebra.' If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines." (1887, quoted in Meinke and Tucker 1992: 190)

See also

• Information theory
• Quaternion
• Maxwell's equations
• Phase (matter)
• Statistical mechanics
• Thermodynamics
• Entropy
• Free energy
• Gibbs free energy
• Gibbs entropy, Gibbs inequality, Gibbs paradox, Gibbs-Helmholtz equation, Gibbs algorithm, Gibbs distribution, Gibbs state
• Gilbert N. Lewis
• William Rowan Hamilton
• Lars Onsager
• Ludwig Boltzmann
• William Stanley (physicist)
• Oliver Heaviside
• Lists: List of physicists, Timeline of thermodynamics, List of physics topics, List of notable textbooks in statistical mechanics

References

ISBN links support NWE through referral fees

• Gibbs Symposium, D. G. Caldi, and George D. Mostow. 1990. Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989. Providence, RI: American Mathematical Society. ISBN 0821801570.
• Obituary Notices: Josiah Willard Gibbs. Proceedings, American Philosophical Society. 1903. 42:xvi-xvii. ISBN 1422373509.
• Moyer, Albert E. 1983. American physics in transition: a history of conceptual change in the late nineteenth century. The History of modern physics, 1800-1950, Los Angeles: Tomash Publishers. 3:97-105. ISBN 0938228064.
• Crowe, Michael J. 1967. A history of vector analysis. Notre Dame: University of Notre Dame Press. 150-161.
• 1947. The Early Work of Willard Gibbs in Applied Mechanics, New York, Henry Schuman ISBN 1881987175
• 1961. Scientific Papers of J Willard Gibbs, 2 vols. Bumstead, H. A., and Van Name, R. G., eds. ISBN 0918024773
• Elementary Principles in Statistical Mechanics.
• Online bibliography.
• American Institute of Physics, 2003 (1976). Josiah Willard Gibbs
• Bumstead, H. A., 1903. "Josiah Willard Gibbs" American Journal of Science XVI(4).
• Crowther, J. G., 1969. Famous American Men of Science. ISBN 0836900405
• Donnan, F. G., Haas, A. E., and Duhem, P. M. M., 1936. A Commentary on the Scientific Writings of J Willard Gibbs. ISBN 0405125445
• Hastings, Charles S. ,1909. Josiah Willard Gibbs. Biographical Memoirs of the National Academy of Sciences 6:372–393.
• Longley, W. R., and R. G. Van Name, eds., 1928. The Collected Works of J Willard Gibbs.
• Meinke, K., and Tucker, J. V., 1992, "Universal Algebra" in Abramsky, S., Gabbay, D., and Maibaum, T. S. E., eds., Handbook of Logic in Computer Science: Vol. I. Oxford Univ. Press: 189-411. ISBN 0198537611
• Muriel Rukeyser, 1942. Willard Gibbs: American Genius. Woodbridge, CT: Ox Bow Press. ISBN 0918024579.
• Seeger, Raymond John, 1974. J. Willard Gibbs, American mathematical physicist par excellence. Pergamon Press. ISBN 0080180132
• Wheeler, L. P., 1952. Josiah Willard Gibbs, The History of a Great Mind. ISBN 1881987116
• Edwin Bidwell Wilson (1931) "Reminiscences of Gibbs by a student and colleague," Scientific Monthly 32:211-27.

External links

• John J. O'Connor and Edmund F. Robertson. Josiah Willard Gibbs at the MacTutor archive
• Friel, Charles Michael, "J. Willard Gibbs."
• Jolls, Kenneth R., and Daniel C. Coy, "Gibbs models." Iowa State University.

Credits

New World Encyclopedia writers and editors rewrote and completed the Wikipedia article in accordance with New World Encyclopedia standards. This article abides by terms of the Creative Commons CC-by-sa 3.0 License (CC-by-sa), which may be used and disseminated with proper attribution. Credit is due under the terms of this license that can reference both the New World Encyclopedia contributors and the selfless volunteer contributors of the Wikimedia Foundation. To cite this article click here for a list of acceptable citing formats.The history of earlier contributions by wikipedians is accessible to researchers here:

• Josiah Willard Gibbs  ^history

The history of this article since it was imported to New World Encyclopedia:

• History of "Josiah Willard Gibbs"

Note: Some restrictions may apply to use of individual images which are separately licensed.