Gibbs, Josiah Willard (1839–1903)
Gibbs came from an academic family in New Haven, Connecticut. His father was a noted philologist, a graduate of Yale and professor of sacred literature there from 1826 until his death in 1861. The younger Gibbs grew up in New Haven and graduated from Yale College, having won a number of prizes in both Latin and mathematics. He continued at Yale as a student of engineering in the new graduate school and, in 1863, received one of the first Ph.D. degrees granted in the United States. After serving as a tutor in Yale College for three years, giving elementary instruction in Latin and physics, Gibbs left New Haven for further study in Europe. He spent a year each at the universities of Paris, Berlin, and Heidelberg, attending lectures in mathematics and physics and reading widely in both fields. He was never a student of any of the luminaries whose lectures he attended (the list includes Liouville and Kronecker in mathematics, and Kirchhoff and Helmholtz in physics) but these European studies, rather than his earlier engineering education, provided the foundation for his subsequent scientific work. A qualification was a life-long fondness for geometrical reasoning, evident in Gibbs's scientific writings, but first developed in his dissertation.
Gibbs returned to New Haven in 1869. He never again left America and seldom left New Haven except for annual summer holidays in northern New England and a very occasional journey to lecture or attend a meeting. Gibbs never married and lived all his life in the house in which he had grown up, less than a block from the college buildings. In 1871, two years before he published his first scientific paper, Gibbs was appointed professor of mathematical physics at Yale. He held that position without salary for nine years, living on inherited income. It was during this time that he wrote the memoirs on thermodynamics that, in most estimates, constitute his greatest contribution to science. Gibbs declined the offer of a paid appointment at Bowdoin College in 1873, but he was tempted to leave Yale in 1880 when he was invited to join the faculty of the newly-founded Johns Hopkins University in Baltimore. Only then did Yale provide Gibbs a salary, as tangible evidence of the high regard his colleagues had for him and of his importance to the University. Gibbs remained at Yale and continued to teach there until his death, after a brief illness, in 1903.
Gibbs worked on electromagnetism during the 1880s, concentrating on optics and particularly on James Clerk Maxwell's electromagnetic theory of light, and on statistical mechanics from at least the mid-1880s until his death. The latter research resulted in his seminal Elementary Principles in Statistical Mechanics, published in 1902. However, it seems more appropriate in this place to briefly describe Gibbs's memoirs on thermodynamics.
In his first work on thermodynamics in 1873, Gibbs immediately combined the differential forms of the first and second laws of thermodynamics for the reversible processes of a system to obtain a single "fundamental equation": 
an expression containing only the state variables of the system in which U, T, S, p and V are the internal energy, temperature, entropy, pressure, and volume, respectively. Noteworthy here is the assumption, which Gibbs made at the outset but which was not common at the time, that entropy is an essential thermodynamic concept. At the same time, the importance of energy was also emphasized. As Gibbs wrote at the beginning of his great memoir, "On the Equilibrium of Heterogeneous Substances," whose first installment appeared in 1876: "The comprehension of the laws which govern any material system is greatly facilitated by considering the energy and entropy of the system in the various states of which it is capable." The reason, as he then went on to explain, is that these properties allow one to understand the interactions of a system with its surroundings and its conditions of equilibrium.
As was usual with him, Gibbs sought to resolve the problem in general terms before proceeding to applications. Again beginning with the differential forms of the first two laws (which, in effect, define the state functions U and S), but this time for any process, whether reversible or irreversible, he combined the two expressions to yield the general condition of equilibrium for any virtual change: 
where W is the external work. If a system is isolated, so that δW= 0, this condition becomes: 
for constant S and U, respectively. The second inequality, which Gibbs showed to be equivalent to the first, immediately indicates that thermodynamic equilibrium is a natural generalization of mechanical equilibrium, both being characterized by minimum energy under appropriate conditions.
The first and probably most significant application of this approach was to the problem of chemical equilibrium. In a heterogeneous system composed of several homogeneous phases, the basic equilibrium condition leads to the requirement that temperature, pressure, and the chemical potential (a new concept introduced by Gibbs) of each independent chemical component have the same values throughout the system. From these general conditions, Gibbs derived the phase rule: 
that cornerstone of physical chemistry, which specifies the number of independent variations δ in a system of r different coexistent phases having n independent chemical components.
Among many other valuable results in his memoir on heterogeneous equilibrium is a formulation of the Gibbs free energy, also called the Gibbs function, which is defined by the equation 
where H is the enthalpy, that is, the sum of the internal energy of a body orsystem and the product of its-pressure and volume. It is useful for specifying the conditions of chemical equilibrium at constant temperature and pressure, when G is a minimum. More generally, Gibbs's memoir greatly extended the domain covered by thermodynamics, including chemical, electric, surface, electromagnetic, and electrochemical phenomena into one integrated system.
Gibbs's thermodynamic writings were not as widely read—much less appreciated—as they deserved to be in the decade following their appearance. One reason is that they were published in the obscure Transactions of the Connecticut Academy of Sciences. Gibbs sent offprints of his memoirs to many scientists, but only Maxwell seems to have recognized their importance. That changed after Wilhelm Ostwald published a German translation in 1892. In the meantime, continental scientists such as Helmholtz and Planck independently developed Gibbs's methods and results, unaware of his prior work.
Another reason for lack of interest is the severity of Gibbs's style. Austere and logically demanding, it was a challenge even for mathematicians as distinguished as Poincaré. The same severity extended to Gibbs's lectures, which his few students found clear and well-organized, but not easy to understand, owing to their great generality and meticulous precision.
A third reason is that Gibbs made no effort to promote or popularize his results. He seems to have been a solitary, self-contained, and self-sufficient thinker, confident in his ability, who worked at his own unhurried pace, neither needing nor wanting feedback from others. An attitude of detachment from the work of his students plus his own solitary habit of work is undoubtedly responsible for the fact that Gibbs founded no "school" or group of students to develop his ideas and exploit his discoveries.
Bibliography
Deltete, R. J. (1996). "Josiah Willard Gibbs and Wilhelm Ostwald: A Contrast in Scientifc Style." Journal of Chemical Education 73(4):289–295.
Klein, M. J. (1972). "Gibbs, Josiah Willard," in Dictionary of Scientific Biography, Vol. 5, ed. C. G. Gillispie. New York: Scribner.
Klein, M. J. (1989). "The Physics of J. Willard Gibbs in His Time." In Proceedings of the Gibbs Symposium. Yale University, May 15–17, 1989, ed. D. G. Caldi and G. D. Mostow. New York: American Mathematical Society.
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