# Page:Popular Science Monthly Volume 74.djvu/555

JOSIAH WILLARD GIBBS

551

 JOSIAH WILLARD GIBBS AND HIS RELATION TO MODERN SCIENCE. II
By FIELDING H. GARRISON, M.D.,

ASSISTANT LIBRARIAN, ARMY MEDICAL LIBRARY, WASHINGTON, D. C.

The Thermodynamic Potentials.[1]—In 1869 the physicist F. Massieu communicated to the French Academy of Sciences the discovery of two algebraic functions from which all the thermodynamic properties of a fluid may be derived.[2] These "fonctions characteristiques" of Massieu contain in latent form two of the four relations which Gibbs derived independently from his general thermodynamic equation and which have since been variously interpreted as the fundamental functions or thermodynamic potentials of heterogeneous chemical systems. Mathematically they are simplifications which dispense with the necessity of endless transformations of equations and formulæ, evolving, as Bryan says, "order out of chaos."[3] As the foundations of thermodynamics are its two laws, so the potentials may be regarded as the coping stones of the edifice, and all recent progress in the science, as in the physics of gas mixtures, osmosis, elastic solids or electrolysis has been made with their aid. The four potentials are now interpreted as the "free energy" ${\displaystyle (\psi )}$ and the "modified available energy" or total thermodynamic potential ${\displaystyle (\zeta )}$ for constant temperature, and the intrinsic energy ${\displaystyle (\epsilon )}$ and heat function ${\displaystyle (\chi )}$ for constant entropy.[4] Of these the first two are the most important, being the analogues of the Newtonian or gravitational potentials (potential energies) of mechanical systems, generalized, as Larmor says, "so as to include the temperature" and connoting thermal effects,[5] just as the Maxwellian potentials connote effects of electromotive force. They

1. Tr. Connect. Acad., III., 144-52.
2. "J'appelle cette fonction fonction caracteristique du corps: en effet, lorsqu'elle est connue, on peut en tirer toutes les propriétés du corps que l'on considère dans la thermodynamique. . . Je rapellerai d'ailleurs qu'une fois la fonction caracteristique d'un corps déterminée, la theorie thermodynamique de ce corps est faite." F. Massieu, Compt. rend. Acad. d. sc, Paris, 1869, LXIX., 859, 1058.
3. Bryan, "Thermodynamics," Leipzig, 1907, 109.
4. If ${\displaystyle \epsilon ,\tau ,\eta ,\rho }$ and ${\displaystyle v}$ represent the energy, temperature, entropy, pressure and volume of a chemical or thermodynamic system, its thermodynamic potentials will be the intrinsic energy ${\displaystyle \epsilon }$ obtained by integrating Gibbs's fundamental equation, the free energy ${\displaystyle \psi =\epsilon -\tau \eta }$, the total thermodynamic potential or "modified" available energy ${\displaystyle \zeta =\epsilon -\tau \eta +\rho v}$ and the heat function ${\displaystyle \chi =\epsilon +\rho v}$.
5. Larmor, "Encycl. Britan.," 10th ed., XXVIII., 167.