Page:Popular Science Monthly Volume 74.djvu/555

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The Thermodynamic Potentials. —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. 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." 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" $$(\psi)$$ and the "modified available energy" or total thermodynamic potential $$(\zeta)$$ for constant temperature, and the intrinsic energy $$(\epsilon)$$ and heat function $$(\chi)$$ for constant entropy. 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, just as the Maxwellian potentials connote effects of electromotive force. They