Page:Popular Science Monthly Volume 74.djvu/556

552 represent that part of the energy of a system which is due to changes in its mass or structure rather than to thermal or molecular changes, and so can take part freely in physico-chemical transformations. For this reason the potential $$\psi$$, which is the difference between the total energy of a system and its bound (molecular) energy, was called the "free energy" of the system by Helmholtz, who rediscovered the principle independently, not knowing that Gibbs had forestalled his labors by at least six years. In lecturing on the subject during the later period of his life, Helmholtz, with his usual breadth of spirit, was inclined to assign complete priority to his predecessor, while both Gibbs and Helmholtz have acknowledged their indebtedness to Massieu.

Criteria of Equilibrium and Stability.—Gibbs's conditions for the complete equilibrium of an isolated homogeneous chemical substance are that its pressure, temperature and the chemical potentials of its components should be constant throughout the mass, since changes of pressure and temperature disturb mechanical and thermal equilibrium, while difference of potentials destroys stability and precipitates chemical change. For an isolated heterogeneous system, as an enclosed liquid and a gas in contact, the following maxima and minima are criteria of complete equilibrium: The system must have and maintain the greatest entropy consistent with constant energy; or for adiabatic systems (at constant entropy), the intrinsic energy $$(\epsilon)$$ or heat function $$(\chi)$$ should have minimum values for constant volume or pressure, respectively, but for isothermal systems (at constant temperature) the free energy potential $$(\psi)$$ or the thermodynamic potential $$(\zeta)$$ should have minimum values for constant volume or pressure. Any deviation from these maxima or minima will again disturb equilibrium and produce changes of physical or chemical state. The essential feature of spontaneous chemical change is, then, either constant increase of entropy in self-contained or adiabatic systems or a corresponding decrease of free (mechanically available) energy in systems at uniform