552 TEE POPULAR SCIENCE MONTHLY 



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 ij/, 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 prin- 

 ciple 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 0/ 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 chem- 

 ical 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 (c) or heat func- 

 tion (x) should have minimum values for constant volume or pressure, 

 respectively, but for isothermal systems (at constant temperature) the 

 free energy potential (i/^) or the thermodynamic potential {t) should 

 have minimum values for constant volume or pressure. Any deviation 

 from these maxima or minima will again disturb equilibrium and pro- 

 duce 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 



" " Deshalb hat Gibbs, der auch diese Form der Darstellung zuerat fand, 

 die Function A das isotherme Potential genannt." Helmholtz, " Vorles. iiber 

 theoret. Physik," Leipzig, 1903, VI., 269. See, also, the lecture in his biography 

 by L. Koenigsberger, Braunschweig, 1903, II., 369: "In diesem Sinne hat Herr 

 Gibbs die Grosse F. das isotherme Potential des Korpersystems genannt, ich 

 selbst habe dafiir den Namen der freien Energie vorgeschlagen, well dieselbe 

 ArbeitsJiquivalente darstellt, deren Ueberfiihrung in andere Formen der Energie 

 nicht denselben Einschrankungen unterliegt wie die der Warme." For Lord 

 Kelvin's relation to the discovery of the free energy potential see Proc. Roy. 

 Soc. Lond., 1908, LXXXL, No. A 543, pp. xlvi-xlvii. 



"' " M. Massieu appears to have been the first to solve the problem of repre- 

 senting all the properties of a body of invariable composition which are con- 

 cerned in reversible processes by means of a single function." Gibbs, Am. J. 8c., 

 1878, 3. s., XVI., foot-note to p. 445. 



