JO SI AH WILLARD GIBBS 551 



JOSIAH WILLAKD GIBBS AND HIS EELATION TO 

 MODERN SCIENCE. II 



By fielding H. GARRISON, M.D., 



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



The Thermodynamic Potentials.^^ — In 1869 the physicist F. Mas- 

 sieu communicated to the French Academy of Sciences the discovery 

 of two algebraic functions from which all the thermodynamic proper- 

 ties 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 sys- 

 tems. Mathematically they are simplifications which dispense with 

 the necessity of endless transformations of equations and formulae, 

 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 sci- 

 ence, as in the physics of gas mixtures, osmosis, elastic solids or elec- 

 trolysis has been made with their aid. The four potentials are now 

 interpreted as the " free energy " (xp) and the " modified available 

 energy" or total thermodynamic potential (^) for constant tempera- 

 ture, and the intrinsic energy (c) and heat function (x) 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 



^ Tr. Connect. Acad., III., 144-52. 



" " J'appelle cette fonction fonction caracteristique du corps: en effet, 

 lorsqu'elle est connue, on pent en tirer toutes les propri^t^s du corps que Ton 

 consid&re dans la thermodynamique . . . Je rapellerai d'ailleurs qu'une fois la 

 fonction caracteristique d'un corps d6terminee, la theorie thermodynamique de 

 ce corps est faite." F. Massieu, Compt. rend. Acad. d. sc, Paris, 1869, LXIX., 

 859, 1058. 



'^ Bryan, " Thermodynamics," Leipzig, 1907, 109. 



^ If e, t, 7), p and v represent the energy, temperature, entropy, pressure and 

 volume of a chemical or thermodynamic system, its thermodynamic potentials 

 will be the intrinsic energy e obtained by integrating Gibbs's fundamental equa- 

 tion, the free energy \f/ = e — tri, the total thermodynamic potential or "modi- 

 fied " available energy f = e — tri -f- pv and the heat function x = e + pv. 



"Larmor, " Encycl. Britan.," 10th ed., XXVIII., 167. 



