46 president's address — section a. 



Von Helmholtz's enunciation of the doctrine of " free enerjiy "(d) 

 — a mathematical deduction from the laws of thermodynamics — and his 

 application of it to the circuit, at length brought order out of chaos. It 

 fixed, definitely and for all time, the true relation between electromotive 

 force and thermochemical data, by proving that the transformations of 

 free energy, not those of the total intrinsic energy, are the real measure 

 of electromotive force. It furnished a definition of the latter quantity, 

 in terms of energy and entropy, expressed by the equation — 



E= - |-(U-T0) 



— an equation independently arrived at by Willard Gibbs — and thus 

 led to a general theory of voltaic action, free from every trace of dis- 

 putable hypothesis. An almost equal service was rendered to the 

 theory by the demonstration that the free energy, so far from being a 

 mathematical abstraction, is in reality a definite physical property, 

 capable of expression in terms of measurable quantities ; Helmholtz's 

 application of his results to the determination of the electromotive 

 forces of the migrationless concentration cell (e) — the " simple liquid 

 cell " as he called it — and of the gas battery, made this quite clear ; 

 at the same time the striking agreement between the observed electro- 

 motive forces and the computed changes of free energy practically settled 

 the nature of electromotive force. In another direction, his establish- 

 ment of the equation — now well known as " Helmholtz's Law " — 



E - T^-^ = - ^il = H 

 9T Pq 



attracted even a larger share of attention, as it expressed the difference 

 between the electromotive force and the algebraic sum of the heats 

 of formation of the cell products — the " bound energy " — in terms of 

 the easily measurable temperature co-eflftcient of , the electromotive 

 force : thus rendering the experimental verification of the thermo- 

 dynamic theory an easy matter, even in cases where the calculation 

 of the free energy change was impossible. Since the year 1887 we have 

 been assured that the change in the free energies of the constituents 

 of a cell, produced by the passage through it of unit quantity of elec- 

 tricity, is the numerical measure of its electromotive force ; in fact, 

 they are but two different names for the same physical quantity. But 

 a new difficulty, of a purely practical character, arose at once : the 

 deduction of the changes of free energy from other quantities more 

 amenable to measurement proved to be an exceedingly difficult task 

 in all cases, and, at first sight, an impossibility in most. 



■{d) Sitzungsb. d. Akad. Wiss., Berlin, 1882. A better name for this function would 

 be — " potential energy of isothermal transformation," had not " free energy " 

 established itself in scientific nomenclature. It must not be forgotten that 

 the free energy of a working substance may be greater or less than its intrinsic 

 energy, according as it absorbs heat from or gives heat to its surroundings 

 when undergoing a " free " transformation, i.e., one which, like the free 

 expansion of a gas, will always take place in the absence of certain definite 

 constraints. 



^e) Sitzungsb. d. Akad. Wiss., Berlin, 1882, 1887. Monatsb. d. Akad. Wiss., 

 Berlin, 1883. 



