Page:The New International Encyclopædia 1st ed. v. 20.djvu/261

* VOLTAIC CELL. 213 VOLTAIC CELL. chemical energy into the cuergj' of an electric current. Long ago the question arose whether all the elieniical energy transl'ornied in a voltaic cell is tlius converted in its entirety into electrical energy. The chemical processes going on in the ceil involve a loss in the intrinsic i-nei'gy of the materials. Does tliis loss eijual the energy which takes the form represented by the electric cur- rent 'I. Lord Kelvin and llehnlioltz at iirst an- swered the question in the allirmative. Accord- ing to this view it is a simple matter to calculate the electromotive force of any given voltaic com- bination from the heats of formation of the com- pounds undergoing chemical change. The quan- tity of electricity transjxjrted through a cell, vhen a gram equivalent of zinc enters into solu- tion, and a gram equivalent of other substances undergoes a concurrent change, may be obtained by dividing the atomic weiglit of zinc by its elect roehemical equivalent. The result is UC,- 540 coulombs. This (juantity muKi])licd by the electromotive force of the cell must equal the electrical energy given out while one gram <'qniva- lent of zinc goes into solution. If this product is placed equal to the algebraic sum of the heats of formation of all the chemical changes involved in the cell, the value of the electromo- tive force is readily obtained from the equation. Thus the heat of formation of a gram equiva- lent (32.5 grams) of zinc as ZnSO, is 121.000 calories; of copper (31.7 grams), as CuSOj, is 95,700 calories. The difference is 25.300 calories. In other words, the reaction in the Daniell cell may be written CuSO^ + Zn = ZnS04+ Cu + 25.300 calories. Then Er/ = 25,300 X 4.19 watts, where q is the quantity of electricity (90.540 coulombs) cor- responding to one gram equivalent. From this equation E is 1.098. the electromotive force of the Daniel] cell. This value agrees very closely with the observed value. It was soon found, how- ever, that other cells did not show equally good agreement with the theory. In some the electro- motive force is smaller tlian the value calculated from the heats of formation, and in a few it is larger. Finally, Willard Gibbs in America, and Heimholtz in (Jermany. independently expressed the true relationship between the chemical en- ergy transformed and the electrical energy devel- oped. The Helralioltz equation may be written as follows : e^.^+t'II. q <l II in which H is the sum of all the heats of forma- tion e.xpi-essed in mechanical measure, q is the quantity of electricity transported through the cell by one gram equivalent of any substance. T is the absolute temperature (on a scale whose zero is — 273° C), and clE/dT is the tempera- ture coefficient of the electromotive force of the cell. From this equation it is obvious that the actual electromotive force is smaller than the value calculated from thermal data alone when- ever the temperature coefficient of the cell is negative, and it is larger wlien the temperature coefficient is positive. In the former case, only a portion of the transformed chemical energy ap- pears as the energy of the current : the remainder heats the cell. In the latter case, the electrical energy given out by the cell is in excess of the chemical energy transformed, and the cell con- verts some of its heat into electrical energj' and so cools in action. The Gibbs-Helniholtz equa- tion represents our most assured knowledge of the relations between the chemical, electrical, and tbermal cpnintitics involved in a voltaic cell, and it has licen fully established by experiment. See Walker, liilroduction lo I'hijuicul Chemintry (London, 1891), and Carliart, "Therniodynamics of Voltaic Cell," in Physical lieview for July, 1900. It has been demonstrated also by experiment that the change in the electromotive force of a cell per degree of temperature is equal to the sum of all the thermal electromotive forces per degree, taken with their proper sign, at all contacts of dissimilar substances in the cell. The thermo-electromotive force between zinc and a solution of zinc sulphate is directed from the solution to the metal. The same is true of copper and copper sulphate, while the thermo- 2 2 ^Z ,<? _ ^^ ^^ ^ -^^ ■ 020 - h^^* - °^° .y ^.t ^ ^^ ,^ ,^*'' A^ .010 T^^ ^^^ H i^ § .^^- ><? 20" 30° Fio. 14. 40" 50° electromotive force between equidense solutions of the sulphates of zinc and copper is practically zero. If a Daniell cell be so constructed that one side or electrode ma.v be heated independently of the other, it will have a positive coefficient if the positive electrode and the solution about it be heated, and a negative coefficient if the z y' a" ^^ A,^ y ^ ,^'^  Ti ,010 -p^ -- 5j---^ « * »■-''■ O ^^ ^•^*'^ > ^^ — •* ^ 20 30 Fig. 1.1 40" 50 negative side be heated. Since both zinc and cop- per, each in a solution of its sulphate, tend to become positive when heated, or to play the role of copper in a sim])le voltaic element, it follows that the thermo-electromotive force at the cop- per electrode of a Daniell cell is in the same direction as that of the cell itself, while that at