The legal valve of the electromotive force of the Clark cell is 1.434 volts at 15° C. Recent determinations have shown that the probable vahie is nearer 1.433 volts. '1'lle older deter minations were made by means of the silver volt ameter, but the electrochemical equivalent of silver is not known with any greater degree of accuracy than the electromotive force of the Clark cell. A number of very careful deter minations have been made of the ratio between the electromotive forces of the Clark cell at 15° C. and the cadmium cell at 20' C. The mean of these determinations. made at the Gorman Reiehs mist all:, due weight hieing given to each deter mination, is as follows: Clark at 15 : cadmium at 20^=1.4000.
Also Clark at : cadmium at 20 =1.42280. These two relations give Clark 0° — Clark 15° — volt. if the electromotive force of the Clark evil at 15° is 1.4333, that of the cadmium cell at 20° is 1.01S9 volts. If the Clark he pill at 1.133. the cadmium will be 1.0187. The electromotive force of the cadmium cell as made by Weston is 1.0192, at 20° C.
From I he point of view of energy a voltaic cell is a device for the direct conversion of potential chemical energy into the energy of an electric current. Long ago the question arose whether all the chemical energy transformed in a voltaic cell is thus converted in its entirety into electrical energy. 'the chemical processes going on in the cell involve a loss in the intrinsic energy of the materials. Does this loss equal the energy which takes the form represented by the electric cur rent ? Lord Kelvin and Helmholtz at first. an swered the question in the affirnmtive. 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 transported through a cell, when 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 weight of zinc by its eleetrochemical equivalent. The result is 90, 540 coulombs. This quantity multiplied by the electromotive force of the cell must equal the electrical energy given out while one gram equiva 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 is 95,700 calories. The difference is 25,300 calories. In other words, the reaction in the Daniell cell may be written CuS( Zn = Cu + 25,300 calories.
Then Eli = 25,300 X 411) watts, where q is the quantity of electricity (96.541) coulombs) eor iesponding to one gr:(in equivalent. From this equation E is 1.008. the electromotive force of the Daniell cell. This value agrees very closely with the observed value. It was soon found. how ever, that other cells (lid not show equally good agreement with the theory. In some the electro motive force is smaller than the value calculated from the heats of formation, and in a few it is larger. Finally, Willard Gibbs in America. and Helmholtz in Germany, independently expressed the true relationship between the chemical en ergy transformed and the electrical energy devel oped. The Echnholtz equation may be written as follows: II E= — +T art in which H is the sum of all the heats of forma tion expressed 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 dE/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 coeffieient of the cell is negative, and it is larger when the temperature coefficient is positive. In the former case, only a portion of the transformed chemical energy ap pear; 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 energy and so cools in action. The Gibbs-lIclinholtz equa tion represents our most assured knowledge of the relations between the chemical. electrical, and thermal quantities involved in a voltaic cell, and it has been fully established by experiment. See Wa I kyr, 1n( rod net ion to Physical Chemistry (London, 1891), and Ca d'art, of Voltaic Cell," in Physien1 riem for July, P.100.