Third Class.—Dielectrics

182.] The electrical effects due to heat were discovered before the thermal effects due to the electric current, but the application of the thermal effects of the current to determine the electromotive forces acting along different portions of the circuit is due to Sir W. Thomson† . It is manifest that in a het- erogeneous circuit we cannot determine the electromotive force acting from the point A to the point B by simply connecting these points by wires to the electrodes of a galvanometer or electrometer, for we are ignorant of the elec- tromotive forces acting at the junctions of these wires with the matter of the circuit at A and B.

But if we cause a current of known strength to flow from A to B, and if this current causes the generation of a quantity of heat equal to H in that portion of the circuit, and if no chemical, magnetic or other permanent effect takes place in the matter of the conductor between A and B, then we know that if Q is the total quantity of electricity which has been transmitted from A to B, and E the electromotive force in the direction from B to A which the current has to overcome, then the work done by the current is QE. This work is done within a definite region, namely the portion AB of the conductor, and it is entirely expended in generating heat within that region.

Hence, if the [The energy expended in driving the current will, if not otherwise employed, be ultimately converted into heat through the frictional resistance of the metals. The heat produced by this ir- reversible action must be distinguished from the Thomson and Peltier effects, and is represented on the Thermo-electric diagram by the area ABbaA.] † Trans. R. S. Edin. 1854.MEASUREMENT OF ELECTROMOTIVE FORCE. 160 quantity of heat generated in the portion AB is H, as expressed in dynamical measure, we have the equation QE = H, and since Q and H are capable of being measured we can determine the electromotive force E acting against the current. When the electromotive force acts in the same direction as the current is flowing, the quantity of heat generated is negative; or, in other words, there is an absorption of heat.

In this investigation we must remember that E represents the whole electro- motive force acting against the current. Now part of this electromotive force arises from the electric resistance of the conductor. This part always acts against the current, and is proportional to the current according to Ohm’s law.

The other part of the electromotive force acts in a definite direction, either from A to B or from B to A, and is independent of the direction of the current. It is generally this latter part of the electromotive force which is referred to as the electromotive force from A to B.

It is easy to eliminate the part due to resistance by making two experiments in which currents of equal strength are made to flow in one case from A to B and in the other from B to A. The excess of the heat generated in the second case over that generated in the first case, per unit of electricity transmitted, is numerically equal to twice the electromotive force from A to B.

183.] The total electromotive force round any circuit is easily measured by breaking the circuit in a place where it is homogeneous, and determin- ing the difference of potentials of the two ends. This may be done by any of the ordinary methods for determining electromotive force or difference of potentials, because in this case the two ends are of the same substance and at the same temperature. But we cannot by this method determine how much of this electromotive force has its seat in a particular part of the circuit, as for instance, between A and B, where A and B are of different substances or at different temperatures. The only method by which we can determine where the electromotive force acts is that of measuring the heats generated or absorbed during the transmission of a unit of electricity from A to B.E. M. F. BETWEEN METAL AND ELECTROLYTE. 161

184.] In the cases we have hitherto considered the only permanent effect of the current has been the generation or absorption of heat, for metals are not altered in any respect by the continuous flow of a current through them. But when the current flows from a metal to an electrolyte or from an elec- trolyte to a metal, there are chemical changes, and in applying the principle of the conservation of energy we must take account of these as well as of the thermal effects.

We shall consider the current as flowing through an electrolyte from the anode to the cathode. The fundamental phenomenon of electrolysis is the liberation of the components or ions of the electrolyte, the anion at the anode and the cation at the cathode. This is the only purely electrolytic effect; the subsequent phenomena depend on the nature of the ions, the electrodes and the electrolyte, and take place according to chemical and physical laws in a manner apparently independent of the electric current. Thus the ion, when liberated at the electrode, may behave in several different ways, according to the conditions in which it finds itself. It may be in such a condition that it acts neither on the electrode nor on the electrolyte, as when it is a gas which escapes in bubbles, or substance insoluble in the electrolyte, which is precip- itated. It may be deposited on the surface of the electrode, as hydrogen is on platinum, and may adhere to it with various degrees of tenacity, from mere juxtaposition up to chemical combination. If it is soluble in the electrolyte, it will diffuse through the electrolyte according to the ordinary law of diffu- sion, and the rate of this diffusion is not, so far as we know, affected by the existence of the electric current through the electrolyte, for it is only when in combination, and not when in mere solution, that the current produces the electrolytic transfer of the ions. Thus when hydrogen is an ion, part of it may escape in bubbles, part of it may be condensed on the electrode, and part of it may be absorbed into the electrolyte without combination, and travel through it by ordinary diffusion.

185.] The liberated ion may also act chemically on the electrode or on the electrolyte. The results of such action are called secondary products of electrolysis, and these secondary products may remain at the surface of the electrodes, or may become diffused through the electrolyte. Thus, when the same current is passed, first through a solution of sulphate of soda between platinum electrodes, and then through sulphuric acid, equal volumes of oxygen are given off at the anodes of the two electrolytes, and equal volumes of hydrogen, each equal to double the volume of oxygen, are given off at the cathodes.

E. M. F. BETWEEN METAL AND ELECTROLYTE

But if the electrolysis is conducted in suitable vessels, such as U-shaped tubes or vessels with a porous diaphragm, so that the substance surrounding each electrode may be examined, it is found that at the anode of the sul- phate of soda there is an equivalent of sulphuric acid as well as an equivalent of oxygen, and at the cathode there is an equivalent of soda as well as two equivalents of hydrogen. It would at first sight appear as if (according to the old theory of the constitution of salts) the sulphate of soda were elec- trolysed into its constituents, sulphuric acid and soda, while the water of the solution is electrolysed at the same time into oxygen and hydrogen. But this explanation would involve the assumption that the same current which pass- ing through dilute sulphuric acid electrolyses one equivalent of water, when it passes through solution of sulphate of soda electrolyses two equivalents, one of the salt and one of water, and this would be contrary to the law of electro- chemical equivalents. But if we suppose that the components of sulphate of soda are not SO3 and Na2 O, but SO4 and Na2 —not sulphuric acid and soda but sulphion and sodium—then an equivalent of sulphion travels to the an- ode and is set free, but being unable to exist in a free state, it breaks up into sulphuric anhydride and oxygen, one equivalent of each. At the same time [two] equivalents of sodium are set free at the cathode, and then decompose the water of the solution, forming two equivalents of soda [NaHO] and two of hydrogen.

In the dilute sulphuric acid, the gases collected at the electrodes are the constituents of water, namely one volume of oxygen and two volumes of hydrogen. There is also an increase of sulphuric acid at the anode, but its amount is less than one equivalent. 186.] It follows from these considerations that in order to ascertain the electromotive force acting from a metal to an electrolyte, we must take ac- count of the whole permanent effects of the passage of one unit of electricity from the metal to the electrolyte. Thus, if the electrolyte is sulphate of zinc, with zinc electrodes, a certain amount of heat is generated at the anode for every unit of electricity and at the same time one equivalent of zinc combines with one equivalent of sulphion and forms sulphate of zinc. Now the quan- tity of heat generated when one equivalent of zinc combines with oxygen is known from the experiments of Andrews and others, and also the heat gener- ated when an equivalent of oxide of zinc combines with sulphuric acid, and is dissolved in water so as to form a solution of sulphate of zinc of the same strength as that which surrounds the electrode. The sum of these quantities of heat, which we may call H, is equivalent to the total work done by the chem- ical action at the anode, which is therefore J H [where J represents Joule’s equivalent, or the mechanical equivalent of heat]. Let h be the quantity of heat generated at the anode during the passage of one unit of electricity, and let E be the electromotive force acting from the zinc to the electrolyte, that is, in the direction of the current. Then the work done in generating heat is J h, and the work done in driving the current is E so that the equation of work is JH = Jh + E or E = J (H − h).

Of these quantities H is known very accurately but it is somewhat difficult to measure h, the quantity of heat generated at the electrode, because the electrode must be in contact with the electrolyte, and therefore a large and unknown fraction of the heat generated will be carried away by conduction and convection through the electrolyte. The only method which seems likely to succeed is to compare the stationary temperature at a certain distance from the electrode with the temperature at the same point when in the place of the electrode we put a fine wire of known resistance through which we pass a known current so as to generate heat at a known rate. If the temperatures are equal in the two cases we may conclude that the heat is generated at the same rate in the zinc electrode and in the wire. But if the current is a strong one a very sensible portion of the whole heat generated will be due to the work done by the current in overcoming the ordinary resistance of the electrode and the electrolyte. As the electrode is generally made of a

MEASUREMENT OF ELECTROMOTIVE FORCE

metal whose resistance is very small compared with that of the electrolyte, this frictional generation of heat will take place principally in the electrolyte. This frictional generation of heat may be made very small compared with the reversible part by diminishing the strength of the current, but then the rate of generation of heat becomes so small that it is difficult to measure it in the presence of unavoidable thermal disturbances, such as arise from changes in the temperature of the air, &c. The experimental investigation is therefore one of considerable difficulty, and I am not aware that the electromotive force from a metal to an electrolyte has as yet been measured even approximately∗ . If, however, we assume that the electromotive forces from the metals A and B to the electrolyte C are A and B respectively, and that the thermo-electric powers of these metals at the temperature θ are a and b respectively, then the electromotive force from A to B at their junction is (b − a)θ.

The total electromotive force round the circuit in the cyclical direction ABC is (b − a)θ + B − A.