96 ELECTRICITY [ELECTROMOTIVE FOIICE. Thermo- ectno sion. Cum- imagined conditions. There can be no doubt, however, that, when the two unequally heated ends of a wire com posed of the same metal throughout are brought together, a thermoelectric current is in general the consequence. Such currents were, it appears, observed by Hitter 1 in 1801, when cold and hot pieces of zinc wire were brought into contact. Becquerel, Matteucci, Magnus, and others have experimented on this subject. The results obtained are, no doubt, greatly influenced by the state as to oxida tion, &c., of the surfaces of the metals experimented on, as has been pointed out by Franz and Gaugain. The experimental conditions are, in truth, very complicated, and a discussion of the matter would be out of place here. 2 We may mention, however, that, at the instance of Professor Tait, Mr Durham 3 made experiments on the transient current which arises when the unequally heated ends of a platinum wire are brought into contact. It was found that the first swing of a galvanometer of moderately long period was proportional to the temperature difference and independent of the mean temperature through a con siderable range. Gumming, who experimented on thermoelectricity about j-^g saine tj me ag S ee beck, and apparently independently, discovered the remarkable fact that the thermoelectric order of the metals is not the same for high temperatures as for low. He found that, when the temperature of the hot junction in a circuit of iron and copper, or iron and gold, is gradually raised, the electromotive force increases more and more slowly, reaches a maximum at a certain temperature T, then decreases to zero, and finally changes its direction. The higher the temperature of the colder junction, so long as it is less than T, the sooner the reversal of the electromotive force is obtained. If the temperature of the hot junction be T + T, where r is small, then the reversal of the electromotive force takes place when the temperature of the colder junction is T - T . If both junctions, A and B, be at the temperature T, then either heating or cooling A will cause a current in the same direction round the circuit, and either heating or cooliny B will cause a current in the opposite direction. The reversal of the current may be shown very conve niently in the manner recommended by Sir Wm. Thomson. 4 A circuit is formed by soldering an iron wire to the copper terminal wires of a galvanometer. If one junction be at the temperature of the room and the other at 300 C. or thereby, a current flows from copper to iron across the hotter junction ; but, if we raise the temperature of both junctions over 300C., one being still a little hotter than the other (which can be managed by keeping both in a lamp flame, one in a slightly hotter place than the other), then the current will flow from iron to copper across the hot junction. If both junctions be allowed to cool, the di/er- ence between their temperatures remaining the same, the current will decrease, becoming zero when the mean tempe rature of the two junctions is about 280" C ; and, on still further lowering the mean temperature, it will set again in the opposite direction, i.e., from copper to iron across the hot junction. The fundamental facts of thermoelectric in version were confirmed by Becquerel, 5 Hankel, 6 Svanberg, 7 <fec. ; but the matter rested there till it was taken up 8 by Sir Wm. Thomson 9 in the course of his classical researches on the applications of the laws of thermodynamics to phy sical problems. 1 Wiedemann, Bd. i. 627. 2 Consult AViedemann, Bd. i. 627, &c., and Mascart, t. ii 932 &c 3 Proc. R.S.E., 1871-2. 4 Bakerian Lecture, Phil. Tram., 1856, p. 699. 5 Ann. de, Chim. et de Phys., 1826. 6 Pogg. Ann., 1844. 7 Pogg. Ann., 1853 ; cf. Wiedemann, Bd. i. 623. 8 In consequence, it appears, of a remark of Joule s, cf. Proc. K.S.E., 1874-5. p. 417. Trans. R.S.E., 1851. The application of the first law of thermodynamics leads to no difficulty; and it indicates that the heat absorbed accord ing to Peltier s law, in the ordinary case when a current passes from copper to iron across the hotter of the junctions, minus the heat evolved at the colder junction where the current passes from iron to copper, is to be looked on as a source of part at least of the energy of the thermoelectric current. If absorption or evolution of heat occur any where else than at the junctions, this must be taken account of in a similar manner. The application of the second law is of a more hypo thetical character. It is true that the Peltier effects, as we may for shortness call the heat absorption and evolution at the junctions, are reversible in this sense that we might suppose the thermoelectric current, whose energy arises wholly or partly from the excess of the heat absorbed at the junction A over that evolved at the junction B, used to drive an electromagnetic engine and raise a weight ; and that we might suppose the potential energy thus obtained again expended in sending, by means of an electromagnetic machine, a current in the opposite direction round the circuit, absorbing heat at B, evolving heat at A, and thus restoring the inequality of temperature. This process, however, must always be accompanied by dissipation of energy, (1) by the evolution of heat in the circuit accord ing to Joule s law, and (2) by conduction from the hotter towards the colder parts of the wires. The first of these effects varies as the square of the current strength, while Peltier s effect varies as the current strength simply ; so that the former might be made as small a fraction of the latter as we please by sufficiently reducing the current, and thus, theoretically speaking, eliminated. The second form of dissipation could not be thus got rid of, and could only be eliminated in a circuit of infinitely small thermal but finite electric conductivity, a kind of circuit not to be realized, as we know (see above p. 51). Still it seems a reasonable hypothesis to assume that the Peltier effects, and other heat effects if any, which vary as the first power of the strength of the current, taken by themselves are subject to the second law of thermodynamics. Let us now further assume that all the reversible heat effects occur solely at the junctions. Let n, n denote the heat (measured in dynamical equivalents) absorbed and evolved, at the hot and cold junctions respectively in a unit of time by a unit current. Let E be the electromotive force of an electromotor maintaining a current I, in such a direction as to cause absorption of heat at the hot junction. Then, if R be the whole resistance of the circuit, we have, by Joule s law and the first law of thermodynamics, El + nI-n l~KI 2 , (i), supposing the whole of the energy of the current wasted in heat. Hence we get T E + n ~ n R (2 >- It appears then that, owing to the excess of the absorption of heat at the hot junction over the evolution at the cold junction, there arises an electromotive force IT - II helping to drive the current in the direction giving heat absorption at the hot junction. We may suppose (and shall hence forth suppose) that E = 0, and then the current will be maintained entirely by the thermoelectro/uotive force. If we now apply the second law, we get y - y = , 6 and 6 being the absolute temperatures of the hot and cold junctions. Hence n n 3 ) . e = <P or. in other words, IT = CO, where C is a constant depend- tioB
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