HEVLIWG EFFECTS.] E L E C T li I C I T Y 57 heat ; while the same current would have generated in wires of equal resistance 26 and - 32 units respectively, er Reversible Heating E/vcts. Peltier 1 was the first to . discover an effect of this nature. He found that, when an electric current passes over a junction of antimony with bismuth, the order of the metals being that in which we have named them, there is an evolution of heat at the junc tion ; and, when the current passes in the opposite direc tion, there is an absorption of heat, so that the temperature of the junction falls. Here, therefore, there is an effect which cannot vary as the square of the current strength, but must be some function of the current strength, whose principal term at least is s ome odd power. The Peltier effect, as it is now called after its discoverer, may be demonstrated by inserting a soldered junction of antimony and bismuth into a Riess s thermoelectrometer. "When the current
- r*
goes BiSb, the fluid will rise in the stern, indicating absorption of > heat; when it goes SbBi, the fluid will fall, indicating evolution of heat. Or ve may use Peltier s cross, which consists ot two pieces, one of bismuth I .B , and the other of anti mony AA , soldered together in the form of a cross (fig. 28). A and B are connected by a wire through a gal vanometer G. A and B are con nected with a battery C through a commutator D, by means of which the sin-rent can be sent either from A to B or from B to A through the junc tion. The thermoelectric current in dicated by the galvanometer shows that the junction is heated in the first in stance and cooled in the second. Fig. 28. By leading the current of a Grove s cell for five minutes through a BiSb junction, Lenz 2 succeeded in freezing a small quantity of water which had been placed in a hole in the junction, and previ ously reduced to C. The temperature of the ice formed fell to -4-5C. of The Peltier effect is different for different pairs of metals. r Peltier and Becquerel 3 found that the metals could be ar ranged in the following order : Bi, Gs, 4 Ft, Pb, Sn, Cu, Au, Zn, Fe, Sb . If the current pass across a junction of any two of these metals, cold or heat is generated according as the current passes the metals in the direction of the arrow or in the opposite direction ; and the Peltier effect between the metals is greater the farther apart they are in the series. We shall see later on that this is none other than the thermoelectric series. Von Quintus Icilius 5 showed that the Peltier effect is directly proportional to the strength of the current. He passed a voltaic current through a tangent galvanometer (serving to measure it) and a thermopile of 32 BiSb couples. The current was allowed to pass for a fixed time, then the battery was removed and the thermoelectric current of the pile measured by means of a delicate mirror galvanometer. The current of the battery heats the pile in part uniformly according to Joule s law : this causes no unequal heating of the junction, and therefore no thermoelectric current ; and in part unequally, so that one set of junctions are cooler and the other warmer than the mass of the metal : this causes a thermoelectric current, which, since the tempera ture differences are small (see below, p. 97), maybe taken to be proportional to the temperature difference, that is, to the double of the Peltier effect at each set of junctions. ft is interesting to note the analogy here with the polar ization of an electrolytic cell. We turn a battery on to 1 Ann. de Chim. et de Phys., 1834. 8 See Wiedemann s Oalvanismus, Bd. i. 689. Ann. de Chim. et de Phys., 1847. . 4 Gs = German Silver.
- p ogg . Ann->
1853 the thermopile, and polarize it, as it were. Then, when we remove the battery and close the pile, we get a return cur rent, which might be called the polarization current of the thermopile. In general the Peltier effect is, as we have seen, mixed up with Joule s effect, and makes itself felt by producing a disturbance at the junction. Thus Children 6 found that, when a strong current passed through two mercury cups joined by a thin platinum wire, so that the wire became red hot, the temperature of the mercury in the cups next the + pole of the battery rose to 121 F., while in the cup next the - pole the temperature was only 112 F. Frank- enheim 7 studied the two effects together. He made a Peltier s cross of the pair of metals to be examined, passed a current I through the cross first in one direction and then in the other, and deter mined by means of a delicate galvanometer the thermoelectric cur rent generated in each case, which is very nearly proportional to the heat produced. If a and b be the heat from Joule and Pel tier effects respectively, and i and i the observed thermoelectric currents, then i = C(a + b), i = C(a-b); whence a = (i + i )-r-2C, and b = (i-i )-i-2G. In this way he found that a was proportional to I 2 , and b to I. Thus the whole heat developed may be expressed by aI 2 6I. We get in this way a verification of the results both of Joule and of Von Quintus Icilius. Further experiments have been made on this subject by Thomson. Edlund and Le Roux ; and Sir W. Thomson was led by a effect. remarkable train of reasoning to discover another rever sible heating effect. W T e prefer to leave these matters for the present, to return to them when we consider thermo electric sources of electromotive force. The Peltier effect between metals and liquids and other reversible effects will also come UD again under the Origin of Electromotive Force. Theoretical Deduction of the Formulae. The above for- Theory multe for the heat developed in wires by statical and dyna- p f ueal mical electricity may be deduced from a common formula, 1! 1? . which can be deduced from Ohm s law. Let P, Q be two points of a linear circuit, and let E be the differ- ence between the potentials at P and Q, then, if there be no other electromotive force in the portion PQ, the work done by a unit of + electricity in passing from P to Q is E. Hence, if I be the strength of the current, so that Idt units of electricity pass from P to Q in time dt, then the amount dw of work done by the current in time dt is Elcft. But, by Ohm s law, E = RI, hence dtt-^El-dt ....... (7). Since the whole of this work is spent in heat, we may for w write H, which denotes the boat 8 generated in PQ. If the current bt constant, we get immediately H = RI ! , which is Joule s law (6). If the current be variable, il=fRl 3 dt t from which we may very easily deduce the formula for the discharge of n battery of Leyden jars. For, applying Ohm s law to the whole circuit whose resist ance is R + S, we have, if U denote the potential of the inside coatings at time t, I = _L. . Also the capacity of each of the n jars being C, wo have for the charge y = nCU, and I=- -* Hcnco H = R /is, i ,. iClv at = - - - R + S. R q* R + S 2nC } l !-dt=- - dt R + S (8), where q and V have the same meanings as in (3). (8) agrees with (3), except that we have reckoned the heat developed in a portion of the circuit whose resistance is R instead of S, as in (3). It appears, therefore, that the theoretical formula (7), when properly interpreted, covers both cases. If there were a junction of heterogeneous metals in the part PQ of the circuit, at which the potential suddenly fell by an amount n, then work equal to Tlldt would be done by the current in pass ing over the junction, and we should have to write dW = RI 2 cft + nIc (9). Had there been a rise of potential at the junction, we should have written - n instead of + n. If all the work done at the junction is transformed into heat, W = H as before, and for a constant current, H = RF< + nl< . ... (10). 8 Phil. Trans., 1815. 7 Pogg. Ann., xvi. 1854. 8 Measured, of course, in dynamical equivalents.
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