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LEAD . S.O co° 4000 q 0 h Ni —x2058- E See also:Nickel. =_8. 75 t t See also:Peltier effect, and that the difference of potential in the substance of the metals when the See also:circuit is See also:complete cannot be greater than the coefficient P. The Peltier effect, it may be objected, See also:measures that See also:part only of the potential difference which depends upon temperature, and can therefore give no See also:information about the See also:absolute potential difference. But the See also:reason for concluding that there is no other effective source of potential difference at the junction besides the Peltier effect, is simply that no other appreciable See also:action takes See also:place at the junction when a current passes except the Peltier See also:generation or absorption of See also:heat. 2o. Convection Theory.—The See also:idea of convection of heat by an electric current, and the phrase " specific heat of See also:electricity " were introduced by See also:Thomson as a convenient mode of expressing the phenomena of the Thomson effect. He did not intend to imply that electricity really possessed a See also:positive or negative specific heat, but merely that a quantity of heat was absorbed in a See also:metal when unit quantity of electricity flowed from See also:cold to hot through a difference of temperature of 10. The absorption of heat was considered as representing an See also:equivalent See also:conversion of heat See also:energy into See also:electrical energy in the See also:element. The element might thus be regarded as the seat of an E.M.F., dE=sdT, where dT is the difference of temperature between its ends. The potential diagrams already given have been See also:drawn on this See also:assumption, that the Thomson effect is not really due to convection of heat by the current, but is the measure of an E.M.F. located in the substance of the conductor. This view with regard to the seat of the E.M.F. has been generally taken by the See also:majority of writers on the subject. It is not, however, necessarily implied in the reasoning or in the equations given by Thomson, which are not founded on any assumptions with regard to the seat of the E.M.F., but only on the See also:balance of heat absorbed and evolved in all the different parts of the circuit. In fact, the equations themselves are open to an entirely different See also:interpretation in this respect from that which is generally given. Returning again to the equations already given in § 11 for' an elementary thermocouple, we have the following equivalent expressions for the E.MpF. dE, namely, dE =dP+ (s' —s")dT = (P/T)dT = pdT = (p" — p')dT, in which the coefficient, P, of the Peltier effect, and the thermoelectric See also:power, p, of the couple, may be expressed in terms of the difference of the thermoelectric See also:powers, p' and p", of the See also:separate metals with respect to a neutral See also:standard. So far as these equations are concerned, we might evidently regard the seat of the E.M.F. as located entirely in the conductors them-selves, and not at all at the junctions, if p or (p'' —p') is the difference of the E.M.F.s per degree in corresponding elements of the two metals. In this See also:case, however, in See also:order to See also:account for the phenomenon of the Peltier effect at the junctions, it is necessary to suppose that there is a real convection of heat by an electric current, and that the coefficient P or pT is the difference of the quantities of heat carried by unit quantity of electricity in the two metals. On this See also:hypothesis, if we confine our See also:attention to one of the two metals, say p", in which the current is supposed to flow from hot to cold, we observe that p"dT expresses the quantity of heat converted into electrical energy per unit of electricity by an E.M.F. p" per 1° located in the element dT. It happens that the absolute magnitude of p" cannot be experimentally determined, but this is immaterial, as we are only concerned with See also:differences. The quantity of heat liberated by convection as the current flows from hot to cold is represented in the See also:equation by dP=d(pT). Since d(p"T) = p"dT+Tdp", it is clear that the balance of heat liberated in the element is only Tdp"=s"dT, namely, the Thomson effect, and is not the equivalent of the E.M.F. p"dT, because on this theory the absorption of heat is masked by the convection. If p is See also:constant there is no Thomson effect, but it does not follow that there is no E.M.F. located in the element. The Peltier effect, on the other See also:hand, may be ascribed entirely to convection. The quantity of heat p"T is brought up to one See also:side of the junction per unit of electricity, and the quantity of heat p'T taken away on the other. The balance (p"—p')T is evolved at the junction. If, therefore, we are prepared to admit that an electric current can carry heat, the existence of the Peltier effect is no See also:proof that a corresponding E.M.F. is located at the junction, or, in other words, that the conversion of heat into electrical energy occurs at this point of the circuit, or is due to the contact of dissimilar metals. On the contact theory, as generally adopted, the E.M.F. is due entirely to See also:change of substance (dP—Tdp); on the convection theory, it is due entirely to change of temperature (pdT). But the two expressions are equivalent, and give the same results. 21. Potential Diagrams on Convection Theory.—The difference between the two theories is most readily appreciated by See also:drawing the potential diagrams corresponding to the supposed locations of the E.M.F. in each case. The contact theory has been already illustrated in fig. 4. Corresponding diagrams for the same metals on the convection theory are given in fig. 5. In this See also:diagram the metals are supposed to be all joined together and to be at the same See also:time potential at the cold junction at o° C. The See also:ordinate of the See also:curve at any temperature is the difference of potential between any point in the metal and a point in lead at the same temperature. Since there is no contact E.M.F. on this theory, the ordinates also represent the E.M.F. of a thermocouple metal- lead, in which one junction is at o° C. and the other at t° C. For this reason the potential diagrams on the convection theory are more See also:simple and useful than those on the contact theory. The curves of E.M.F. are in fact the most natural and most convenient method of recording the numerical data, more particularly in cases where they do not admit of being adequately represented by a See also:formula. The See also:line of lead is taken to be See also:horizontal in the diagram, because the thermoelectric power, p, may be reckoned from any convenient zero. It is not intended to imply that there is no E.M.F. in the metal-lead with change of temperature, but that the value of p in this metal is nearly constant, as the Thomson effect is very small. It is very probable that the absolute values of p in different metals are of the same sign and of the same order of magnitude, being large compared with the differences observed. It would be theoretically possible to measure the absolute value in some metal by observing with an See also:electrometer the P.D. between parts of the same metal at different temperatures, but the difference would probably be of the order of may one-hundreuth of a volt for a difference of too° ° C. It would be sufficiently difficult to detect so small a difference under the best conditions. The difficulty would be greatly increased, if not rendered practically insuperable, by the large difference of temperature. 22. See also:Conduction Theory.—In Thomson's theory it is expressly assumed that the reversible thermal effects may be considered separately without reference to conduction. 
In the conduction theory of F. W. G. Kohlrausch (Pogg. See also:Ann., 1875, vol. 156, p. 6o1), the fundamental postulate is that the thermo-E.M.F. is due to the conduction of heat in the metal, which is contrary to Thomson's theory. It is assumed that a flow of heat Q, due to conduction, tends to carry with it a proportional electric current C = aQ. This is interpreted to mean that there is an E.M.F. dE=—akr dT= —EMT, in each element, where k is the thermal conductivity and +4000 .See also:Scale of Temperature Centryrades -200 — 100 0 +100 +200 r the specific resistance. The " thermoelectric constant," 0, of Kohlrausch, is evidently the same as the thermoelectric power, p, in Thomson's theory. In order to explain the Peltier effect, Kohlrausch further assumes that an electric current, C, carries a heat-flow, Q=AOC, with it, where " A is a constant which can be made equal to unity by a proper choice of See also:units." If A and 0 are constant, the Peltier effects at the hot and cold junctions are equal and opposite, and may therefore be neglected. The See also:combination of the two postulates leads to a complication. By the second postulate the flow of the current increases the heat-flow, and this by the first postulate increases the E.M.F., or the resistance, which therefore depends on the current. It is difficult to see how this complication can be avoided, unless the first postulate is abandoned, and the heat-flow due to conduction is assumed to be See also:independent of the thermoelectric phenomena. By applying the first See also:law of See also:thermodynamics, Kohlrausch deduces that a quantity of heat, COdT, is absorbed in the element dT per second by the current C. He wrongly identifies this with the Thomson effect, by omitting to allow for the heat carried. He does not make any application of the second law to the theory. If we apply Thomson's See also:condition P=TdE/dT=Tp, we have A=T. If we also assume the ratio of the current to the heat-flow to be the same in both postulates, we have a =1 /TO, whence 02 = kr/T. This condition was applied in 1899 by C. H. J. B. Liebenow (Wied. Ann., 68, p. 316). It simplifies the theory, and gives a possible relation between the constants, but it does not appear to remove the complication above referred to, which seems to be inseparable from any conduction theory. L. Boltzmann (Sitz. Wien. Akad., 1887, vol. 96, p. 1258) gives a theoretical discussion of all possible forms of expression for thermoelectric phenomena. Neglecting conduction, all the expressions which he gives are equivalent to the equations of Thomson. Taking conduction into account in the application of the second law of thermodynamics, he proposes to substitute the inequality, Td/dET—P<2Nl T(vk'r'+^lk"r"), instead of the equation given by Thomson, namely, P=TdE/dT. Since, however, Thomson's equation has been so closely verified by See also:Jahn, it is probable that Boltzmann would now consider that the reversible effects might be treated independently of conduction. 23. Thermoelectric Relations.—A number of suggestions have been made as to the possible relations between heat and electricity, and the mechanism by which an electric current might also be a See also:carrier of heat. The simplest is probably that of W. E. See also:Weber (Wied. Ann., 1875), who regarded electricity as consisting of atoms much smaller than those of See also:matter, and supposed that heat was the kinetic energy of these electric atoms. If we suppose that an electric current in a metal is a flow of negative electric atoms in one direction, the positive electricity associated with the far heavier material atoms remaining practically stationary, and if the atomic heat of electricity is of the same order as that of an equivalent quantity of See also:hydrogen or any other element, the heat carried per See also:ampere-second at o° C., namely P, would be of the order of •030 of a See also:joule, which would be ample to account for all the observed effects on the convection theory. Others have considered conduction in a metal to be analogous to electrolytic conduction, and the observed effects to be due to " See also:migration of the ions." The majority of these theories are too vague to be profitably discussed in an See also:article like the See also:present, but there can be little doubt that the study of See also:thermoelectricity affords one of the most promising roads to the See also:discovery of the true relations between heat and electricity. Alphabetical See also:Index of Symbols. a, b, c = Numerical constants in formulae. C= Electric Current. E= E.M.F. = Electromotive Force. k =Thermal Conductivity. P = Coefficient of Peltier Effect. p = dE/dt = Thermoelectric Power. Q= Heat-flow due to Conduction. R= Electrical Resistance; r, Specific Resistance. s = Specific Heat, or Coefficient of Thomson Effect. t =Temperature on the Centigrade Scale. T=Temperature on the Absolute Scale. (H. L. Additional information and CommentsThere are no comments yet for this article.
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