LEAD. S.O
co°
4000 q 0 h
Ni —x2058 E
Nickel. =_8. 75
t t
Peltier effect, and that the difference of potential in the substance of the metals when the circuit is complete cannot be greater than the coefficient P. The Peltier effect, it may be objected, measures that part only of the potential difference which depends upon temperature, and can therefore give no information about the absolute potential difference. But the 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 action takes place at the junction when a current passes except the Peltier generation or absorption of heat.
2o. Convection Theory.—The idea of convection of heat by an electric current, and the phrase " specific heat of electricity " were introduced by Thomson as a convenient mode of expressing the phenomena of the Thomson effect. He did not intend to imply that electricity really possessed a positive or negative specific heat, but merely that a quantity of heat was absorbed in a metal when unit quantity of electricity flowed from cold to hot through a difference of temperature of 10. The absorption of heat was considered as representing an equivalent conversion of heat energy into electrical energy in the 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 drawn on this 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 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 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 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 power, p, of the couple, may be expressed in terms of the difference of the thermoelectric powers, p' and p", of the separate metals with respect to a neutral 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 themselves, 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 case, however, in order to 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 hypothesis, if we confine our 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 differences. The quantity of heat liberated by convection as the current flows from hot to cold is represented in the 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 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 hand, may be ascribed entirely to convection. The quantity of heat p"T is brought up to one
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 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 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 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 diagram the metals are supposed to be all joined together and to be at the same time potential at the cold junction at o° C. The ordinate of the 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 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 formula. The line of lead is taken to be 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 metallead 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 electrometer the P.D. between parts of the same metal at different temperatures, but the difference would probably be of the order of may onehundreuth 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. 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. Ann., 1875, vol. 156, p. 6o1), the fundamental postulate is that the thermoE.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
.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 heatflow, Q=AOC, with it, where " A is a constant which can be made equal to unity by a proper choice of 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 combination of the two postulates leads to a complication. By the second postulate the flow of the current increases the heatflow, 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 heatflow due to conduction is assumed to be independent of the thermoelectric phenomena. By applying the first law of 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 condition P=TdE/dT=Tp, we have A=T. If we also assume the ratio of the current to the heatflow 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 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 carrier of heat. The simplest is probably that of W. E. Weber (Wied. Ann., 1875), who regarded electricity as consisting of atoms much smaller than those of 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 hydrogen or any other element, the heat carried per amperesecond at o° C., namely P, would be of the order of •030 of a 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 " migration of the ions." The majority of these theories are too vague to be profitably discussed in an article like the present, but there can be little doubt that the study of thermoelectricity affords one of the most promising roads to the discovery of the true relations between heat and electricity.
Alphabetical 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= Heatflow 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. C.)
End of Article: LEAD 

[back] HENRY CHARLES LEA (1825–1909) 
[next] LEAD (pronounced iced) 
There are no comments yet for this article.
Do not copy, download, transfer, or otherwise replicate the site content in whole or in part.
Links to articles and home page are encouraged.