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# Thermoelectricity

## electromotive, force, temperature, metals, circuit, junctions and constants

THERMOELECTRICITY. If an elec trical circuit is constructed partly of one metal and partly of another, and ohe of the points of junction between the dissimilar metals is heated while the other is kept cool, a current.of elec tricity will be caused to flow in the circuit. This fundamental fact was discovered by See beck in 1821. The electricity thus generated is not in any wise different from that which is generated by an ordinary galvanic battery; but on account of its mode of production it is called "thermo-electricity." The electromotive force that is set up in a circuit under the cir cumstances here described is always quite small, and its intensity depends (1) upon the nature of the metals of which the circuit is composed, (2) upon the difference in temperature between the two junctions where the dissimilar metals come together and (3) upon the average tem perature of these junctions. For the sake of definiteness, let the two metals of which the circuit is composed be designated by the letters X and Y. The phenomena of thermo-electricity may then be described in the following mathe matical language: It is known from experiment that when the two metals X and Y are brought together so that their point of contact has the temperature 7', an electromotive force exists be tween the two, which tends to send a current (say) from X into Y; and it is also known that the magnitude of this electromotive force can be expressed as a parabolic function of the temperature, T. Thus if E is the electromotive force in question, the facts of experiment can be adequately expressed by a relation of the form E = a + bT cr; where a b and c are constants whose values depend upon the natures of the metals X and Y. In the actual circuit there are necessarily two junctions across which electromotive forces of this character exist. Let the temperatures of these junctions be respectively T, and T,. Then the foregoing formula shows that across the junction whose temperature is T, there is an electromotive force of intensity, E1= a ± bT, cr,, tending to send a current from X into Y; and across the junction whose temperature is T, there is a similar electromotive force of intensity a + bT,-F cr, also tending to send a current from X into Y.

These electromotive forces being opposed to each other, so far as the production of a current around the circuit is concerned, the effective electromotive force around the circuit is the difference between E, and E.; and if we denote this effective electromotive force by the letter F, we have F —Ei=b (T,—T1) + cal —71), Or F fb-f-c(T. Tin From this last equation it is evident that so long as the average temperature of the two junctions is constant (or, in other words, so long as T, + T. is constant), the electromotive force will he proportional to the difference in temperature between the two functions. But it is also evident that when the average tem perature of the two junctions is such that the relation b c(T, TO =0 is fulfilled (or, in other words, when the aver age temperature of the two junctions is numer ically equal tu—b/2c), there will be no ther mo-electromotive force in the circuit (and, therefore, no current), no matter what the difference in temperature between the two junctions may be. This average temperature, for which there is no thermo-electric effect in a circuit, has a definite value for every pair of metals, and is known as the "neutral tem perature" for that pair. The values of the constants b and c, in the foregoing formulae, could be determined experimentally, and recorded in tabular form for various pairs of metals. It is usual, however, to record the experimental data in a somewhat different man ner, as we proceed to explain. If the average of the two temperatures T1 and T, be denoted by To, then the formula for the effective elec tromotive force, F, may be written F= T.) (b.+ 2cTo).

The constants b and c refer, it will be un derstood, to a particular pair of metals; but it is found that their values can be satisfactorily represented as the diffe-ences between constants which can be stated for the two metals sep arately. Thus b can be expressed in the form b = B' — B" and 2c can be expressed in the form 2c= CC— C"; B' and C' being constants whose values depend solely upon the metal X, and B" and C" being constants whose values depend, in a similar manner, solely upon the metal Y. The expression for the effective electromotive force F can, there fore, be written thus: