The Peltier Effect

The discrimination between the different laws of electrodynamic force is closely connected with the question whether in an electric current there are two kinds of electricity moving in opposite directions, or only one kind moving in one direction.

On the unitary hypothesis, that the current consists in a transport of one kind of electricity with a definite velocity relative to the wire, it might be expected that a coil rotated rapidly about its own axis would generate a magnetic field different from that produced by the same coil at rest.

Experiments to determine the matter were performed by A. Föppl[84] and by E. L Nichols and W. S. Franklin,[85] but with negative results.

The latter investigators found that the velocity of electricity must be such that the quantity conveyed past a specified point in a unit of time, when the direction of the current was that in which the coil was travelling, did not differ from that transferred when the current and coil were moving in opposite directions by as much as one part in ten million, even when the velocity of the wire was 9096 cm./sec.

They considered that they would have been able to detect a change of deflexion due to the motion of the coil, even though the velocity of the current had been considerably greater than a thousand million metres per second.

Progress was made in the science of thermo-electricity.[86]

Faraday’s laboratory note-book entry dated July 28, 1836 reads:[87]

“Surely the converse of thermo-electricity ought to be obtained experimentally. Pass current through a circuit of antimony and bismuth.”

Unknown to Faraday, the experiment here indicated had already been made, although its author had arrived at it by a different train of ideas.

In 1834 Jean Charles Peltier[88] (b. 1785, d. 1845) attempted the task, which was afterwards performed with success by Joule,[89] of measuring the heat evolved by the passage of an electric current through a conductor.

He found that a current produces in a homogeneous conductor an elevation of temperature, which is the same in all parts of the conductor where the cross-section is the same.

But he did not succeed in connecting the thermal phenomena quantitatively with the strength of the current—a failure which was due chiefly to the circumstance that his attention was fixed on the rise of temperature rather than on the amount of the heat evolved.

But incidentally the investigation led to an important discovery—namely, that when a current was passed in succession through two conductors made of dissimilar metals, there was an evolution of heat at the junction; and that this depended on the direction of the current; for if the junction was heated when the current flowed in one sense, it was cooled when the current flowed in the opposite sense.

This Peltier effect, as it is called, is quite distinct from the ordinary Joulian liberation of heat, in which the amount of energy set free in the thermal form is unaffected by a reversal of the current; the Joulian effect is, in fact, proportional to the square of the current-strength, while the Peltier effect is proportional to the current-strength directly.

The Peltier heat which is absorbed from external sources when a current i flows for unit time through a junction from one metal B to another metal A may therefore be denoted by

where T denotes the absolute temperature of the junction. The function

is found to be expressible as the difference of two parts, of which one depends on the metal A only, and the other on the metal B only; thus we can write

In 1851 a general theory of thermo-electric phenomena was constructed on the foundation of Seebeck’s[90] and Peltier’s discoveries by W. Thomson.[91] Consider a circuit formed of 2 metals, A and B.

Let one junction be maintained at a slightly higher temperature (T + δT) than the temperature T of the other junction.

As Seebeck had shown, a thermo-electric current will be set up in the circuit. Thomson saw that such a system might be regarded as a heat-engine, which absorbs a certain quantity of heat at the hot junction, and convorts part of this into electrical energy, liberating the rest in the form of heat at the cold junction. If the Joulian evolution of heat be neglected, the process is reversible, and must obey the second law of thermodynamics; that is, the sum of the quantities of heat absorbed, cach divided by the absolute temperature et which it is absorbed, must vanish. Thus we have

so the Peltier effect

{\displaystyle \textstyle \prod _{B}^{A}(T)} must be directly proportional to the absolute temperature T. This result, however, as Thomson well knew, was contradicted by the observations of Cumming, who had shown that when the temperature of the hot junction is gradually increased, the electromotive force rises to a maximum value and then decreases.

The contradiction led Thomson to predict the existence of a hitherto unrecognized thermo-electric phenomenon-namely, a reversible absorption of heat at places in the circuit other than the junctions. Suppose that a current flows along a wire which is of the same metal throughout, but varies in temperature from point to point. Thomson showed that heat must be liberated at some points and absorbed at others, so as either to accentuate or to diminish the differences of temperature at the different points of the wire.

Suppose that the heat absorbed from external sources when unit electric charge passes from the absolute temperature T to the temperature (T + δT) in a metal A is denoted by SA(T).δT. The thermodynamical equation now takes the corrected form

Since the metals A and B are quite independent, this gives

This equation connects Thomson’s “specific heat of electricity” SA(T) with the Peltier effect.

In 1870 P. G. Tait[92] found experimentally that the specific heat of electricity in pure metals is proportional to the absolute temperature. We may therefore write

{\displaystyle \rho _{A}}, denotes a constant characteristic of the metal � A. The thermodynamical equation then becomes

where πA denotes another constant characteristic of the metal. The chief part of the Peltier effect arises from the term πAT.

By the investigations which have been described in the present chapter, the theory of electric currents was considerably advanced in several directions. In all these researches, however, attention was fixed on the conductor carrying the current as the seat of the phenomenon. In the following period, interest was centred not so much on the conductors which carry charges and currents, as on the processes which take place in the dielectric media around them.