Thermo-electric Inversion

164.] Cumming in 1823 discovered several cases in which the thermo- electric order of two metals as observed at ordinary temperatures becomes inverted at high temperatures. The lines corresponding to these metals on the thermo-electric diagram must therefore cross one another at some intermedi- ate temperature, called the Neutral Temperature for these metals. Tait has recently investigated the lines which represent a considerable num- ber of metals in the thermo-electric diagram, and he finds that for most met- als they are nearly if not exactly straight lines. The lines for iron and nickel however have considerable sinuosities, so that they may intersect the straight lines belonging to another metal in several different points corresponding to several different neutral temperatures.

Thermal effects of the Current.

165.] By applying the principle of the conservation of energy to the case of a thermo-electric current, it is easy to see that certain thermal effects must accompany the electric current.

Let us consider what takes place while one unit of electricity is transmit- ted across any section of the circuit. The work done on the electric current is the product of the electromotive force into the quantity of electricity trans- mitted, and since this latter quantity is unity, the work is numerically equal to the electromotive force, and is represented by the area ABba in the thermo- electric diagram. If the current is allowed to flow without anything to impede it except the resistance of the circuit, the whole of the work will be converted into heat, but if the resistance of any part of the circuit such as a long and fine wire greatly exceeds that of the thermo-electric couple, the heat generated in that part of the circuit will greatly exceed that generated in the thermo-electric couple itself. Instead of allowing the current to generate heat, we may make it drive a magneto-electric engine, and so convert any given proportion of the work into mechanical work.

PELTIER EFFECT. 150 Thus for every unit of electricity which is transmitted, a certain amount of work is done by the thermo-electric forces on the current. The only source of this work is the heat of the thermo-electric couple, and therefore, by the principle of the conservation of energy, we conclude that an amount of heat, dynamically equivalent to this work, must have disappeared in some part of the circuit.

166.] Now Peltier∗ in 1834 found that when an electric current is made to pass from one metal to another which has a higher thermo-electric power, the junction is cooled, or, since there is no permanent change in the metals, there is a disappearance of heat. When the current is made to flow in the opposite direction the junction is heated, indicating a generation of heat. This thermal effect of the current at the junction is of quite a different kind from the ordinary generation of heat by the current while it overcomes the resistance of a conductor. The latter, which we may call with Thomson the frictional generation of heat, is the same when the direction of the current is reversed, and varies as the square of the strength of the current. The former which we shall call the Peltier effect, is reversed when the current is reversed, and depends simply on the strength of the current.

167.] But Thomson has shewn that besides the Peltier effect, there must in certain metals be another re- versible thermal effect of the current. The current must gen- erate or absorb heat when it passes from hotter to colder or from colder to hotter parts of the same metal. Thus, let a thermo-electric couple of copper and iron be kept with one junc- tion AB at the neutral tempera- Fig. 37. ture which is about 280°C, and the other, ab, at some lower temperature. The thermo-electric current is from copper to iron at the hot junction AB and from iron to copper at the cold ∗ Annales de Chimie et de Physique, lvi. p. 371 (1834).THOMSON EFFECT. 151 junction ab.

Now the Peltier effect at the hot junction, AB, is zero, for that junction is at the neutral temperature, and the Peltier effect at the cold junction, ab, is a generation of heat, for the current is there passing from the metal of higher to the metal of lower thermo-electric power. Hence the absorption of heat which must exist in order to account for the work done by the current must take place in some other part of the circuit, either in the copper where the current is flowing from cold to hot, or in the iron where it is flowing from hot to cold, or in both metals. This thermal effect of the current was predicted by Thomson as the result of reasoning similar to that here given. He afterwards verified this prediction experimentally, and found that in iron unequally heated a current from hot to cold cools the metal, while a current from cold to hot heats it, and that the reverse thermal effect takes place in copper. We shall refer to this thermal effect as the Thomson effect.

168.] Thomson has shewn that a very close analogy subsists between these thermo-electric phenomena and those of a fluid circulating in a tube consist- ing of two vertical branches connected by two horizontal branches. A fluid, heated in one part of the circuit, and passing on into cooler parts of the sys- tem, will give out heat, and when it passes from colder to warmer parts will absorb heat, the amount of heat emitted or absorbed depending on the specific heat of the fluid. According to this analogy, positive or vitreous electricity carries heat with it in copper as if it were a real fluid, but in iron it behaves as if its specific heat were a negative quantity, which cannot be the case in a real fluid. Hence Thomson expresses the fact by saying that negative or resinous electricity carries heat with it in iron. Neither kind of electricity, therefore, can be regarded in this respect as a real fluid. We may therefore adhere to the usual convention, and speaking of the positive electricity only, we may say that in copper it behaves as if its specific heat were positive, and in iron as if it were negative.

169.] M. Le Roux∗ , who has made some very careful experiments on the Thomson effect, finds that in lead the specific heat of electricity is either zero or very small indeed. Professor Tait has therefore adopted lead as the ∗ Annales de Chimie et de Physique (4), x. p. 243 (1867).SPECIFIC HEAT OF ELECTRICITY. 152 standard metal in his thermo-electric measurements.

170.] We may express both the Peltier and the Thomson effects by stating that when an electric current is flowing from places of smaller to places of greater thermo-electric power, heat is absorbed, and when it is flowing in the reverse direction heat is generated, and this, whether the difference of thermo- electric power in the two places arises from a difference in the nature of the metal or from a difference of temperature in the same metal. Fig. 38.