Phenomena Of An Electric Current Which Flows Throug Heterogeneous Media

1. Thermo-electric phenomena.

160.] Seebeck, in 1822, discovered that if a circuit is formed of two dif- ferent metals, and if the two junctions of the metals are kept at different tem- peratures, an electric current tends to flow round the circuit. If the metals are iron and copper at temperatures below 280°C, the current flows from copper to iron through the hotter junction. There is therefore, in general, an electro- motive force acting in a definite direction round the circuit, whenever the two junctions are at different temperatures.

In a circuit formed of any number of metals all at the same temperature, there can be no current, for if there were a current it might be constantly employed to work a machine or to generate heat in a conductor, and this without any energy being supplied to the system from without, for in order to keep the circuit at a constant temperature nothing is required except to prevent heat from entering or leaving it.

Hence at any given temperature the electromotive force in a circuit of three metals, A, B, C must be zero for the whole circuit. Hence if the electromotive force from C to A is a, and that from C to B is b, and that from B to A x, then in the circuit A, B, C, the total electromotive force is a − b − x = 0, so that x, the electromotive force from B to A is represented by a − b, where a and b are quantities determined by observation of the electromotive force from any third metal C to the metals A and B.

We may express this by saying that the quantities a and b are the potentials of the metals A and B with respect to a third metal C at the given temperature. The potential of A with respect to B is a − b. The actual determination of the relative potentials of the metals will be explained in Art. 182.

161.] It has been shewn by Magnus∗ that if a circuit be formed of a sin- gle metal, no current will be formed in it, however the temperature and the ∗ [Pogg. Ann. 1851.]LAW OF MAGNUS. 146 Fig. 33.

section of the conducting circuit may vary in different parts. Since in this case there is necessarily conduction of heat, and consequently dissipation of energy, we cannot, as in the former case, consider the result as self-evident. The electromotive force, for instance, between two portions of the circuit at given temperatures might depend on the length or the mode of variation of the section of the intermediate portion of the circuit.

In fact the experiments of Le Roux and others have shewn that the law of Magnus is no longer applicable in a circuit in which there is a very abrupt variation of temperature, as at the instant when the circuit is closed by a hot wire coming in contact with a cold wire of the same metal.

Even without any physical discontinuity of the circuit such as is implied in the contact of two separate pieces of wire, a sufficiently abrupt variation of temperature may be produced by taking a thick wire and filing down a certain length of it till it is very thin. If the junction of the thick and the thin portions is placed in a flame, the thin portion will be heated so much more rapidly than the thick portion, that the variation of temperature will be so abrupt that the law of Magnus fails, and we obtain a current in a circuit of one metal; we must therefore modify the statement of the law of Magnus as follows:—

The electromotive force from one point of a conductor of homogeneous metal to another depends only on the temperature of these points unless at any part of the conductor a sensible variation of temperature occurs between points whose distance is within the limits of molecular action. Thermo-electric power of a metal at a given temperature. 162.] Let us now consider a linear circuit made up of alternate pieces of two metals, say lead and iron. We shall assume lead to be the standard metal, and study the properties of iron in relation to lead.

147 Fig. 34.

In the figure the pieces of iron are distinguished by shading. Let the temperatures of the junctions be those indicated in the figure, in which the temperatures of the extremities of each piece of iron differ by one degree, but the temperatures of the extremities of each of the intermediate pieces of lead are equal.

The total electromotive force round the circuit is the sum of the electromotive forces due to the thermo-electric action of the different pairs of junctions. Now if we consider the pairs A and B, C and D, E and F be- longing to the pieces of iron we find that the temperature rises one degree in each piece, but if we take the pairs B and C, D and E belonging to the pieces of lead, the temperature in each piece is uniform and therefore there is no electromotive force in these pieces. We may therefore leave the interme- diate pieces of lead out of account, and consider the electromotive force due to the junctions A and F as equivalent to the sum of the electromotive forces of the three pairs of junctions A and B, C and D, E and F.

Hence if a diagram is constructed in which the axis OZ is marked with the degrees of the thermometric scale and in which the area 0°P Q1° represents the electromotive force when the junctions are at 0° and 1° and so on, then the electromotive force when the junctions are at any given temperatures will be represented by the area included between the axis, the ordinates at the given temperatures and the line P QRST.

163.] Any ordinate such as 0°P, 1°Q, &c., is called the Thermoelectric Power of iron with respect to lead at 0°, 1°, &c., and is reckoned positive when, for a small difference of temperature, the current is from lead to iron through the hot junction.

148 Fig. 35. We may also on the same diagram construct other lines, the ordinates of which represent the thermo-electric powers of any other metals with respect to lead, being reckoned positive and measured upwards when for a small dif- ference of temperatures the current sets from lead to that metal through the hot junction. Such a diagram is called a thermo-electric diagram, and from it we can deduce the electromotive force due to any pair of metals with their junctions at any given temperatures.

Thus if a A is the line representing the metal A, and b B another represent- ing the metal B, and T, t the temperatures of the junctions, the electromotive force of the circuit is represented by the area ABbaA and it acts in the direction indi- cated, namely, from the metal A to the metal B through the hot junction. If, instead of lead, we had assumed any other metal as the standard metal, the dia- gram would have been altered in form, but all areas measured on the diagram would have remained the same, the change of form being due to a shearing strain in which the slipping is along vertical lines.

Fig. 36.