Thermo-electric Diagram

178.] The most convenient method of studying the theory of thermo- electric phenomena is by means of a diagram in which the temperature and electric entropy of a metal at any instant are represented by the horizontal and vertical coordinates of a point on the diagram. Thus, if OC represents the temperature, reckoned from absolute zero on the thermodynamic scale, of a piece of a certain metal, and if CA represents the electric entropy corresponding to the same piece of metal, then the point A will indicate by its position in the diagram the thermo-electric state of the piece of metal. In the same way we may find other points in the diagram corresponding to the same metal under other conditions or to other metals. Fig. 40.

If in the path of an electric current electricity passes from one metal to another or from one portion of a metal to another at a different temperature, the different points of the electric circuit will be represented by correspond- ing points on the thermo-electric diagram. The path of the current will thus be represented by a line or path on the thermo-electric diagram. When the current flows in a single metal, A, from a point at a temperature OC to another at a temperature Oc, the path is represented by the line Aa, the points of which represent the state of the metal at intermediate temperatures. The form of the path depends on the nature of the metal and on the other influences which act on it besides temperature, such as stress and strain. Professor Tait, however, finds that for most of the metals except iron and nickel, the path on the thermo-electric diagram is a straight line.

SPECIFIC HEAT OF ELECTRICITY

When the current flows from the metal A to another metal B at the same temperature, the path is represented by AB, a vertical straight line. The circuit traversed by the electric current will thus be represented by a circuit on the thermo-electric diagram.

The heat generated while a unit of electricity moves along the path Aa is represented by the area of the figure AaQP A, bounded by the path Aa, the horizontal ordinate at a, the line of zero temperature and the horizontal ordinate at A. If this area lies on the right of the path, it represents heat generated; if it lies to the left of the path it represents heat absorbed. 179.] If electricity were a fluid, running through the conductor as water does through a tube, and always giving out or absorbing heat till its temper- ature is that of the conductor, then in passing from hot to cold it would give out heat and in passing from cold to hot it would absorb heat, and the amount of this heat would depend on the specific heat of the fluid. In the diagram the specific heat of the fluid at A would be represented by the line αP, where α is the point where the tangent to the path at A cuts the line of zero temperature, and P is the intersection with the same line of the horizontal ordinate through A.

The line Aaα in the diagram is such that the electric entropy increases as the temperature rises. This is the case with copper, and therefore we may assert that the specific heat of electricity in copper is positive. In other metals, as for instance iron, the electric entropy diminishes as the temperature rises, as is represented by the line βbB. The specific heat of electricity in such metals is negative, and at B is represented by the line βT. 180.] Thomson, who discovered first from theory and then by experimental verification the thermal effect of an electric current in an unequally heated metal, expresses the fact by saying that vitreous electricity carries heat with it in copper, while resinous electricity carries heat with it in iron.

ELECTROMOTIVE FORCE.

We must remember, however, that these phrases are not intended by Thom- son, and must not be understood by us, to imply that electricity either positive or negative is a fluid which can be heated or cooled and which has a definite specific heat. Since, therefore, the whole set of phrases are merely analog- ical we shall adhere to the ordinary convention according to which vitreous electricity is reckoned positive, and we shall say that the specific heat of elec- tricity is positive in copper but negative in iron.

The obvious fact that no real fluid can have a negative specific heat need not disturb us, for we do not assert that electricity is a real fluid. 181.] Let us next consider a circuit consisting of two linear conductors of the metals A and B respectively, the two junctions being kept at different temperatures, represented in the diagram by OC and Oc. This electric circuit will be represented in the diagram by the circuit AabBA. If the current flows in the direction AabB till one unit of electricity has been transmitted, the following thermal effects will take place.

(1) In the metal A heat will be generated as the electricity flows from the hot junction to the cold junction. The amount of this heat is represented by the area AaQP A. (2) At the cold junction, where the electricity passes from the metal A to the metal B, heat will be generated. The amount of this heat is represented by the area abSQa. (3) In the metal B heat will be generated as the electricity flows from the cold junction to the hot junction. The amount of this heat is represented by the area bBT Sb. (4) At the hot junction, where the electricity passes from the metal B to the metal A, heat will be absorbed. The amount of this heat is represented by the area BAP T B. The reverse order of the letters shews that this area is to be taken negatively.

MEASUREMENT OF ELECTROMOTIVE FORCE

The whole heat generated is therefore represented by the area AabBT P A, and the whole heat absorbed by BAP T B. The total effect is therefore an absorption of heat represented by the area AabBA. The energy corresponding to this heat cannot be lost. It is transformed into electrical work spent upon the current by an electromotive force acting in the direction of the current. Since the quantity of electricity transmitted by the current is supposed to be unity, the energy, which is the product of the electromotive force into the quantity of electricity transmitted, must be equal to the electromotive force itself.

Hence the electromotive force is represented by the area AabBA, and it acts in the direction represented by the order of the letters—that is, Hot, metal A, cold, metal B, hot. This electromotive force will, if the resistance of the circuit is finite, pro- duce an actual current∗ . It was by means of such currents that the thermo- electric properties of metallic circuits were first discovered by Seebeck in 1822.