PART IV. THERMO-ELECTRICITY

CHAPTER X

THERMO-ELECTRICITY

498. Thermo-Electric Junction. In 1821, while making experiments on the difference of potential which appears to exist between two different metals when placed in contact (see § 545), Seebeck noticed that if a circuit is formed which is composed of two wires of different metals joined together at their ends, and if the junctions are at different temperatures, a current will in general be produced in the circuit. Thus if two copper wires, which are connected to the terminals of a galvanometer, are connected at their other ends to a piece of iron wire, and one of the junctions of the copper and iron is heated, a current will be indicated by the deflection of the galvanometer. The direction of the current will be from the hot to the cold junction in the iron. current is said to be a thermo-electric current.

This

If, while the cold junction is kept at a constant temperature, the temperature of the hot junction is gradually raised, the current in the circuit will gradually increase up to a certain point, this temperature being called the neutral point for the two given metals. If the temperature of the hot junction is raised above the neutral point the current in the circuit will decrease, till, when the temperature of the hot junction is as much above the neutral point as that of the cold junction is below, there will be no current in the circuit; while if the temperature of the hot junction is yet further raised, the direction of the current will be reversed.

It is possible to arrange the metals in a series such that if wires of any two of them are joined together to form a circuit, and one of the junctions is heated, the thermo-electric current will in the first metal on the list go from the hot junction to the cold, it being supposed that the mean temperature of the hot and cold junctions has some given value. The following is such a thermo-electric series for a mean temperature of about 50° C. : antimony, iron, zinc, silver, tin, copper, bismuth. Of course the order of the metals will vary with the temperature, for the neutral temperature for some of the combinations is quite low, and the neutral points for the different combinations vary very much.

499. Thermo-Electric Power and Thermo-Electric Diagrams.f we take some metal as a standard-lead is the one usually takennd form a thermo-electric couple between this metal and another, and

attach a lead wire to the other end of this second metal, then, if while the temperature of one of the lead-metal junctions is kept constant, say at o° C., the temperature of the other junction is raised to different temperatures, there will be produced a difference of potential between

the free ends of the lead wires. This difference of potential is the thermo-electric E.M.F. due to the temperature difference between the hot and cold junctions. If a series of measurements of this thermoelectric E.M.F. is made for different temperatures of the hot junction, that of the cold junction being kept constant at o C., and the results are plotted on a curve, the temperatures of the hot junction being taken as abscissæ and the corresponding E.M.F.'s as ordinates, a curve of the form of those shown in Fig. 476 will be obtained. These curves represent the thermo-electric E.M.F.'s of some metals taken with reference to lead in terms of microvolts, ie. 10 volts, and degrees Centigrade.

Since in each case the temperature of the one junction is kept constant at o C., and that when the temperatures of the two junctions is the same the thermo-electric E.M.F. is zero, all the curves must pass through the origin of co-ordinates. The temperatures at which the curves have a horizontal tangent, that is, when the E. M.F. is a maximum in one direction or the other, is the neutral temperature for the given metal taken with reference to lead. Thus the temperature of the neutral point for a platinum-lead couple is - 150°, and that for a zinc-lead couple is - 200°.

It is found that the curves showing the relation between the thermoelectric E.M.F., E, and the temperature, t, of the hot junction, the other junction being at o°, is approximately a parabola. Hence, since the equation of a parabola can be written in the form

y=ax+2x2,

where a and b are constants, the relation between the thermo-electric E.M.F. and the temperature can be expressed by a formula of the form

where the values of a and b depend on the nature of the metal. Those who are acquainted with analytical geometry will see that the maximum value of E occurs when is equal to -ab. Hence there exists the following relations between the constants a and b, the neutral temperature, and the E.M.F. E' of the junction, when one junction is at o° and the other is at the neutral temperature

t' = - ab, E' = -a2/2b.

In the following table the values of the coefficients a and b for a few metals are given. The sign of a is such that when at the hot junction the current passes from lead to the given metal a is positive, or, in other words, when a is positive the current flows in the metal considered from the hot junction to the cold. The values of the constants are so chosen

that if is measured in degrees Centigrade the thermo-electro-motive force is given in microvolts, that is, in 106 volts.

Suppose that the thermo-electric E.M.F. between a given metal, A, and lead when the cold junction is at o° and the hot junction is at a temperature 1 is E, then we have seen that

E=at+t

2

Suppose now that the temperature of the hot junction is raised through a small interval dt, so that it becomes t+dt, then, if the new value of E is called E+SE, we have

or, since by supposition &t is very small, we may neglect the term which involves the product of the square of this very small quantity into b, which, as will be seen from the table, is itself small. Hence

If now we subtract the value of the E.M.F. at from that at 1+dt, we get

SE=ast+btôt.

That is, an increase, ot, in the temperature of the hot junction produces an increase of SE or adt + btôt in the E.M.F. Now the ratio of the increase in the E.M.F. produced by a small rise in the temperature of the hot junction to this increase in temperature, or, in other words, the rate of increase of E.M.F. with temperature, is called the thermo-electric power of the metal A with respect to lead at the temperature . If Q is the thermo-electric power, then

Q=a+bt.

This expression shows that the thermo-electric power varies as the first power of the temperature, so that if a curve is drawn such that the abscissæ are temperatures and the ordinates are the corresponding values of the thermo-electric power, this curve will be a straight line. This is at once evident if the constant term a is subtracted, which is equivalent

to decreasing all the ordinates by the same amount, when the new ordinates will be 6 times the corresponding abscissæ, that is, the ordinates are directly proportional to the abscissæ, and hence the curve must be a straight line.

In Fig. 477 the lines showing the connection between the thermoelectric power and the temperature are given. Such a series of curves are called a thermo-electric diagram, and from them we can deduce the different thermo-electric properties of various combinations of metals.

Before considering this diagram in detail, we must consider two laws which have been found by experiment to hold in all thermo-electric circuits. The first of these is that if E, is the E.M.F. acting round a circuit composed of two metals when the temperature of the cold junction is t, and that of the hot junction is to, and E, is the E.M.F. when the temperature of the cold junction is 1 and that of the hot junction is t

then the E.M.F. when the temperature of the cold junction is t, and that of the hot junction is t will be E1+ E. But we have seen that if the temperature of the hot junction is increased by 8t the E.M.F. is increased by Qôt, where 2 is the thermo-electric power at the temperature Hence the E.M.F., when the temperature of the hot junction is t, will be the sum of the quantities obtained by multiplying the values of Q for each interval St, starting at the temperature of the cold junction, by the interval and continuing the process up to the temperature t.

The second law is that if we have a circuit containing three metals, A, B, and C, and keep the junctions BC and CA both at the same temperature, f, while the junction AB is kept at the temperature, then the E.M.F. acting in the circuit will be the same as that which would exist in a circuit composed of the metals A and B alone, in which one junction was kept at the temperature t, and the other at t. Thus the inter