ELECTRICAL) .
The electromagnetic unit of potential difference is defined to be a potential difference such that the work required to move one electromagnetic unit of charge across it is equal to one erg. The practical unit of potential difference is called a volt, and is de fined to be a potential difference such that the work required to take one coulomb across it is equal to ten million ergs. Since the coulomb is one-tenth of an electromagnetic unit of charge, it follows that the volt is equal to one hundred million, or Tog, electromagnetic units of potential difference. The potential dif ference, in electromagnetic units, between two points in an electric field is equal to the work per electromagnetic unit of charge required to move a charge from one point to the other.
This result is known as Ohm's Law. The ratio of the current to the potential difference is called the conductivity of the wire, and the reciprocal of the conductivity is called the resistance. The practical unit of resistance is called an ohm, and is defined to be a resistance such that a potential difference of one volt pro duces a current through it of one ampere. If a potential difference P volts between the ends of a wire gives a current C amperes, the resistance R of the wire in ohms is given by R = P/C. It is found that the resistance of a wire is proportional to its length and inversely proportional to its cross section. Thus the resist ance R of a wire of length l and cross section a is given by R = pl/a, where p is a constant which depends on the nature and physical state of the material of the wire. This constant p is called the spe cific resistance of the material. (See ELECTRICITY, CONDUCTION OF.) The methods of measuring resistances are described in the article INSTRUMENTS, ELECTRICAL.
A unit of power frequently used in electrical engineering is the watt, which is equal to ten million ergs per second. Thus, since the electrical energy of a current of C amperes flowing across a potential difference of P volts is CPX Io' ergs per sec., we see that the product CP is equal to the electrical power in watts. A kilowatt is a power of one thousand watts.
Thermoelectricity.—If a circuit is made by joining the ends of two wires of different metals, e.g., iron and copper, it is found that, if one of the junctions is kept at a higher temperature than the other, a current flows round the circuit. In the case of iron and copper, the direction of the current is from copper to iron at the hotter junction, provided the average temperature of the two junctions is less than about 600° C. Currents so obtained are called thermoelectric currents, and the branch of electricity dealing with such phenomena is called thermoelectricity.
If a current from a battery is passed through a wire consisting of two different metals, it is found that there is an evolution of heat at the junction between the two metals when the current is in one direction, and an absorption of heat when the current is in the other direction. The heat absorbed when a current C is passed for a time t is equal to irCt, where it is a constant de pending on the metals used and on the temperature of the junc tion. With iron and copper at the ordinary temperature, heat is absorbed when the current flows from copper to iron across the junction. This effect is called the Peltier effect after its dis coverer. The constant 7r is called the Peltier coefficient. Com paratively large thermoelectric effects are obtained in several cases with two metals having very similar properties; e.g., bis muth and antimony, or iron and nickel, give large thermoelectric currents. Large effects are also obtained in many cases with a metal and one of its alloys with a small amount of some other metal.
Another thermoelectric effect was discovered by William Thomson (Lord Kelvin). He found that there is a reversible heat effect in a wire when a current flows between two points in the wire which are at different temperatures. If one point A is at a temperature and the other point B at a temperature and a current C flows in the wire from A to B, then the re versible heat H developed in the wire in a time t is given by H = where o- is a constant depending on the nature of the wire. This constant Q is called the specific heat of the electricity in the wire, and the effect is called the Thomson effect. This heat effect is said to be reversible, because it changes from an absorption of heat to an evolution when the current is re versed. In this way it can be distinguished from the ordinary heating effect of a current in a wire, which, as we have seen, varies as the square of the current and is always an evolution of heat. The specific heat of electricity is positive in some sub stances and negative in others. The Thomson effect can be demonstrated easily by passing a current through a U-shaped piece of platinum wire so that it is heated to a red heat. If then the lower end of the U is dipped into water, one side of it becomes visibly hotter than the other. On one side the current is flowing down from the hot end to the cold end, and on the other side the current is flowing up from the cold end to the hot end. The specific heat of electricity is negative in platinum, so the side on which the current is going up is the hotter.
If a circuit is made up by joining together several pieces of wire of different materials, and if all the junctions are kept at the same temperature, there is no current. If the temperature of one only of the junctions is raised, then the current is the same as that which would be obtained in a circuit of the same resist ance, composed of the two metals at the heated junction. It is supposed that there is a potential difference between two metals at a junction between them, and that this potential difference varies with the temperature of the junction. If we have a circuit consisting of three metals A, B and C, and if V B denotes the potential difference between A and B, then, if all three junctions are at the same temperature we have, since there is no current, VA B+ VCA = 0, or VAB = VAC - VBC. This is known as the law of intermediate metals. The theory of the thermocouple, and its use for measuring temperature, are described under THER MOMETRY.
The Thermodynamical Theory of Thermoelectricity, due to Lord Kelvin, is, based on the assumption that the electrical energy developed is derived from the reversible heat effects in the circuit. The ordinary non-reversible heat effect is proportional to the square of the current, and so becomes negligible compared with the reversible effects when the current is very small. We may suppose an electromotive force applied to the circuit nearly equal and opposite to the thermoelectromotive force, so that the current is kept very small and can be reversed by changing slightly the applied electromotive force.
According to the second law of thermodynamics the sum of the amounts of heat absorbed, each divided by the temperature at which it is absorbed, is equal to zero, hence This, with P gives ir=PT and TdP/dT= — (a'A It is found experimentally that a for lead is practically zero, so that, in the case of a circuit consisting of a wire of lead and a wire of the metal B, we have TdP/dT It was shown by P. G. Tait, that, with circuits of any metal, or any alloy, and lead, the thermoelectric power P is a linear function of the temperature T, so that P = a+bT, where a and b are constants depending on the nature of the metal or alloy. Hence o-= bT.
If the electromotive force of a circuit of any two metals with the junctions at and is E,, and with the junctions at and T2 is E2, then, with the junctions at and it is found to be It follows from this that the electromotive force E of a circuit with junctions at temperatures and T2 is given by the Tait found that his experimental values of E could be repre sented quite accurately by this parabolic expression. If the mean temperature of the two junctions is equal to then E= o.
The electromotive force of a circuit of the two metals A and B is equal, as we have seen, to E—E', or to + 2 (b — b') — . The thermoelectric power of the circuit d(E—E')/dT is therefore equal to a—a'+(b—b')T, or to P—P'. It appears that, if we know the values of a and b for circuits of different metals and lead, we can easily calculate the electro motive forces, thermoelectric powers, Peltier coefficients and specific heats of electricity for circuits containing any of the metals. If 0 denotes the temperature on the centigrade scale, so that T = 6+273, then P = a + bT = a+ 273b + be; or if a=a+273b, then P=a+b9.
The following table gives the values of a and b for several metals and lead. These values give P in micro-volts per degree C. The neutral point is equal to — (a/b) °C.
Metal a b Metal a b Sodium . • —4.4 —0.02r Bismuth . —86 —o•65 Copper . . 2.8 o•oo8 Iron i3.4 —0.032 Magnesium . Nickel . . —0.030 Zinc . . 2.5 o•oi6 Cobalt . . Mercury . —3.r7 —0.0i73 Platinum . — 3.0 Antimony . 24 .. Constantan . —34.3 —o•o6o The values of these constants depend on the state of purity and physical condition of the metal.
For the applications of the thermoelectric effect to temperature measurement see THERMOMETRY.