PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

Excerpts

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  It is manifest that in a heterogeneous circuit we cannot determine the electromotive force acting from the point A to the point B by simply connecting these points by wires to the electrodes of a galvanometer or electrometer, for we are ignorant of the electromotive forces acting at the junctions of these wires with the matter of the circuit at A and B.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  In this treatise we have avoided making any assumption that electricity is a body or that it is not a body, and we must also avoid any statement which might suggest that, like a body, electricity may receive or emit heat.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  During the passage of one unit of electricity through any section of the circuit one electrochemical equivalent of each of the electrolytes is electrolysed. There is therefore a definite amount of chemical action corresponding to a definite quantity of electricity passed through the circuit.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  It does not appear that there is much polarization at the surface of the zinc plate when immersed in a solution of sulphate of zinc or in dilute sulphuric acid. The principal seat of polarization is at the surface of the negative metal.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  When the current flows through the solution from the zinc to the copper no hydrogen appears on the copper plate, but copper is deposited on it.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  Seebeck, in 1822, discovered that if a circuit is formed of two different metals, and if the two junctions of the metals are kept at different temperatures, an electric current tends to flow round the circuit.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  Thomson has shewn that a very close analogy subsists between these thermo-electric phenomena and those of a fluid circulating in a tube consisting of two vertical branches connected by two horizontal branches.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  We may, however, without any such assumption, make use of the idea of entropy, introduced by Clausius and Rankine into the theory of heat, and extend it to certain thermo-electric phenomena, always remembering that entropy is not a thing but a mere instrument of scientific thought, by which we are enabled to express in a compact and convenient manner the conditions under which heat is emitted or absorbed.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  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.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  The only method by which we can determine where the electromotive force acts is that of measuring the heats generated or absorbed during the transmission of a unit of electricity from A to B.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  Let E be the electromotive force of the circuit; then the work done in driving one unit of electricity through the circuit is numerically equal to E.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  ‘The electromotive force of an electrochemical apparatus is in absolute measure equal to the mechanical equivalent of the chemical action on one electrochemical equivalent of the substance.’

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  Thus in a battery the electrodes of which are connected by a short thick wire the current is very strong and the heat is generated principally in the cells of the battery and to a much smaller extent in the wire; but if the wire is long and thin, the heat generated in the wire is far greater than that generated in the cells, but if we take into account the heat generated in the wire as well as that generated in the cells, we find that the whole heat generated for each grain of zinc dissolved is the same in both cases.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  Or if the circuit includes an electromagnetic engine which is employed to do work, the heat generated in the circuit is less than that corresponding to the zinc consumed by an amount equal to the heat which would be generated if the work done by the engine were entirely expended in friction.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  It is only the strictly reversible processes that must be taken into account in calculating the electromotive force of the circuit.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  The principal seat of polarization is at the surface of the negative metal. When the fluid in which the negative metal is immersed is dilute sulphuric acid, it is seen to become covered with bubbles of hydrogen gas, arising from the electrolytic decomposition of the fluid.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  The only difference is that diffusion is always going on, while the current flows only when the battery is in action.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  These defects, however, are more than counterbalanced in all cases where exact measurements are required, by the fact that Daniell’s cell exceeds every other known arrangement in constancy of electromotive force.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  In a voltaic circuit the sum of the electromotive forces from zinc to the electrolyte, from the electrolyte to copper, and from copper to zinc, is not zero but is what is called the electromotive force of the circuit---a measurable quantity. Of these three electromotive forces only one can be separately measured by a legitimate process, that, namely, from copper to zinc.

Equations

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  a - b - x = 0

  Around a circuit of three metals A, B, C at one temperature, the total electromotive force is zero, so the force from B to A equals a minus b.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  (\phi_2 - \phi_1)(t - t_1)

  The Peltier effect at a junction is of this form, the product of the increase in thermo-electric power and the temperature measured from a reference point below any observed temperature.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  (\phi_2 - \phi_1) \theta

  By the second law of thermodynamics the heat absorbed at the junction may be written as the difference of thermo-electric powers times the absolute temperature.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  \xp\dfrac{H}{\theta}

  A body receiving a quantity of heat H at temperature theta increases its entropy by H divided by theta.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  QE = H\text{,}

  The work done by a current Q carried across a region against an electromotive force E equals the heat H generated in that region, by conservation of energy.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  (b-a)\theta+B-A\text{.}

  The total electromotive force round the circuit ABC is the thermo-electric term (b minus a) times theta plus the electrolytic terms B minus A.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  JH &= Jh + E

  The work equation at the anode: the chemical heat JH equals the heat generated there, Jh, plus the work E done in driving the current.

• PHENOMENA OF AN ELECTRIC CURRENT WHICH FLOWS THROUGH HETEROGENEOUS MEDIA

  E &= J(H - h)\text{.}

  The electromotive force from metal to electrolyte is the mechanical equivalent of heat times the difference between total chemical heat and heat generated at the electrode.

Problems

No exercises in this chapter.