Thermoelectric phenomena

As a first illustration of the theory presented in the last two sections, let us consider thermoelectric effects which involve the flow of heat Jq and electric current Ig in conducting wires (in which the subscript indicates that the flow corresponds to the flow of electrons). The entropy production per unit volume due to these two irreversible processes and the Unear phenomenological laws associated with it are 

Fourier s law (16.1.3) of heat conduction is valid when the electric field E = Q. Comparing the heat conduction term Jq = — /T )LqqdT/dx to Fourier s law (16.1.3), leads to the identification 

We can now specify more precisely what is meant by the near-equilibrium linear regime. It means that Lqq, Lee, etc., may be treated as constants. Since T x) is a function of position, such an assumption is strictly not valid. It is valid only in the approximation that the change in T from one end of the system to another is small compared to the average T, i.e. if the average temperature is Tavg, then r(x) — Tavgl/ Tavg 1 for all x. Hence we may approximate and use Kr g in place of kT.  

To find the relation between Lee and the resistance R, we note that V = — A(t) = IqEdx in which I is the length of the system. The current is independent of x. At constant temperature (ST/0jc = 0), the current is entirely due to electrical potential difference. Integrating (16.3.5) over the length of the system, we obtain 

Comparing this equation with Ohm s law (16.1.5a), we make the identification 

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The primary thermoelectric phenomena considered in practical devices are the reversible Seebeck, Peltier, and, to a lesser extent, Thomson effects, and the irreversible Eourier conduction and Joule heating. The Seebeck effect causes a voltage to appear between the ends of a conductor in a temperature gradient. The Seebeck coefficient, L, is given by... 

Besides the reversible production of heat at the junctions, there is an evolution of heat all round the circuit due to frictional resistance, this Joule s heat being proportional to the square of the current, and hence not reversed with the latter. There is also a passage of heat by conduction from the hotter to the colder parts. But if the current strength is reduced, the Joule s heat, being proportional to its square, becomes less and less in comparison with the Peltier heat, and with very small currents is negligible. We shall further assume that the reversible thermoelectric phenomena proceed independently of the heat conduction, so that the whole circuit may be treated as a reversible heat... 

In a thermocouple, heating one junction of a bimetallic couple and cooling the other produces electromotive force in the circuit. This observation was originally was made by Seebeck in 1821. Besides the use of thermocouples, transistor electronics and semiconductors are important areas of interest for thermoelectric phenomena. Thermocouples made of semiconductors can develop relatively large electromotive potentials and are used to convert heat into electricity. 

Joule s law is strictly accurate so long as the conductor in which the evolution of heat is measured is homogeneous and at a uniform temperature throughout. If these conditions are not complied with, deviations from the law are obtained, and the evolution of heat is found to be no longer completely irreversible. By raising the temperature of certain parts of the circuit, electric currents can now be obtained. These reversible phenomena are called thermoelectrical phenomena in the more restricted sense of the term. In common with all other reversible processes, they must follow certain regularities, which are deter-... 

Since electrical energy can be converted at will into mechanical energ ", a thermoelectric current, is capable of doing work at the expense of the heat which is supplied from the outside to the circuit at the hot junction (E >E. In his classical thermodynamical theory W. Thomson assumed that the thermoelectrical phenomena were strictly reversible, except for the production of Joule heat, which becomes negligible as the current strength approaches zero. In this limiting case, therefore, the heat produced or absorbed at the junctions is equal... 

An elementary thermocouple circuit is shown in Fig. 16.16. The EMF generated in this circuit is a function of the materials used and the temperatures of the junctions. It is useful to describe briefly the basic thermoelectric phenomena or effects that are related to the Seebeck effect and are present in thermocouple measurements. They include two well-known irreversible phenomena—Joule heating and thermal conduction—and two reversible phenomena—the Peltier effect and the Thompson effect. 

There are three thermoelectric phenomena that result from correlation between propagation of heat through a conductor and displacement of the current carriers in the conductor. The Seebeck effect (Ref 1) consists of formation of an electric current in an electrical circuit formed by two dissimilar conductors if the contacts between the conductors are held at different temperatures. A reverse phenomenon, the Peltier effect (Ref 2), consists of formation of a temperature difference between the contacts in a circuit of this type if an electric current is created in the circuit by an external current source to which the circuit is connected. W. Thomson (Lord Kelvin), who explained both effects (Refs. 3,4), predicted and experimentally confirmed the existence of another thermoelectric phenomenon, named the Thomson effect, which consists of absorption or release of heat in a uniform conductor with a current passing through it when a temperature gradient (positive or negative) is present along the current direction. 

The terminology of EPH originated from the thermoelectric phenomena in Physics. Dated back to more than 100 years ago, such as the Seebeck effect, the Peltier effect and the Thomson effect were successionally discovered. The Peltier heat was first found by the French physicist Peltier in 1834. The Peltier effect shows that the heat flow would be generated on the junction between two different metals in an electric current circumstance. The junction acts as a heat sink or as a heat source, which depends on the direction of the electric current. And the strength of the heat was found to be proportional to the current intensity. The Peltier effect can express as [35]... 

Phenomenological equations possessing this form have been used to describe thermo osmosis and thermoelectric phenomena. 

Tritt, T. M. (2011). Thermoelectric phenomena, materials, and applications. Annual Review of Materials Research, 41, 433-448. 

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