## The Seebeck Effect

Consider a length of pipe filled with a gas that is at uniform temperature. Clearly, both pressure and concentration are also uniform. However, if one end of the pipe is heated to a higher temperature than the other, the higher pressure on the hotter side will cause some flow of gas toward the colder end. When steady state is reestablished, the flow ceases and the pressure is again uniform. According to the perfect-gas law, p = nkT, constant pressure means the nT product is also constant. Consequently, the concentration of the gas will be higher at the colder end than at the hotter end of the pipe.

^A fuller treatment of this subject is found in Goldsmid (1986).

Conduction electrons also behave as a gas. If there is a temperature gradient, their concentration in a conducting bar will be higher in the cold side, which, as a consequence, becomes negatively charged with respect to the hotter. The resulting electric potential is the Seebeck voltage, a quantity that depends both on the temperature difference and on the nature of the conductor. If the carriers in the bar are holes, then the colder side will become positive with respect to the hotter. Thus, the polarity of the Seebeck voltage depends on the material of the conductor.^

An external connection is needed to tap into the voltage developed in the conducting bar. However, the external wire is submitted to the same temperature differential as the bar itself and will develop its own Seebeck voltage. If the external wire is made of the same material as the bar, the two voltages exactly cancel one another. If, however, the connection is made with a different material, then a net voltage may become available.

A thermocouple must always consist of two dissimilar materials, most often of opposing polarity so that the individual Seebeck voltages add up. Since the external connections wires are attached to the open ends of the thermocouple, which presumably are at the same temperature, these wires contribute no additional thermoelectric voltage.

Thermocouples are low-impedance devices (low voltage and large current) and, for many applications, must be connected in series forming a thermoelectric battery. See Figures 5.18 and 5.19.

In a thermocouple battery, individual cells are electrically in series and thermally in parallel. Thus, if A is the heat conductance of one single cell, then nA is the heat conductance of a battery of n cells. By the same token, the resistance of the battery is nR when R is the resistance of one

Short circuit