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I have been thinking recently about geothermal power and thermoelectric generators. Specifically, I am pondering a design involving a loop of two different metals, about two miles long, placed in a hole drilled into the earth. This would cause the Seebeck Effect between the junctions of the two metals.

Reading the Seebeck coefficient equation: $$V_s=S\Delta T$$

There seems no input for "length of the wire". Is this correct? Are there other practical issues that would cause inefficiencies in such a design?

PhysicsStudent
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1 Answers1

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No, the thermoelectric voltage measured at the cold junction of a thermocouple does not depend on the length of each wire composing the thermocouple.

However, if you increase the length of a thermocouple, you increase the resistances of the wires, thus increasing Joule losses when driving a load, making such kind of thermoelectric generator totally inefficient (and thermoelectric generators, even when designed for maximum efficiency, have a terribly low efficiency).

Furthermore, the difference between the temperatures at the earth's surface and at a depth of 3 km is just around tens of degrees Celsius, and thus the generated thermoelectric power would not be spectacular.

Finally, to obtain a tiny bit of power you would have to use a thermopile, that is, a series of thermocouples where each one would be several kilometres long.

I'm sorry to say that your system would be totally inefficient with a disproportionate cost.

Massimo Ortolano
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