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The physics principle involved is the "thermoelectric effect" or "Seebeck effect". It was discovered in 1821, by a German physicist Thomas Johann Seebeck. He discovered that when any conductor is subjected to a thermal gradient, it will generate a voltage. By using a dissimilar metal connected to the original metal to complete the circuit creates a circuit in which the two "legs" generate different voltages, leaving a small difference in voltage available for measurement. That difference increases with temperature, and is between 1 and 70 microvolts per degree Celsius (V/C) for standard metal combinations. Such device is a "thermocouple".
A thermocouple can produce current, which means it can be used to drive some processes directly, without the need for extra circuitry and power sources.
Thermocouples can be connected in series to form a "thermopile", where all the hot junctions are exposed to a higher and all the cold junctions to a lower temperature. The output is the sum of the voltages across the individual junctions, giving larger voltage and power output. Using the radioactive decay of transuranic elements as a heat source, this arrangement has been used in "nuclear batteries" to power spacecraft.
On earth, thermopiles can be used to generate electricity from the heat collected by solar panels.