Why do we assume that Joule heating in a thermoelectric leg is evenly divided towards the hot and cold junctions?
What is the thermodynamic principle behind this assumption?
Any detailed explanation would be highly appreciated.
Dear Omar,
Your questions are interesting and useful.
Thermoelectric effect is used to generate an electromotive force between the terminals of two different material junctions when one of the junctions is held at higher temperature than the other. The device is constructed such that the outer terminal material is different from the inner material. The emf induced is proportional to the temperature difference between the two junctions and the contact difference of potential. The two materials are either semiconductors or metals. Semiconductor is preferred for the inner material because it has relatively lower thermal conductivity than metals which leads to sustaining a higher temperature gradient between the the hotter and the colder junction. So, from the principle point of view the maximum temperature difference between the hotter and the colder junction is limited by the thermal resistance of the inner material and the heat flow rate from the hotter to the colder junction. So, it is a matter of heat transfer through the the inner material between the hotter and the colder junction. Therefore the device works better when the the thermal resistance between the two junction increases.
Mathematically expressed:
T2-T1= Rth * q with Rth is the thermal resistance and q is the rate of heat flow or the thermal flux.
wish you success
@Omar. Yes, the assumption 'Joule heating in a thermoelectric leg is evenly divided towards the hot and cold junctions' is based on thermodynamic principle. It is based on the first law of thermodynamics (energy balance in a thermoelectric leg) combined with one dimensional heat conduction equation with internal heat generation. This derivation has been explicitly derived in the Book "Electronic refrigeration" by Prof. H J Goldsmid, (Page No: 8-9).
Note: Page 8-9 of the book is attached as image file for your reference.
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