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Equations are solved to give the variations in temperature, density, and potential, when a solid has electrical currents, heat currents, and particle diffusion. Solutions are presented in one dimension for currents down a bar. These solutions are used to calculate the efficiency of a thermoelectric refrigerator, which is optimized to give the coefficient of performance (COP). The COP depends upon the temperature difference ΔT, but does not depend upon the density difference Δn between the two ends of the bar.
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G. D. Mahan (2000) studied this question.
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