The Thomson effect describes the heating or cooling of a current-carrying conductor when a temperature gradient exists along its length. Heat is produced or absorbed when current flows through a material with a temperature gradient. The rate of heat production per unit length is given by [latex]\frac{dQ}{dx} = -\mathcal{K} J \frac{dT}{dx}[/latex], where [latex]\mathcal{K}[/latex] is the Thomson coefficient.
The Thomson effect arises because the Seebeck coefficient of a material is generally dependent on temperature. As charge carriers move along a conductor from a hot region to a cold region (or vice versa), their average energy changes not only due to the temperature but also due to the changing Seebeck coefficient. When an electric current (J) flows through a conductor with a temperature gradient ([latex]frac{dT}{dx}[/latex]), this effect becomes apparent.
If the current flows in the same direction as the heat flow (from hot to cold), heat may be absorbed or released depending on the sign of the Thomson coefficient ([latex]mathcal{K}[/latex]) for that material. This heating or cooling is distinct from and superimposed upon the irreversible Joule heating ([latex]I^2R[/latex]) that always occurs. The Thomson effect is crucial for a complete 热力学 description of thermoelectric phenomena and is linked to the Seebeck and Peltier effects through the Kelvin relations, which are foundational to the field.
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