Module 4 : THERMOELECTRICITY
Lecture 21 : Seebeck Effect
  We can represent the effect of the thermal gradient responsible for the diffusive motion of the carriers by an effective field $\vec E^\prime$. This effective field is proportional to the thermal gradient and can be written as
\begin{displaymath}E^\prime = \sigma\frac{dT}{dx}\end{displaymath}
  where $\sigma$ is known as the Thomson coefficient for the material of the conductor. The Thomson electromotive force ${\cal E}_{Th}$ is given by
 
\begin{displaymath}{\cal E}_{Th} = \int E^\prime dx = \int_{T_1}^{T_2}\sigma dT\end{displaymath}
  where $T_1$ and $T_2$ are the temperatures at the two ends of the rod.
  Thomson effect is a manifestation of the Thomson emf described above. Clearly, one cannot demonstrate the existence of the emf by using it to drive a current in a close circuit. This is because if one uses a single metal with a temperature gradient, the integral around a close loop is zero. For dis-similar metals, Peltier effect dominates over Thomson effect.
When a current is passed through a homogeneous conductor with a temperature gradient, the rate of heat production per unit volume is given by
 
\begin{displaymath}\dot Q = \rho I^2 - \sigma I \frac{dT}{dx}\end{displaymath}
 
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