# 熱電效應

## 塞贝克效应

${\displaystyle V=\int _{T_{1}}^{T_{r}}S_{\mathrm {B} }(T)\,dT+\int _{T_{2}}^{T_{1}}S_{\mathrm {A} }(T)\,dT+\int _{T_{r}}^{T_{2}}S_{\mathrm {B} }(T)\,dT=\int _{T_{1}}^{T_{2}}\left(S_{\mathrm {B} }(T)-S_{\mathrm {A} }(T)\right)\,dT.}$

SASB是金属A和B的塞貝克係數T1T2是两块金属结合处的温度。塞贝克系数取决于温度和材料的分子结构。如果塞贝克系数在实验的温度范围内接近常数，以上方程可以近似成：

${\displaystyle V=(S_{\mathrm {B} }-S_{\mathrm {A} })\cdot (T_{2}-T_{1}).}$

## 完整熱電方程式

${\displaystyle \mathbf {J} =\sigma (-{\boldsymbol {\nabla }}V-S\nabla T).}$

${\displaystyle {\dot {e}}=\nabla \cdot (\kappa \nabla T)-\nabla \cdot (V+\Pi )\mathbf {J} +{\dot {q}}_{\text{ext}},}$

${\displaystyle \kappa }$熱導率。第一項是傅里葉熱傳導定律，第二項表示電流攜帶的能量。第三項${\displaystyle {\dot {q}}_{\text{ext}}}$是從外部熱源輸入的熱量(如果適用的話)。

${\displaystyle -{\dot {q}}_{\text{ext}}=\nabla \cdot (\kappa \nabla T)+\mathbf {J} \cdot \left(\sigma ^{-1}\mathbf {J} \right)-T\mathbf {J} \cdot \nabla S.}$

## 参考文献

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