# Derivation of electrical conductivity, Seebeck coefficient and thermal conductivity

 P: 120 1. The problem statement, all variables and given/known data Hi... Don't know if it's actually homework, since it's not, but I hope it's okay to post in here. I am looking for a paper/website/article of some sort, that might have the derivations of the above mentioned coefficients ? It's for calculating the figure of merit: $$Z=\frac{\sigma {{S}^{2}}}{\kappa }$$ 2. Relevant equations The equations if was hoping to maybe find some derivatins of is these three: $$\sigma ={{e}^{2}}\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}$$ $$S=\frac{e{{k}_{B}}}{\sigma }\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}\frac{\varepsilon -\mu }{{{k}_{B}}T}$$ $${{\kappa }_{0}}={{k}_{B}}T\int{d\varepsilon \left( -\frac{\partial {{f}_{0}}}{\partial \varepsilon } \right)\Xi \left( \varepsilon \right)}{{\left[ \frac{\varepsilon -\mu }{{{k}_{B}}T} \right]}^{2}}$$ where: $$$\Xi =\sum\limits_{\overrightarrow{k}}{{{\overrightarrow{v}}_{\overrightarro w{k}}}{{\overrightarrow{v}}_{\overrightarrow{k}}}{{\tau }_{\overrightarrow{k}}}}$$$ 3. The attempt at a solution Don't know if it is possible to find derivations of these, or somewhat similar, or I have to calculate it myself. But I just wanted to try. Thanks in advance. Regards.