Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section B / 12 / ii / Solution

A generator couple has a p-type and an n-type thermoelement joined electrically at the hot face, with their other ends connected through a load at the cold face. The legs are electrically in series and thermally in parallel. Electrically insulating, thermally conducting plates couple them to the hot source and cold sink; metal interconnects carry current. The Seebeck effect provides an open-circuit electromotive force $\mathcal{E}={\alpha }_{np}\Delta T$, where the magnitude of ${\alpha }_{np}$ is the difference between the two leg Seebeck coefficients.

For fixed junction temperatures, constant properties and internal resistance $R$,Differentiate with respect to load resistance:The derivative changes from positive to negative at $R_L=R$, soThe load voltage is then half the open-circuit voltage. The heat source and sink must sustain the temperature difference; an isolated hot object cools as energy is extracted. Maximum power and maximum conversion efficiency are different operating points: the efficiency-optimal load is generally larger than $R$.