Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 1 / Section A(iii) / 6

A thermoelectric generator uses the Seebeck effect: a maintained temperature difference across suitable conductors produces an open-circuit electromotive force. For a pair of legs,when the effective Seebeck coefficient is approximately constant. Repeated p- and n-type legs are usually connected electrically in series and thermally in parallel.

Connecting a load lets part of the heat flowing from the hot side to the cold side become electrical power. Both a heat source and a cold-side heat-removal path are necessary: a uniformly warm device with no maintained temperature difference supplies no sustained output. Internal electrical resistance, heat leakage, contact losses and the finite temperature difference reduce the harvested power; the converter is a heat engine rather than a source of energy from temperature alone.

The same current flows through both resistances, $I=V_{\mathrm{oc}}/(R+R_L)$. The load terminal voltage is $I{R}_L$, smaller than the open-circuit voltage. The electrical battery symbol represents the maintained thermoelectric source under this model; heat input is still required.

At fixed temperature difference and constant internal resistance,Differentiation givesIt is positive below $R_L=R$ and negative above it, while power vanishes for an open or shorted load. Therefore the maximum power transfer theorem givesAt this point $I=V_{\mathrm{oc}}/(2R)$ and half the electromotive force drops across the load. Maximum electrical power is not generally maximum thermal-conversion efficiency. If changing current also changes the temperature difference because the thermal source has finite impedance, the fixed-$\Delta T$ optimization must be reconsidered.