Solution (source code)

= Solution

A <thermoelectric generator> uses the <Seebeck effect> and needs a spatial <temperature gradient>: a couple develops $V\simeq(S_p-S_n)\Delta T$ between hot and cold junctions. It can deliver continuous power under a steady thermal gradient and has no moving parts, but requires sustained heat flow and adequate hot- and cold-side thermal contacts. Thermal conduction, internal <electrical resistance> and the material's <thermoelectric figure of merit> limit conversion.

A <pyroelectric generator> responds to a time-dependent spontaneous <electric polarization>. Under approximately uniform heating or cooling, $I=pA\,dT/dt$ when the electrical boundary condition allows charge flow. It can harvest temporal thermal fluctuations without a persistent spatial gradient. However, at a constant uniform <temperature> its ordinary pyroelectric current stops; practical extraction needs cycling, low-leakage electronics and a suitable load. A large open-circuit voltage is not evidence of a large available average power. Temperature-driven nanowire measurements provide a primary experimental example of this distinction.<Pyroelectric nanogenerators for harvesting thermoelectric energy by Ya Yang and others>[Nano Letters 12 (2012), abstract and temperature-variation mechanism]{ref}