# Is there a theoretical efficiency limit for thermoelectric generators?

Typical Thermoelectric/Seebeck generators operate at 5-8% efficiency.

Is there an upper limit to the conversion of heat flux (temperature differences) directly into electrical energy?

• The upper limit for a heat engine is the Carnot efficiency. Commented Oct 23, 2021 at 14:45

yes, it's the Carnot limit. Efficiency is given by

$$\eta = \frac{T_h-T_l}{T_h} * \frac{\sqrt(1+ZT_m)\,-\, 1}{\sqrt(1+ZT_m)\,+\,T_l/T_h}$$ with $$Z= \frac{S^2 \sigma}{\kappa}$$

S Seebeck coefficient

$$\sigma$$ electrical conductivity

$$\kappa$$ thermal conductivity

for Z called thermoelectric figure of merit there is no limit, although practically we have around 1 - 1,5

Reference for diagrams (sorry in German, but I am sure there a lot of other good papers in English):

Thermoelectric Generators

I think the constraint inefficiency is mostly common thermal conduction, that most of the thermal energy is lost that way. What about insulating the two electrodes from heat conduction and instead rely on heat radiation and use photovoltaics to transform the radiation to electricity? Let the heat side use a material that transmits its energy in a form that the recipient photovoltaic side is most receptive of. This is strictly speaking not a Seebeck device but it is a thermoelectric generator.