What is thermoelectric generation?

Drawing electricity directly from heat by exploiting the Seebeck effect: a temperature difference across joined dissimilar semiconductors produces a voltage. With no moving parts, silence and long life, it is used for waste-heat recovery, spacecraft power (from radioisotope heat) and self-powered sensors.

How efficient is thermoelectric generation?

It depends on the material figure of merit ZT and the temperature difference. Between 500 K and 300 K, against a 40% Carnot limit, ZT = 0.5 gave 4.9%, 1 gave 8.2% and even 2 gave 12.6%. Common materials today (such as bismuth telluride) have ZT around 1, so efficiency is a few percent to about 10%.

How can thermoelectric output be raised?

Heat-exchanger design often matters more than the module itself. In the example, even with 200 K available between hot and cold sides, 1 K/W resistance on each side left the module only 100 K, and output was 25% of ideal; 0.5 K/W raised it to 44%. Balancing module and heat-exchanger resistances is key.

Thermoelectric Conversion (Power Generation) Analysis

Category: Electronics Cooling | Revised 2026-10-01

CAE visualization for thermoelectric theory - technical simulation diagram

Thermoelectric Cooling (Peltier Element)

Theory: drawing voltage from a temperature difference

Overview

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I want to generate thermoelectric power from factory exhaust heat. How do I estimate how much?

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Thermoelectric generation uses the voltage the Seebeck effect produces across semiconductor elements under a temperature difference. Estimation has two stages. First, the efficiency ceiling set by the material, from figure of merit ZT and Carnot efficiency. Second — the important one — the temperature difference actually across the module. The heat exchangers carrying heat from exhaust to module and from module to coolant have their own resistances, so only part of the total difference falls on the module. Output scales with that difference squared, so misjudging it throws the estimate far off.

Maximum efficiency

$$ \eta_{max} = \frac{T_h - T_c}{T_h}\cdot\frac{\sqrt{1 + Z\bar T} - 1}{\sqrt{1 + Z\bar T} + T_c/T_h}, \qquad Z = \frac{\alpha^2}{\rho\,\kappa} $$

$\alpha$ is the Seebeck coefficient, $\rho$ electrical resistivity, $\kappa$ thermal conductivity and $\bar T$ mean temperature. Efficiency approaches Carnot only as ZT goes to infinity; real materials fall well short.

Output and heat exchangers

$$ V_{oc} = \alpha\,\Delta T_m, \qquad P_{max} = \frac{(\alpha\,\Delta T_m)^2}{4R}, \qquad \Delta T_m = \Delta T_{total}\,\frac{R_m}{R_m + R_h + R_c} $$

$\Delta T_m$ is the temperature difference across the module and $R$ its internal electrical resistance (output peaks with an equal load). $R_m$, $R_h$ and $R_c$ are thermal resistances of the module and hot- and cold-side heat exchangers (Peltier and Joule heat neglected).

Coffee Break Trivia

Power that runs probes for half a century

The Seebeck effect was discovered in 1821 by the German Seebeck, who found a compass needle deflected when a junction of dissimilar metals was heated. In metals efficiency was low, and for long it served only for temperature measurement (thermocouples). Semiconductor thermoelectric materials in the 1950s made power generation practical, and the Voyager probes launched in 1977, powered by thermoelectric conversion of plutonium decay heat, still send signals from beyond the planets nearly half a century later. Efficiency may be a few percent, but the longevity of a power source without moving parts is hard to match.

Worked examples

Example 1: figure of merit and efficiency (500 K / 300 K)

ZT	0.5	1.0	1.5	2.0
Max efficiency	4.9%	8.2%	10.7%	12.6%
Share of Carnot (40%)	12%	21%	27%	31%

Example 2: module output

A 127-couple bismuth telluride module (Seebeck 0.0508 V/K, internal resistance 2.0 Ω, thermal conductance 0.5 W/K) across 100 K gives 5.08 V open-circuit and a maximum 3.23 W into a 2.0 Ω load (1.27 A).

Example 3: effect of heat-exchanger resistance

200 K between exhaust and coolant overall, module thermal resistance 2 K/W, varying heat-exchanger resistance on both sides (ideal: all 200 K across the module, 12.9 W):

Resistance each side	Module ΔT	Output	Share of ideal
0.5 K/W	133 K	5.73 W	44%
1.0 K/W	100 K	3.23 W	25%
2.0 K/W	67 K	1.43 W	11%

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Even 1 K/W of heat-exchanger resistance cuts output to a quarter.

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Output goes with temperature difference squared, so halving the difference quarters the output. A module that conducts heat too well can't hold a difference; one that conducts too poorly passes little heat — so output is set by the balance of module and heat-exchanger resistances. Real exhaust is air-like with low heat transfer, making the gas-side exchanger (fins) the hardest part. Raising ZT from 1 to 1.5 is important research, but for a given device halving heat-exchanger resistance often raises output more.

Analysis workflow

Establish heat-source and sink temperatures and the available heat (flow × temperature drop).
Estimate the efficiency ceiling from material ZT.
Line up heat-exchanger, contact and module resistances to find the module temperature difference.
Account for source temperature falling along the flow by summing over segments.
Check joint degradation from thermal cycling and material stability at temperature.

Coffee Break Trivia

“More modules, no more power”

In a waste-heat recovery prototype, doubling the number of thermoelectric modules raised output only about 10%. The gas-side exchanger was unchanged, so adding thermal paths made gas-side resistance a larger share and each module's temperature difference fell. Recomputing the heat flow and enlarging gas-side fin area nearly doubled output. Thermoelectric generation is often decided more by thermal path design than by the generating elements.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Full ΔT on the module	Output grossly overestimated	Divide by series resistances
Neglecting gas-side heat transfer	Little ΔT develops	Design fins
Unmatched load	Lower output	Match internal resistance
Ignoring temperature drop along flow	Downstream output overestimated	Compute in segments
Ignoring contact resistance	Reduced ΔT	Clamping and TIMs

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I'd like to try related calculations.

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Try the ZT figure of merit calculator and Seebeck EMF calculator. Related pages include thermoelectric (Peltier) cooling, heat sink design, thermal resistance and thermal interface materials.

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