Electric potential difference → Useful heat

Matrix context

D = disequilibrium row · C = coupling family column. A cell reads the state of the atlas for that pair.

D.06 × C.01 · Electric potential difference × Thermoelectricfamily: ThermoelectricD.06 × C.07 · Electric potential difference × Thermophotovoltaicfamily: ThermophotovoltaicD.06 × C.20 · Electric potential difference × Photothermalfamily: Photothermal

Typed bounds on this route

Every limit the atlas holds for this route, as constraint records: reached through bounded_by claims on the route's own entities. Hard bounds (an upper bound or a formula) decide the thermodynamic-bound check above; benchmarks, constitutive relations and resource limits are listed and never decisive. No prose limit exists anywhere (pass 42).

• Carnot limit · formula-bound · hard, filtered out by its applicability
  η ≤ 1 − T_c/T_h for any heat engine between reservoirs at T_h and T_c
• Visible-band fraction of thermal emission · formula-bound · hard, filtered out by its applicability
  η_vis ≤ ∫₃₈₀ⁿᵐ⁷⁸⁰ⁿᵐ B_λ(λ, T) dλ / σT⁴ — the share of a thermal emitter's radiated power that Planck's distribution places in the visible band at the emitter temperature
• Landsberg limit · formula-bound · hard, filtered out by its applicability
  η ≤ 1 − (4/3)(T_c/T_s) + (1/3)(T_c/T_s)⁴ for conversion of blackbody radiation at T_s with a sink at T_c; 93.3 % at 6000 K / 300 K

Steps

1. 01
   Electric potential difference —drives→ Ettingshausen effectestablishedclaim record

   electrical → thermal

   • a current in a conductor with a perpendicular magnetic field

   solid · conductor required · magnetic field required

   refs [1] [2]
2. 02
   Ettingshausen effect —produces→ Temperature gradientestablishedclaim record

   thermal → thermal

   refs [2] [3]
3. 03
   Temperature gradient —drives→ Thermal emissionestablishedclaim record

   thermal → radiative

   • an emitter hotter than the surface it faces

   refs [4] [5]
4. 04
   Thermal emission —produces→ Photonsestablishedclaim record

   radiative → radiative

   refs [5] [4]
5. 05
   Photons —drives→ Photothermal absorptionestablishedclaim record

   radiative → thermal

   refs [4]
6. 06
   Photothermal absorption —produces→ Heat flowestablishedclaim record

   thermal → thermal

   refs [4]
7. 07
   Heat flow —converts into→ Useful heatestablishedclaim record

   thermal → thermal

   • heat delivered at a temperature above the point of use

   refs [4]

Evidence for the complete composition · 0

No source on record for this exact composition. The sources below support the individual steps, not the route as a whole.

Evidence for the constituent relations · 5

1. [1]
   A. von Ettingshausen, W. Nernst. Ueber das Auftreten electromotorischer Kräfte in Metallplatten, welche von einem Wärmestrome durchflossen werden und sich im magnetischen Felde befinden (1886)

   Annalen der Physik 265, 343–347 · doi:10.1002/andp.18862651010 · crossref ✓ 2026-09-19 · record
2. [2]
   H. B. Callen. The application of Onsager's reciprocal relations to thermoelectric, thermomagnetic, and galvanomagnetic effects (1948)

   Physical Review 73, 1349 · doi:10.1103/PhysRev.73.1349 · crossref ✓ 2026-09-19 · record
3. [3]
   H. J. Goldsmid. Introduction to Thermoelectricity (2nd ed.) (2016)

   Springer Series in Materials Science 121 · doi:10.1007/978-3-662-49256-7 · crossref ✓ 2026-09-19 · record
4. [4]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
5. [5]
   P. T. Landsberg, G. Tonge. Thermodynamic energy conversion efficiencies (1980)

   Journal of Applied Physics 51, R1–R20 · doi:10.1063/1.328187 · crossref ✓ 2026-09-19 · record