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: Thermoelectric

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

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→ Advective heat transportestablishedclaim record

   thermal → thermal

   • a bulk fluid flow connects the hotter and colder regions
   • for forced circulation the flow may be supplied by an external pump rather than generated by buoyancy

   refs [4] [5] [6]
4. 04
   Advective heat transport —produces→ Heat flowestablishedclaim record

   thermal → thermal

   refs [4] [5]
5. 05
   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 · 6

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]
   U.S. Nuclear Regulatory Commission. Pressurized Water Reactors — how a typical commercial PWR works (2025)

   nrc.gov · www.nrc.gov/reactors/power/pwrs · record
6. [6]
   U.S. Department of Energy. DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 of 3 (DOE-HDBK-1012/2-92) (1992)

   DOE-HDBK-1012/2-92, June 1992 · www.energy.gov/sites/default/files/2026-04/DOE-HDBK-1012-92_VOL2.pdf · record