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→ Peltier effectestablishedclaim record

   electrical → thermal · loss to thermal

   • a current through a junction of dissimilar conductors

   solid · conductor required

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

   thermal → thermal

   refs [2]
3. 03
   Temperature gradient —drives→ Heat conductionestablishedclaim record

   thermal → thermal

   q = −κ · ∇T · thermal conductivity κ [W/(m K)]

   refs [3]
4. 04
   Heat conduction —produces→ Heat flowestablishedclaim record

   thermal → thermal

   refs [3]
5. 05
   Heat flow —converts into→ Useful heatestablishedclaim record

   thermal → thermal

   • heat delivered at a temperature above the point of use

   refs [3]

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 · 3

1. [1]
   J. C. A. Peltier. Nouvelles expériences sur la caloricité des courants électriques (1834)

   Annales de Chimie et de Physique 56, 371–386 · paper, no DOI · record
2. [2]
   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
3. [3]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record