Electric potential difference → Electrical work

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.05 · Electric potential difference × Thermogalvanicfamily: Thermogalvanic

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, applies to this route
  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→ Thermogalvanic effectestablishedclaim record

   thermal → electrical · loss to thermal

   ΔE = (ΔS_rxn / nF) · ΔT · thermogalvanic Seebeck coefficient [V/K]

   • two identical electrodes in one redox electrolyte held at different temperatures
   • a redox couple with large reaction entropy (ferri/ferrocyanide gives ≈ −1.4 mV/K)

   liquid · aqueous medium required · temperature gradient required

   refs [3] [4]
4. 04
   Thermogalvanic effect —produces→ Ionic currentestablishedclaim record

   electrical → electrical · loss to thermal

   refs [4]
5. 05
   Ionic current —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes exchange the ionic current for an electronic current through the external load

   refs [5]

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]
   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]
   T. I. Quickenden, Y. Mua. A review of power generation in aqueous thermogalvanic cells (1995)

   Journal of the Electrochemical Society 142, 3985 · doi:10.1149/1.2048446 · crossref ✓ 2026-09-19 · record
4. [4]
   M. F. Dupont, D. R. MacFarlane, J. M. Pringle. Thermo-electrochemical cells for waste heat harvesting – progress and perspectives (2017)

   Chemical Communications 53, 6288–6302 · doi:10.1039/C7CC02160G · crossref ✓ 2026-09-19 · record
5. [5]
   A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

   Wiley · book, no DOI · record