Temperature gradient → Electrical work

Matrix context

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

D.01 × C.33 · Temperature gradient × Thermodiffusivefamily: Thermodiffusive

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
   Temperature gradient —drives→ Ionic thermoelectric effectestablishedclaim record

   thermal → electrical · loss to thermal

   • an electrolyte (liquid, gel or polymer) under a temperature difference; ionic Seebeck coefficients of 1–10 mV/K arise from differential thermodiffusion of cations and anions, without electrode redox entropy

   temperature gradient required

   refs [1] [2]
2. 02
   Ionic thermoelectric effect —produces→ Ionic currentestablishedclaim record

   electrical → electrical

   refs [2]
3. 03
   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 [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]
   M. Bonetti et al.. Huge Seebeck coefficients in nonaqueous electrolytes (2011)

   The Journal of Chemical Physics 134, 114513 · doi:10.1063/1.3561735 · crossref ✓ 2026-09-20 · record
2. [2]
   D. Zhao, A. Würger, X. Crispin. Ionic thermoelectric materials and devices (2021)

   Journal of Energy Chemistry 61, 88-103 · doi:10.1016/j.jechem.2021.02.022 · crossref ✓ 2026-09-20 · record
3. [3]
   A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

   Wiley · book, no DOI · record