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: ThermodiffusiveD.01 × C.21 · Temperature gradient × Electrochemicalfamily: Electrochemical

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
• Onsager–Casimir reciprocity · constitutive-relation · listed, never decisive
  L_ij(B) = ε_i ε_j L_ji(−B): the cross-coefficients of coupled linear transport are equal up to the time-reversal parities ε of the variables and reversal of the magnetic field; L_ij = L_ji is the zero-field, even-parity case
• Free energy of mixing · resource-bound · listed, never decisive
  W ≤ −ΔG_mix ≈ 0.8 kWh per m³ of fresh water into seawater
• Nernst / Gibbs free-energy bound · resource-bound · listed, never decisive
  W_electrical ≤ −ΔG = nFE_cell

Steps

1. 01
   Temperature gradient —drives→ Soret effectestablishedclaim record

   thermal → chemical · loss to thermal

   • a liquid mixture or solution under a steady temperature gradient

   liquid · temperature gradient required

   refs [1] [2]
2. 02
   Soret effect —produces→ Concentration gradientestablishedclaim record

   chemical → chemical

   refs [2]
3. 03
   Concentration gradient —drives→ Concentration cell effectestablishedclaim record

   chemical → electrical · loss to thermal

   E = (RT/zF) · ln(a₁/a₂) · RT/(zF), multiplying the dimensionless logarithm of the activity ratio (25.7 mV/z at 25 °C) [V]

   Temperature is a parameter of the coefficient, not the driving quantity; the cell is driven by the activity (concentration) ratio between the two half-cells.

   • two electrodes of the same kind in solutions of different activity joined by a salt bridge or membrane

   aqueous medium required

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

   electrical → electrical

   refs [3]
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 [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]
   C. Soret. Sur l'état d'équilibre que prend au point de vue de sa concentration une dissolution saline primitivement homogène dont deux parties sont portées à des températures différentes (1879)

   Archives des Sciences Physiques et Naturelles 2, 48–61 · paper, no DOI · record
2. [2]
   S. R. de Groot, P. Mazur. Non-Equilibrium Thermodynamics (1962)

   North-Holland · book, no DOI · record
3. [3]
   A. J. Bard, L. R. Faulkner. Electrochemical Methods: Fundamentals and Applications (2nd ed.) (2001)

   Wiley · book, no DOI · record