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.34 · Temperature gradient × Marangonifamily: MarangoniD.01 × C.24 · Temperature gradient × Turbomachineryfamily: TurbomachineryD.01 × C.14 · Temperature gradient × Electromagnetic inductionfamily: Electromagnetic induction

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
• Betz limit · upper-bound · hard, filtered out by its applicability
  C_p ≤ 16/27 ≈ 59.3% of the kinetic power through the rotor disc

Steps

1. 01
   Temperature gradient —drives→ Marangoni effectestablishedclaim record

   thermal → kinetic · loss to thermal

   • thermocapillary case: surface tension falls with temperature, so a temperature gradient along the interface drives flow toward the cold side

   liquid · temperature gradient required

   refs [1] [2]
2. 02
   Marangoni effect —produces→ Fluid flowestablishedclaim record

   kinetic → kinetic

   refs [1] [2]
3. 03
   Fluid flow —drives→ Aerodynamic and hydrodynamic liftestablishedclaim record

   kinetic → mechanical · loss to thermal

   • a rotor or vane in the produced stream at a working angle of attack; the driven flow must carry a directed momentum flux for a blade to load

   bulk flow required

   refs [3] [4]
4. 04
   Aerodynamic and hydrodynamic lift —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [4]
5. 05
   Mechanical motion —drives→ Electromagnetic inductionestablishedclaim record

   mechanical → electrical · loss to thermal

   • a magnet moving relative to a coil

   conductor required · magnetic field required

   refs [5] [6]
6. 06
   Electromagnetic induction —produces→ Charge carriersestablishedclaim record

   electrical → electrical · loss to thermal

   refs [5] [7]
7. 07
   Charge carriers —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • carriers driven through an external load at the potential difference the source maintains

   refs [8]

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 · 8

1. [1]
   L. E. Scriven, C. V. Sternling. The Marangoni Effects (1960)

   Nature 187, 186-188 · doi:10.1038/187186a0 · crossref ✓ 2026-09-20 · record
2. [2]
   Q. Dai et al.. Directional interfacial motion of liquids: Fundamentals, evaluations, and manipulation strategies (2021)

   Tribology International 154, 106749 · doi:10.1016/j.triboint.2020.106749 · crossref ✓ 2026-09-20 · record
3. [3]
   A. Betz. Das Maximum der theoretisch möglichen Ausnützung des Windes durch Windmotoren (1920)

   Zeitschrift für das gesamte Turbinenwesen 26, 307–309 · paper, no DOI · record
4. [4]
   S. L. Dixon, C. A. Hall. Fluid Mechanics and Thermodynamics of Turbomachinery (7th ed.) (2014)

   Butterworth-Heinemann · doi:10.1016/C2011-0-05059-7 · crossref ✓ 2026-09-19 · record
5. [5]
   M. Faraday. Experimental researches in electricity (1832)

   Philosophical Transactions of the Royal Society 122, 125–162 · doi:10.1098/rstl.1832.0006 · crossref ✓ 2026-09-19 · record
6. [6]
   S. P. Beeby, et al.. A micro electromagnetic generator for vibration energy harvesting (2007)

   Journal of Micromechanics and Microengineering 17, 1257 · doi:10.1088/0960-1317/17/7/007 · crossref ✓ 2026-09-19 · record
7. [7]
   L. D. Landau, E. M. Lifshitz, L. P. Pitaevskii. Electrodynamics of Continuous Media (Course of Theoretical Physics, Vol. 8, 2nd ed.) (1984)

   Pergamon · book, no DOI · record
8. [8]
   N. W. Ashcroft, N. D. Mermin. Solid State Physics (1976)

   Holt, Rinehart and Winston · book, no DOI · record