Electric potential difference → Mechanical 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.34 · Electric potential difference × Marangonifamily: MarangoniD.06 × C.24 · Electric potential difference × Turbomachineryfamily: Turbomachinery

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
   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→ 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 [3] [4]
4. 04
   Marangoni effect —produces→ Pressure gradienttheoretically predictedclaim record

   kinetic → mechanical · loss to thermal

   • a thermocapillary-driven liquid plug moves in a closed-ended microchannel and compresses the trapped gas; the pressure rise is the load presented to the compliant membrane

   Kept below demonstrated: the Odukoya device measured heater and droplet behaviour, while the pressure field feeding the membrane (about 0.1 kPa for a 13 μm deflection in the model) comes from the force balance, not a measurement.

   refs [5] [6]
5. 05
   Pressure gradient —drives→ Aerodynamic and hydrodynamic liftestablishedclaim record

   mechanical → mechanical · loss to thermal

   • a pressure difference driving flow through a turbine stage

   bulk flow required

   refs [7]
6. 06
   Aerodynamic and hydrodynamic lift —produces→ Mechanical motionestablishedclaim record

   mechanical → mechanical

   refs [7]
7. 07
   Mechanical motion —converts into→ Mechanical workestablishedclaim record

   mechanical → mechanical · loss to thermal

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

   Nature 187, 186-188 · doi:10.1038/187186a0 · crossref ✓ 2026-09-20 · record
4. [4]
   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
5. [5]
   P. S. Glockner, G. F. Naterer. Surface tension and frictional resistance of thermocapillary pumping in a closed microchannel (2006)

   International Journal of Heat and Mass Transfer 49(23–24), 4424–4436 · doi:10.1016/j.ijheatmasstransfer.2006.05.005 · record
6. [6]
   A. Odukoya, G. F. Naterer. Transient response of thermocapillary pumping of a droplet in a micro heat engine (2013)

   International Journal of Heat and Mass Transfer 58, 202–212 · doi:10.1016/j.ijheatmasstransfer.2012.11.009 · record
7. [7]
   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
8. [8]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

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