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.07 · Electric potential difference × Thermophotovoltaicfamily: ThermophotovoltaicD.06 × C.18 · Electric potential difference × Photovoltaicfamily: Photovoltaic

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
• Visible-band fraction of thermal emission · formula-bound · hard, filtered out by its applicability
  η_vis ≤ ∫₃₈₀ⁿᵐ⁷⁸⁰ⁿᵐ B_λ(λ, T) dλ / σT⁴ — the share of a thermal emitter's radiated power that Planck's distribution places in the visible band at the emitter temperature
• Shockley–Queisser limit · upper-bound · hard, filtered out by its applicability
  η ≤ 33.7% for a single p–n junction under unconcentrated AM1.5 sunlight
• Landsberg limit · formula-bound · hard, filtered out by its applicability
  η ≤ 1 − (4/3)(T_c/T_s) + (1/3)(T_c/T_s)⁴ for conversion of blackbody radiation at T_s with a sink at T_c; 93.3 % at 6000 K / 300 K

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→ Thermal emissionestablishedclaim record

   thermal → radiative

   • an emitter hotter than the surface it faces

   refs [3] [4]
4. 04
   Thermal emission —produces→ Photonsestablishedclaim record

   radiative → radiative

   refs [4] [3]
5. 05
   Photons —drives→ Photovoltaic effectestablishedclaim record

   radiative → electronic-excitation · loss to thermal

   • photons from any source, including a thermal emitter, absorbed above the gap

   solid · semiconductor required

   refs [5] [6]
6. 06
   Photovoltaic effect —produces→ Electron–hole pairsestablishedclaim record

   electronic-excitation → electronic-excitation · loss to thermal

   refs [6] [7] [8]
7. 07
   Electron–hole pairs —converts into→ Electrical workestablishedclaim record

   electronic-excitation → electrical · loss to thermal

   • the junction field separates the pair and the carriers reach the contacts before recombining

   solid · semiconductor required

   refs [6] [7]

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]
   A. Bejan. Advanced Engineering Thermodynamics (4th ed.) (2016)

   Wiley · doi:10.1002/9781119245964 · crossref ✓ 2026-09-19 · record
4. [4]
   P. T. Landsberg, G. Tonge. Thermodynamic energy conversion efficiencies (1980)

   Journal of Applied Physics 51, R1–R20 · doi:10.1063/1.328187 · crossref ✓ 2026-09-19 · record
5. [5]
   A. LaPotin, et al.. Thermophotovoltaic efficiency of 40% (2022)

   Nature 604, 287–291 · doi:10.1038/s41586-022-04473-y · crossref ✓ 2026-09-19 · record
6. [6]
   W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells (1961)

   Journal of Applied Physics 32, 510–519 · doi:10.1063/1.1736034 · crossref ✓ 2026-09-19 · record
7. [7]
   C. Kittel. Introduction to Solid State Physics (8th ed.) (2005)

   Wiley · book, no DOI · record
8. [8]
   M. A. Green, et al.. Solar cell efficiency tables (Version 63) (2024)

   Progress in Photovoltaics 32, 3–13 · doi:10.1002/pip.3750 · crossref ✓ 2026-09-19 · record