Radiative imbalance with the sky → Electrical work

Matrix context

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

D.12 × C.20 · Radiative imbalance with the sky × Photothermalfamily: PhotothermalD.12 × C.03 · Radiative imbalance with the sky × Thermoacousticfamily: ThermoacousticD.12 × C.10 · Radiative imbalance with the sky × Piezoelectricfamily: Piezoelectric

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).

• Radiative cooling power bound · resource-bound · listed, never decisive
  net cooling power ≲ 100–150 W/m² under a clear sky
• 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
• Electromechanical coupling factor · formula-bound · hard, applies to this route
  converted fraction per cycle ≤ k² = d²/(s·ε)

Steps

1. 01
   Radiative imbalance with the sky —drives→ Radiative sky coolingreplicatedclaim record

   radiative → thermal

   • an emitter with high emissivity in the 8–13 µm window and high solar reflectance
   • a clear sky; humidity and cloud close the window

   refs [1] [2] [3]
2. 02
   Radiative sky cooling —produces→ Temperature gradientreplicatedclaim record

   thermal → thermal

   • the cooled surface sits a few kelvin below ambient air

   refs [1] [4] [3]
3. 03
   Temperature gradient —drives→ Thermoacoustic effectestablishedclaim record

   thermal → acoustic · loss to thermal

   |∇T_crit| = β T_m ω |p₁| / (ρ_m c_p |u₁|); prime-mover onset requires |∇T| > |∇T_crit| · critical-gradient factor β T_m ω/(ρ_m c_p u₁) [K/(Pa·m)]

   p₁ and u₁ are the local first-order acoustic pressure and particle-velocity amplitudes; β is the volumetric thermal expansion coefficient (β T_m ≈ 1 for an ideal gas); this is the linear short-stack / standing-wave criterion of Swift 1988 — above the critical gradient the stack amplifies the wave, below it the same interaction pumps heat — not a closed-form performance law for every travelling-wave regenerator.

   • temperature gradient along the stack steeper than the critical gradient set by the acoustic pressure and displacement amplitudes
   • a resonant gas column

   gas · temperature gradient required

   refs [5]
4. 04
   Thermoacoustic effect —produces→ Acoustic waveestablishedclaim record

   acoustic → acoustic

   • travelling-wave thermoacoustic regime with a non-zero time-averaged acoustic power flux; pressure and particle velocity have the phase relation required for directed acoustic power (a looped tube or a travelling-wave regenerator), unlike the standing wave of a straight resonator

   gas

   refs [6] [7]
5. 05
   Acoustic wave —drives→ Direct piezoelectric effectdemonstratedclaim record

   acoustic → electrical · loss to thermal

   • sound pressure strains a compliant piezoelectric membrane or plate; standing and travelling waves both serve, the response following the pressure oscillation

   solid

   refs [8] [9]
6. 06
   Direct piezoelectric effect —produces→ Separated surface chargeestablishedclaim record

   electrical → electrical

   refs [10]
7. 07
   Separated surface charge —converts into→ Electrical workestablishedclaim record

   electrical → electrical · loss to thermal

   • electrodes on the charged surfaces connected through a load

   refs [11]

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 · 11

1. [1]
   A. P. Raman et al.. Passive radiative cooling below ambient air temperature under direct sunlight (2014)

   Nature 515, 540–544 · doi:10.1038/nature13883 · crossref ✓ 2026-09-19 · record
2. [2]
   Y. Zhai et al.. Scalable-manufactured randomized glass-polymer hybrid metamaterial for daytime radiative cooling (2017)

   Science 355, 1062–1066 · doi:10.1126/science.aai7899 · crossref ✓ 2026-09-19 · record
3. [3]
   J.-l. Kou et al.. Daytime radiative cooling using near-black infrared emitters (2017)

   ACS Photonics 4, 626–630 · doi:10.1021/acsphotonics.6b00991 · crossref ✓ 2026-09-19 · record
4. [4]
   A. P. Raman, W. Li, S. Fan. Generating light from darkness (2019)

   Joule 3, 2679–2686 · doi:10.1016/j.joule.2019.08.009 · crossref ✓ 2026-09-19 · record
5. [5]
   G. W. Swift. Thermoacoustic engines (1988)

   Journal of the Acoustical Society of America 84, 1145–1180 · doi:10.1121/1.396617 · crossref ✓ 2026-09-19 · record
6. [6]
   T. Yazaki et al.. Traveling Wave Thermoacoustic Engine in a Looped Tube (1998)

   Physical Review Letters 81, 3128–3131 · doi:10.1103/PhysRevLett.81.3128 · record
7. [7]
   S. Backhaus, G. W. Swift. A thermoacoustic-Stirling heat engine: Detailed study (2000)

   Journal of the Acoustical Society of America 107, 3148–3166 · doi:10.1121/1.429343 · record
8. [8]
   Y. Zheng et al.. Thermoacoustic energy harvesting using thermally-stabilized polyacrylonitrile nanofibers (2022)

   Nano Energy 95, 106995 · doi:10.1016/j.nanoen.2022.106995 · record
9. [9]
   J. Smoker et al.. Energy harvesting from a standing wave thermoacoustic-piezoelectric resonator (2012)

   Journal of Applied Physics 111, 104901 · doi:10.1063/1.4712630 · record
10. [10]
    J. F. Nye. Physical Properties of Crystals: Their Representation by Tensors and Matrices (1985)

    Oxford University Press · book, no DOI · record
11. [11]
    H. B. Radousky, H. Liang. Energy harvesting: an integrated view of materials, devices and applications (2012)

    Nanotechnology 23, 502001 · doi:10.1088/0957-4484/23/50/502001 · crossref ✓ 2026-09-19 · record