{
  "title": "Photon accounting, gray-surface radiance and solar heat balance",
  "status": "Analytical teaching study with hypothetical surface and collector parameters; no device performance measurements",
  "rows": {
    "photons": 371,
    "radiance": 684,
    "solar": 765
  },
  "constants": {
    "h_J_s": 6.62607015e-34,
    "c_m_s": 299792458.0,
    "k_J_K": 1.380649e-23,
    "elementary_charge_C": 1.602176634e-19,
    "derived_Stefan_Boltzmann_W_m2_K4": 5.6703744191844314e-08
  },
  "assumptions": [
    "Monochromatic optical power is fixed at 1 W; electrical input, efficacy and material interaction are not modeled.",
    "Planck output is per wavelength in micrometres per area per solid angle, not integrated hemispheric flux.",
    "Surface is opaque, diffuse and gray with wavelength-independent assigned emissivity; surroundings are black, isotropic and isothermal at 293 K; no atmospheric attenuation or instrument response.",
    "Observed radiance includes reflected background and is not an inferred camera temperature.",
    "Solar aperture is projected/effective collecting area, separate from receiver emitting area and land area. Direct irradiance is assigned 800 W/m\u00b2.",
    "Solar optical throughput is 0.7 and absorptivity is 0.9; infrared emissivity is separately 0.8. Solar and thermal spectral averages are not assumed equal.",
    "Receiver temperature is prescribed; losses use view-factor-one large surroundings and assigned convection coefficient. Storage, conduction, piping and cycle conversion are excluded.",
    "Negative residual means external heat would be needed to maintain that temperature with no extraction; it is not silently clamped. No annual yield, construction guidance or device performance follows."
  ],
  "checks": {
    "all_pass": true,
    "photon_power_and_frequency_identity": true,
    "solar_balance_all_rows": true,
    "equal_temperature_reflection_identity": true,
    "Planck_integrated_to_Stefan_Boltzmann_relative_error": 8.477393231842711e-09,
    "blackbody_peak_um_at330K": 8.7811,
    "negative_balance_example_W_at800K_1m2": -3652.2710633085812
  },
  "formulas": {
    "photon": "E=h*c/lambda; rate=P/E",
    "Planck_per_um": "2*h*c\u00b2/(lambda_m^5*expm1(h*c/(lambda_m*k*T)))*1e-6",
    "observed": "epsilon*B(T)+(1-epsilon)*B(Tbackground)",
    "solar": "800*Aprojected*0.7*0.9 - 0.8*sigma*0.2*(T^4-293^4) - 5*0.2*(T-293)"
  },
  "sources": [
    {
      "title": "NIST SI defining constants",
      "url": "https://www.nist.gov/pml/special-publication-330/sp-330-section-2"
    },
    {
      "title": "NBS optical radiation measurements, Planck law",
      "url": "https://nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote910-8.pdf"
    },
    {
      "title": "NIST spectral emittance metrology",
      "url": "https://www.nist.gov/laboratories/tools-instruments/system-infrared-spectral-emittance-materials"
    },
    {
      "title": "NASA thermal control",
      "url": "https://www.nasa.gov/smallsat-institute/sst-soa/thermal-control/"
    },
    {
      "title": "DOE linear solar concentrators",
      "url": "https://www.energy.gov/cmei/systems/linear-concentrator-system-concentrating-solar-thermal-power-basics"
    }
  ]
}