Stefan-Boltzmann Radiated Power Calculator mechanism

Model scope

The core Stefan-Boltzmann power formula is correct, but the specification is ambiguous because it claims to compute either total power or intensity without defining intensity or providing distinct output formulas. It also does not state whether power is emitted power or net exchanged power. The honest-label text appropriately identifies an idealized blackbody/greybody model, but the UI should explicitly label emitted power versus emissive power and document kelvin, square-metre, and emissivity assumptions.

• P=εσAT⁴ is the standard total hemispherical emitted power for a grey, diffuse surface when T is in kelvin, A is surface area in square metres, and ε is treated as an appropriate constant emissivity.
• If the output is intensity in the radiative-exitance sense, the formula is M=εσT⁴ in W/m²; area must not be included. The specification does not define which meaning of intensity is intended. Radiance is directional and requires a different quantity and angular dependence.
• If radiated power means net power exchanged with an environment, the formula must include surroundings, such as P_net=εσA(T⁴−T_surroundings⁴).

Units and conventions

• σ=5.670374419×10^-8 W·m^-2·K^-4 (CODATA value).
• Temperature T must be absolute temperature in kelvin, not degrees Celsius or Fahrenheit.
• Area A must be the radiating surface area in m².
• Emissivity ε is dimensionless and should satisfy 0≤ε≤1; omitting ε is assumed to mean ε=1.
• The intensity output is assumed here to mean hemispherical emissive power, with units W/m², not directional radiance.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "area_m2": 2,
    "temperature_K": 300,
    "emissivity": 1
  },
  "expected_outputs": {
    "power_W": 918.600655878,
    "intensity_W_per_m2": 459.300327939
  },
  "working": "T⁴=300⁴=8,100,000,000 K⁴. Intensity=εσT⁴=1×(5.670374419×10^-8)×8,100,000,000=459.300327939 W/m². Power=Intensity×A=459.300327939×2=918.600655878 W."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The intensity calculation is undefined for zero area because it evaluates 0/0, so the instrument must reject A=0 for intensity. The specification also leaves temperature-unit conventions implicit, allowing a severe Celsius-versus-kelvin misinterpretation.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json