Source: https://guthlabs.ai/docs/instruments/stefan-boltzmann-radiated-power-calculator/

instrument / verified-clean

# Stefan-Boltzmann Radiated Power Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/stefan-boltzmann-radiated-power-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/stefan-boltzmann-radiated-power-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/stefan-boltzmann-radiated-power-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/stefan-boltzmann-radiated-power-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-5

**Evidence ID**: t5-231

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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).

### Unit assumptions

- 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.

## Boundary hardening

**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.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "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."
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

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

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`