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Stefan–Boltzmann Constant from M(T⁴)

A black-body cavity. Measure the radiometric exitance M at several temperatures and recover σ from a fit of M versus T⁴.

University / research· 22 min·Related simulator: ThermodynamicsBlack Body: Planck Spectrum

Goal

Determine σ from M = σ T⁴. The slope of M versus T⁴ is σ.

Equipment

  • Black-body cavity
  • Temperature control
  • Radiometer (M)

Experiment

Theory

The Stefan–Boltzmann law gives the hemispherical exitance of a black body. This lab is not Wien’s displacement: you integrate (the radiometer reports M), you do not hunt λ_max. The bench hides M and σ. You only change T.

Procedure

  1. You only change the cavity temperature T. σ is hidden.
  2. Record. A radiometer logs M with small noise. There is no live M, σ or λ_max marker.
  3. The notebook computes T⁴. Repeat for at least 6 temperatures from about 900 K to 2800 K.
  4. Fit M versus T⁴; the slope is σ. Compare with the reference.

Conclusion

The fitted σ agrees with the Stefan–Boltzmann constant. Main uncertainties: radiometer noise and treating the cavity as a perfect black body.