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Figure 34.6 Planckian curves plotted on semi-log scales from 100 K to 1000 K. The dotted line represents
the locus of maximum radiant emittance at each temperature as described by Wien's displacement law.
1: Spectral radiant emittance (W/cm
2 (μm)); 2: Wavelength (μm).
34.3.3 Stefan-Boltzmann's law
By integrating Planck’s formula from λ = 0 to λ = ∞, we obtain the total radiant
emittance (W
b
) of a blackbody:
This is the Stefan-Boltzmann formula (after Josef Stefan , 1835–1893, and Ludwig
Boltzmann , 1844–1906), which states that the total emissive power of a blackbody is
proportional to the fourth power of its absolute temperature. Graphically,
W
b
represents
the area below the Planck curve for a particular temperature. It can be shown that the
radiant emittance in the interval
λ = 0 to λ
max
is only 25% of the total, which represents
about the amount of the sun’s radiation which lies inside the visible light spectrum.
34
278
Publ. No. 1558550 Rev. a557 – ENGLISH (EN) – October 7, 2011
34 – Theory of thermography