10327203;a4
Figure 20.6 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).
20.3.3
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.
Publ. No. T559733_en-US Rev. a571 – ENGLISH (EN) – November 4, 2011
73
20 – Theory of thermography
