Theory of thermography
19
Figure 19.4
Blackbody spectral radiant emittance according to Planck’s law, plotted for various absolute
temperatures. 1: Spectral radiant emittance (W/cm
2
× 10
3
(μm)); 2: Wavelength (μm)
19.3.2
Wien’s displacement law
By differentiating Planck’s formula with respect to λ, and finding the maximum, we have:
This is Wien’s formula (after
Wilhelm Wien
, 1864–1928), which expresses mathematically
the common observation that colors vary from red to orange or yellow as the temperature
of a thermal radiator increases. The wavelength of the color is the same as the wavelength
calculated for λ
max
. A good approximation of the value of λ
max
for a given blackbody tem-
perature is obtained by applying the rule-of-thumb 3 000/T μm. Thus, a very hot star such
as Sirius (11 000 K), emitting bluish-white light, radiates with the peak of spectral radiant
emittance occurring within the invisible ultraviolet spectrum, at wavelength 0.27 μm.
Figure 19.5
Wilhelm Wien (1864–1928)
The sun (approx. 6 000 K) emits yellow light, peaking at about 0.5 μm in the middle of the
visible light spectrum.
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