Stefan-Boltzmann's Law - FLIR T6 series User Manual

33
Theory of thermography
Figure 33.5 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.
At room temperature (300 K) the peak of radiant emittance lies at 9.7 μm, in the far infra-
red, while at the temperature of liquid nitrogen (77 K) the maximum of the almost insignif-
icant amount of radiant emittance occurs at 38 μm, in the extreme infrared wavelengths.
Figure 33.6 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).

33.3.3 Stefan-Boltzmann's law

By integrating Planck's formula from λ = 0 to λ = ∞, we obtain the total radiant emittance
(W ) of a blackbody:
b
This is the Stefan-Boltzmann formula (after Josef Stefan, 1835–1893, and Ludwig Boltz-
mann, 1844–1906), which states that the total emissive power of a blackbody is propor-
tional to the fourth power of its absolute temperature. Graphically, W represents the
b
area below the Planck curve for a particular temperature. It can be shown that the radiant
emittance in the interval λ = 0 to λ is only 25% of the total, which represents about the
max
amount of the sun's radiation which lies inside the visible light spectrum.
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