Stefan-Boltzmann's Law - FLIR GF300 User Manual

34 Theory of thermography
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 insignifi-
cant amount of radiant emittance occurs at 38 μm, in the extreme infrared wavelengths.
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:
2
Spectral radiant emittance (W/cm (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 ) 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 area
b
below the Planck curve for a particular temperature. It can be shown that the radiant emit-
tance 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.
Figure 34.7 Josef Stefan (1835–1893), and Ludwig Boltzmann (1844–1906)
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