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.
10399303;a1
Figure 20.7 Josef Stefan (1835–1893), and Ludwig Boltzmann (1844–1906)
Using the Stefan-Boltzmann formula to calculate the power radiated by the human
body, at a temperature of 300 K and an external surface area of approx. 2 m
2
, we
obtain 1 kW. This power loss could not be sustained if it were not for the compensating
absorption of radiation from surrounding surfaces, at room temperatures which do
not vary too drastically from the temperature of the body – or, of course, the addition
of clothing.
20.3.4 Non-blackbody emitters
So far, only blackbody radiators and blackbody radiation have been discussed.
However, real objects almost never comply with these laws over an extended wave-
length region – although they may approach the blackbody behavior in certain
spectral intervals. For example, a certain type of white paint may appear perfectly
white in the visible light spectrum, but becomes distinctly gray at about 2 μm, and
beyond 3 μm it is almost black.
20
140 Publ. No. 1557978 Rev. a155 – ENGLISH (EN) – February 6, 2006
20 – Theory of thermography
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