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Figure 34.7 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.
34.3.4 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 .
There are three processes which can occur that prevent a real object from acting like
a blackbody: a fraction of the incident radiation α may be absorbed, a fraction ρ may
be reflected, and a fraction τ may be transmitted. Since all of these factors are more
or less wavelength dependent, the subscript λ is used to imply the spectral depen-
dence of their definitions. Thus:
■
The spectral absorptance α
λ
= the ratio of the spectral radiant power absorbed by
an object to that incident upon it.
■
The spectral reflectance ρ
λ
= the ratio of the spectral radiant power reflected by
an object to that incident upon it.
■
The spectral transmittance τ
λ
= the ratio of the spectral radiant power transmitted
through an object to that incident upon it.
The sum of these three factors must always add up to the whole at any wavelength,
so we have the relation:
34
Publ. No. 1558550 Rev. a557 – ENGLISH (EN) – October 7, 2011
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34 – Theory of thermography