10399303;1
Figure 18.7
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 compen-
sating 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.
18.3.4
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
wavelength 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
μ
m, and beyond 3
μ
m 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 dependence 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 transmit-
ted 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:
18.3 – Blackbody radiation
Publ. No. 1 557 536 Rev. a35 – ENGLISH (EN) – January 20, 2004
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