The Stefan-Boltzmann Law; Non-Blackbody Emitters - FLIR ThermaCAM PM575 Operator's Manual

9.3.3

The Stefan-Boltzmann law

By integrating Planck's formula from λ = 0 to λ = ∞ , we obtain the total radiant
emittance (W ) of a blackbody:
b
4
σT [ ⁄
W = Watt m
b
where
σ = the Stefan-Boltzmann constant = 5.7 x 10
This is the Stefan-Boltzmann formula, which states that the total emissive power of
a blackbody is proportional to the fourth power of its absolute temperature.
Graphically, W
b
perature. It can be shown that the radiant emittance in the interval λ = 0 to λ
only 25 % of the total, which represents about the amount of the sun's radiation
which lies inside the visible light spectrum.
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
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.
9.3.4

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 behaviour in cer-
tain spectral intervals. For example, white paint appears perfectly »white« in the
visible light spectrum, but becomes distinctly »grey« 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 spec-
tral dependence of their definitions. Thus:
• The spectral absorptance α
by an object to that incident upon it.
• The spectral reflectance ρ
by an object to that incident upon it.
© FLIR Systems AB – Publ. No. 557 369 – Ed. A
2
]
represents the area under the Planck curve for a particular tem-
= the ratio of the spectral radiant power absorbed
λ
= the ratio of the spectral radiant power reflected
λ
[9.3.3 — The Stefan-Boltzmann law]
-8 2
Watt/m .
is
max
2
, we
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