10327203;3
Figure 18.6
Planckian curves plotted on semi-log scales from 100 K to 1000 K. The dotted line repre-
sents the locus of maximum radiant emittance at each temperature as described by Wien's displacement
law.
1:
Spectral radiant emittance (W/cm
2
(
μ
m));
2:
Wavelength (
μ
m).
18.3.3
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.
92
Publ. No. 1 557 536 Rev. a35 – ENGLISH (EN) – January 20, 2004
18.3 – Blackbody radiation
