Geoscience Reference
In-Depth Information
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Figure 5.3
Radiant energy
per unit wavelength emitted
by a blackbody with a surface
temperature of 5777 K.
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Wavelength (
μ
m)
directions and absorbs all incident radiation. The area across a small hole in
a container whose internal surface temperature is uniform approximates the
behavior of a black body.
The spectral irradiance, i.e., radiant energy emitted per unit wavelength by a
blackbody,
R
l
, expressed as function of the surface temperature
T
s
(in K) is shown
in Fig. 5.3 and is given by
Planck's Law
, which has the form:
C
1
R
=
λ
(5.1)
⎡
⎛
C
⎞
−
⎤
5
l
exp
1
⎜
2
⎟
⎢
⎥
⎝
l
T
⎠
⎣
⎦
s
where
C
1
λ
max
, at
which most blackbody radiation is emitted is given by
We i n's L aw
, which has the
form:
=
3.74
×
10
−16
W m
−2
and
C
2
=
1.44
×
10
−2
K. The wavelength,
2897
l
=
[with
l
in
μ
m and
T
S
in K]
(5.2)
max
T
s
The total flux of radiation,
R
, emitted by a blackbody per unit area of surface per
unit time is given by the
Stefan
-
Boltzmann Law
, which has the form:
∞
∫
4
RRd T
=
l
=
σ
(5.3)
l
s
0
in which
Boltzmann constant,
R
is in W m
−2
and
T
s
is in K. Together Equations (5.2) and (5.3) require that as the surface tem-
perature rises, the maximum wavelength at which most radiation is emitted
σ
=
5.67
×
10
−8
W m
−2
K
−4
is the Stefan
−
