Geoscience Reference
In-Depth Information
All radiation
absorbed
R
R
R
x
ε
λ
R
Grey
surface
Black
surface
Grey
surface
Black
surface
R
x
ρ
λ
Same temperature
R
x
α
λ
R
x
τ
λ
Emitted radiation
Incident radiation
Figure 5.4
The difference between blackbody and gray surfaces in terms of the parameters that characterize their relative
behavior.
becomes less and the amount of radiation emitted increases. Consequently, there
is more radiation emitted per unit area from the Sun than from the Earth's surface
and it is emitted at shorter wavelengths.
Radiation exchange for 'gray' surfaces
The amount of radiation emitted from and absorbed by real surfaces is less than
that from a perfect blackbody and the extent of this reduction is quantified in
terms of parameters that characterize the natural surface. Emitting surfaces that
are imperfect blackbodies are sometimes called
gray
surfaces. Figure 5.4 illustrates
the emission and absorption of energy by a gray surface.
Definitions of the radiation properties that characterize gray surfaces are as
follows:
The emissivity
,
: the ratio of radiant energy flux emitted at given wavelength by
a gray surface relative to that emitted by a blackbody at the same temperature.
e
l
●
The absorptivity
,
: the proportion of radiant energy incident on a surface
at given wavelength that is absorbed.
a
l
●
The reflectivity
,
: the proportion of radiant energy incident on a surface at
given wavelength that is reflected.
r
l
●
The transmissivity
,
: the proportion of radiant energy incident on a sur-
face at given wavelength that is transmitted to a subsurface medium.
t
l
●
Because all of the energy incident on a surface must go somewhere, it follows that
(
a
l
1, which in turn means
a
l
,
r
l
and
t
l
necessarily must all lie in the
range zero to one. Also, there must be equality between the energy absorbed and
the energy emitted otherwise the temperature of a body hanging isolated inside an
evacuated, isothermal container would rise or fall continuously. The
Kirchoff 's
Principle
follows as a consequence of this and states that:
+
r
l
+
t
l
)
=
ae
=
(5.4)
l
l
