Environmental Engineering Reference
In-Depth Information
MW
m
2
e,S
A
S
M
e,S
=
(2.5)
= 63.11
Every square metre of the sun's surface emits a radiant power of 63.11 MW.
One fifth of a square kilometre of the sun's surface emits radiant energy of
400 EJ per year. This amount of energy is equal to the total primary energy
demand on Earth at present.
The sun's irradiance can be approximated to that of a black body. The
Stefan-Boltzmann law
:
(2.6)
M
e
(T)
=
•
T
4
can be used to estimate the
surface temperature of the sun
,
T
sun
. With the
Stefan-Boltzmann constant
= 5.67051
•
10
-8
W/(m
2
K
4
), it becomes:
M
e,S
=
4
T
sun
= 5777 K
(2.7)
The surface,
A
SE
, of a sphere with the sun as its centre and with a radius equal
to the average distance from the Earth to the centre of the sun (
r
SE
= 1.5
•
10
8
km) receives the same total radiant power as the surface of the sun
A
S
(Figure
2.2). However, the specific emission,
M
e,S
, or the energy density measured over
one square metre, is much higher at the sun's surface than at the sphere
surrounding the sun.
With
M
e,S
•
A
S
=
E
e
•
A
SE
and substituting
A
SE
= 4
•
π
•
r
S
2
, the irradiance
at the Earth,
E
e
, finally becomes:
A
S
A
SE
r
S
2
r
2
SE
E
e
=
M
e,S
•
=
M
e,S
(2.8)
•
Earth
A
SE
r
SE
A
S
r
S
Sun
Figure 2.2
The Radiant Power through the Surface of a Sphere with Radius
r
SE
is the Same as through the Surface of the Sun
