Environmental Engineering Reference
In-Depth Information
This spectrum (Figure 1.3) wasmeasured by an automated spectrometer carried in
a satellite well beyond the earths atmosphere. The sharp dips in this spectrum are
atomic absorption lines, the sort of feature that can be understood only within
quantum mechanics. The atoms in question are presumably in the suns
atmosphere.
We are interested in the properties of the sun that is not only the source of all
renewable energy, excluding the geothermal and tidal energies and including
biofuels that are grown renewably by photosynthesis, but also serves as a model
for fusion reactions that might be implemented on earth. The power density at the
surface of the sun can be calculated from this measured power density shown
in Figure 1.3. If the radiation power density just above the earth is measured as
1366W/m
2
, then the power density at the surface of the sun can be obtained as
2
m
2
10
7
W
m
2
P
¼
1366 W
=
ð
D
es
=
R
s
Þ
¼
6
:
312
=
;
ð
1
:
3
Þ
using the values above for the distance to the sun and the suns radius, D
es
and R
s
,
respectively. Since we have a good estimate of the suns surface temperature T from
the peak position in Figure 1.3, we can use this power density to estimate the
emissivity
e
, using the relation P
¼ es
SB
T
4
. This gives emissivity
e ¼
0.998, which
seems reasonable.
Before we turn to an introductory discussion of how the sun stays hot, let us
consider thermal radiation from the earth, raising the question of the energy balance
for the earth itself. The earths surface is 70% ocean, and it seems the average
temperature T
E
must be at least 273 K. Assuming this, the power radiated from the
earth is
4
4
p
R
E
s
SB
ð
P
¼
T
E
Þ
:
ð
1
:
4
Þ
Initially, we suppose that this power goes directly out into space. (A more accurate
estimate of the earths temperature is 288 K, see Ref. [3], p. 11.
Using R
E
160.6 PW. Let us
compare this with an estimate of the absorbed power from the sun, being more
realistic by taking the Albedo (fraction re
ected) as 0.3. So power absorbed is 174 PW
(1
¼
6173 km and taking emissivity
e¼
1, this is P
¼
121.8 PW. Since the earth maintains an approximately constant temper-
ature, this comparison indicates that a net loss discrepancy of 38.8 PW, if we neglect
any heat energy coming up fromthe core of the earth. (It is estimated that heat owup
from the earths center is Q
0.3)
¼
10
13
W
0.0443 PW, which is relatively small.
Of this, 80% is from continuing radioactive heating and 20% from secular cooling
of the initial heat. 44.3 TWis a large number (a bit larger than shown in Table 1.1), but
on the scale of the solar in
¼
4.43
¼
ux it is not important in our approximate estimate. So, we
will neglect this for the moment) [6].
Thus, a straightforward estimate of power radiated from earth exceeds the well-
known in
ow. To resolve the discrepancy, it seems most plausible that the radiated
energy does not all actually leave earth, but a portion is re
ected back. A greenhouse
effect reduces the black body radiation 160.6 PW down close to the 121.8 PW net
radiation input from the sun (Figure 1.4). We can treat this as return radiation from a
