Environmental Engineering Reference
In-Depth Information
is in the visible corresponding toT T
5973 K. (The sharp dips seen in Figure 1.1 attest
to the wavelength resolution of the measurement, but are not central to our question
of the energy input to earth. These dips are atomic absorption lines presumably from
simple atoms and ions in the atmosphere surrounding the sun).
A related aspect of the radiation is the pressure it exerts, which is U/3
¼
(4/3 c)
s
SB
T
4
. It is estimated that the temperature at the center of the sun is 1.5
10
7
K, which
10
8
)] s/m 5.67
10
8
W/ m
2
K
4
corresponds
to radiation pressure [4/(3
3
10
7
K)
4
(1.5
101 kPa. This is large but a small part of
the total hydrostatic pressure of 340 Gbar at the center of the sun.
The area under this curve measured above the earths atmosphere represents
1366W/m
2
available at all times (and over billions of years). A fraction,
a
(the
albedo, about
a¼
¼
0.126 Gbar, where 1 bar
¼
0.3), of this is re
ectedbackintospace.However,ifwetakethe
radius of the earth as 6371 km, then the power intercepted, neglecting
a
,is
1.74
10
17
W
174 PW (petawatts). By comparison, the worldwide power con-
sumption, for all purposes, in 2008 was 14.7 TW, and the average total electric
power usage in the United Sates in 2004 was 460GW [5], which is only 26 parts per
million (ppm) of the solar energy
flux! If there are 7 billion people on the earth, this
power is 24,900 kWper person. On the basis of 460GWand 294 million persons in
the United States (in 2004), the electrical power usage for 2004 was 1.56 kW per
person in the United States. Worldwide total energy usage per person works out as
14.7 TW/7 billion
¼
2.10 kW per person.
There is thus a vast
flow of energy coming from space, even after we correct for the
re
ected light (albedo), and the absorption effects in the atmosphere. The question of
whether it can be harvested for human consumption is related to its dilute nature. At
ground level in the United States, an average solar power density is about 205W/m
2
.
For example, an auto at 200 HP corresponds to 200
¼
14 920W, and
would require a collection area 73m
2
, much bigger than a solar panel that could be
put on the roof of the car. To supply the whole country, at a conversion ef
ciency
of 20%, a surface area of dimension about 65 miles would provide 460 GW, leaving
open questions of overnight storage of energy and distribution of the energy.
The challenge is to turn the incoming solar
flux (and/or other secondary sources of
sun-based energy, like the wind and hydroelectric power) into usable energy on the
human level. In advanced societies, it represents energy for transportation, presently
indicated by the price per gallon of gasoline, and the cost per kWh of electricity.
Our second interest, in a topic that focuses on nanophysics or quantum physics,
that applies to objects and devices on a size scale below 100 nm or so, is to learn
something about how the sun releases its energy, and to think of ways wemight create
a similar energy generation on earth.
The spectrum in Figure 1.3 closely resembles the shape of the Planck black body
radiation spectrum, plotted versus wavelength, for 5973 K. This spectrum was
measured in vacuum above the earths atmosphere, and directly measures the huge
amount of energy perpetually falling on the earth fromthe sun, quoted as 1366W/m
2
.
If we look at the plot, with units milliwatts/(m
2
nm), the area under the curve is the
power density, W/m
2
. To make a rough estimate, the area is the average value, about
700mW/(m
2
nm), times the wavelength range, about 2000 nm. So this rough
estimate gives 1400W/m
2
.
746 watts
¼
