5. The earth’s entropy balance and a solar society
The difference in entropy of the incoming solar energy and the outgoing radiative heat flow con-
stitutes a natural resource a potential for entropy production. A key question is how this resource
could be put to use. To address this issue, it is necessary to consider how the resource is used
wasted at present as well as in a pristine state of nature.
In nature, the negentropy in solar radiation is partly directed by plants into a path of successive
transformations in living systems. In each trans- formation, entropy is produced while the remain-
ing negentropy is keeping plants and animals alive, or even growing. However, of the solar
energy directed towards Earth, almost a third is reflected back into space. Of the remaining radia-
tion, some is absorbed in the atmosphere so that only a little less than half reaches the Earth’s
surface.
Calculating the exact entropy of the different radiation flows involved is difficult. Theoretical
contributions have been made by Landsberg 1978, Landsberg and Tonge 1980 and Karlsson
1982. For a quantitative analysis, approxima- tions are necessary and such have been described
or attempted by Peixoto et al. 1991, Pelkowski 1994, Weiss 1994, O’Brien and Stephens
1995, Klippel and Mu¨ller 1997 and O’Brien 1997. A simple approximation is to assume inco-
herent blackbody radiation in all stages. Then, the radiation emitted from the Sun is calculated with
Stefan-Boltzmann’s law, Eq. 1. The fraction of that radiation impinging the Earth’s atmosphere
is given by
p r
j 2
4pR
2
, 4
where r
j
is the radius of the Earth 6.4 × 10
6
m and R is the average distance between the Earth
and the Sun 1.5 × 10
11
m. Approximating fur- ther, by assuming that the entropy flow is the
energy flow divided by the temperature, the flow of entropy impinging on the atmosphere is given
by s
T
s 3
r
s
2R
2
p r
j 2
= 0.03 PWK,
5 Here, T
s
is the effective temperature of the Sun and r
s
is the radius of the Sun 6.9 × 10
8
m. Assuming also that the Earth radiates as a black
body for the wavelengths of Earth temperature heat radiation, and assuming the same relation
between energy and entropy flow as above, we get the flow of entropy from the Earth as
s T
j 3
4pr
j 2
= 0.63 PWK,
6 where T
j
is the effective temperature of the Earth, cf. Essex 1984. Note that the temperature of the
Earth used in this expression must be compatible with the energy balance requirement for the
model. Note also that these assumptions give a Carnot efficiency factor for the Earth, i.e. we have
here neglected the small corrections included in Eq. 3.
We see that the Earth emits more entropy than it receives. The difference, 0.6 PWK, corresponds
to the rate of entropy production on the Earth. The rate of commercial energy use of the hu-
man society is : 10 TW. If we assume that the energy is converted to heat at Earth temperature,
the corresponding entropy production is 0.04 TW K. The natural rate of entropy production is
15 000 times larger.
Even considering that only about half the solar radiation avoids reflection and absorption in the
atmosphere, the natural entropy production at the surface of the planet is : 7500 times the produc-
tion of entropy by the human society.
Of the potential entropy production only some 5 is delayed as the negentropy is conserved in
evaporated water and heat in the atmosphere Karlsson, 1990, p. 98. Living plants delay B
0.1 of the potential entropy production by pho- tosynthesis, storing the resource in chemical form
in plants Davis, 1990.
The distribution of these flows of energy and entropy are far from homogenous around the
planet. The entropy production by human com- mercial energy use corresponds to the entropy
production of some 6 × 10
4
km
2
average land surface. On the basis of empirical values for solar
inflow, we see that an area about five times as large, located in African or North American
deserts, is sufficient to substitute global entropy production from commercial sources of energy
with solar energy, which would be converted into entropy-free electricity at 10 efficiency. A square
500 × 500 km of Saharan desert could in this manner substitute all energy used. The part of the
Earth required for providing compensation for societal entropy production is thus quite small.
Even the larger area necessary when allowing for further energy transformations producing en-
ergy carriers like hydrogen or methanol may be easily found without competing with other land-
uses, e.g. Winter et al. 1991. However, it is not likely, or even suggested, that these potentials
should ever be used as there are other ways to channel natural entropy production into the in-
dustrial system via wind energy, bio-mass wastes, hydropower and different solar heat technologies.
The area calculated for appropriation of solar energy is of the same order of magnitude, 10
5
km
2
, as the combined area of hardened roads for cars and of human buildings, or one order of
magnitude less that of global urban areas, 10
6
km
2
. The area used for agriculture is : 10
7
km
2
, and according to Vitousek et al. 1997, \ 10
8
km
2
of land area is already manipulated by hu- man activities. The data is from Meyer and
Turner 1994. Thus, human societies have an enormous po-
tential for expanding their procurement of negen- tropy, without increasing but, if anything, rather
lowering the global rate of entropy production. This may be done without interfering more than
at present with the natural ecosystems and their conversions of energy and materials. It is even
possible to decrease the human appropriation of the products of natural photosynthesis, giving
more room for other species.
6. Concluding remarks