Energy and Human Ambitions on a Finite Planet, 2021a

1 Exponential Growth 8
10 13
<strong>Energy</strong> Production Rate (Watts)
10 12
10 11
10 10
10 9
10 8
1650 1700 1750 1800 1850 1900 1950 2000
year
Figure 1.3: <strong>Energy</strong> trajectory in the U.S. over
a long period. The red line is an exponential
at a 2.9% growth rate, which appears linear
on a logarithmic plot.
result; 2) this rate produces the mathematical convenience of a factor of
8
10 increase every century.
8: Fundamentally, this relates to the fact
that the natural log of 10 is 2.30. The analog
What follows is a flight of fancy that quickly becomes absurd, but we will
chase it to staggering levels of absurdity just because it is fun, instructive,
<strong>and</strong> mind-blowing. Bear in mind that what follows should not be taken
of our future: rather, we can use the absurdity to predict
how our future will not look!
of Eq. 1.7 using 10 in place of 2 <strong>and</strong> p 0.023
for 2.3% growth rate will produce a factorof-ten
timescale t 10 ≈ 100 years.
as predictions 9 9: Do not interpret this section as predictions
of how our future will go.
The sun deposits energy at Earth’s surface at a rate of about 1,000 W/m 2
(1,000 Watts per square meter; we’ll reach a better underst<strong>and</strong>ing for
these units in Chapter 5). Ignoring clouds, the projected area intercepting
the sun’s rays is just A πR 2 ⊕ , where R ⊕ is the radius of the earth,
around 6,400 km. Roughly a quarter of the earth’s surface is l<strong>and</strong>, <strong>and</strong>
adding it all up we get about 30 × 10 15 W hitting l<strong>and</strong>. If we put solar
panels on every square meter of l<strong>and</strong> converting sunlight to electrical
energy at 20% efficiency, 10 we keep 6 × 10 15 W. This is a little over 300
times the current global energy usage rate of 18 TW. What an encouraging
number! Lots of margin. How long before our growth would get us
here? After one century, we’re 10 times higher, <strong>and</strong> 100 times higher after
two centuries. It would take about 2.5 centuries (250 years) to hit this
limit. Then no more energy growth.
But wait, why not also float panels on all of the ocean, <strong>and</strong> also magically
improve performance to 100%? Doing this, we can capture a whopping
130 × 10 15 W, over 7,000 times our current rate. Now we’re talking about
maxing out in just under 400 years. Each factor of ten is a century, so a
factor of 10,000 would be four factors of ten (10 4 ), taking four centuries.
So within 400 years, we would be at the point of using every scrap of
Approximate numbers are perfectly fine for
this exercise.
10: 20% is on the higher end for typical
panels.
The merits of various alternative energy
sources will be treated in later chapters, so
do not use this chapter to form opinions on
the usefulness of solar power, for instance.
In defiance of physical limits.
10,000 is not too different from 7,000, <strong>and</strong> the
“rounding up” helps us conveniently make
sense of the result, since a factor of 10,000
is easier to interpret as four applications of
10×, <strong>and</strong> thus 400 years.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.