Energy and Human Ambitions on a Finite Planet, 2021a

11 Hydroelectric <strong>Energy</strong> 177
indicates that 44,000 TW of solar input goes into evaporation <strong>and</strong> the
hydrological cycle. Why, then, are we only able to use 0.477 TW (0.001%)
of this bounty? Is this a great, untapped renewable resource?
11.2.1 Theoretical Potential
To underst<strong>and</strong> the giant mismatch between solar input <strong>and</strong> hydroelectric
development, we first need to study evaporation.
Definition 11.2.2 The heat of vaporization of water is about 2,250 J per
gram, meaning that every gram of water that goes from liquid to gas (vapor)
requires an energy input of ∼2,250 J.
Box 11.2: Vaporization is Serious <strong>Energy</strong>
To put this in perspective, it takes 100 calories (418 J) to bring one
gram of water from freezing to boiling temperature. Then it takes
another 2,250 J to evaporate the water, which is a far larger quantity.
This is why water in a pot does not all flash into steam once the water
reaches 100 ◦ C, as it would if the evaporation energy was very small.
Instead, a boiling pot will retain water for a good while as energy
continues to be applied before all boiling away.
condensation
10 J per km
gravitational potential energy
0 J left
at sea level
evaporation (2250 J)
1 cm 3 = 1 gram
50 J (at 5 km)
air resistance
(loses energy to
heating air)
8 J left
800 m
Figure 11.4: The hydrological cycle. Sunlight
evaporates water from the surface, at
a cost of 2,250 J per gram. Each kilometer of
height the gram of water gains in forming
clouds costs an additional 10 J. When rain
falls on terrain, most of the gravitational
potential energy is spent, but on average
retains 8 J—based on an average l<strong>and</strong> elevation
of 800 m. The 2,250 J of evaporation
energy is released as heat when the water
condenses into clouds.
So let’s follow the energetics of a gram of water 17 on its journey to a
hydroelectric dam—most of which is represented in Figure 11.4. First,
the sun injects 2,250 J to evaporate that gram. Then let’s say it gets
lofted to 5 km. 18 The gravitational potential energy, mgh, comes to
0.001 × 10 × 5000 50 J. That’s only 2% of the amount that went into
evaporation. 19
When the water condenses in the cloud, it releases 2,250 J of thermal
energy into the cloud/air, then falls back to the ground as rain, offering
50 J of still-available energy. If it falls on the ocean, where it presumably
started, it gives up all 50 J of gravitational potential energy into useless
forms. 20 But if it falls on l<strong>and</strong>—higher than sea level—it retains some
gravitational potential, based on how high that l<strong>and</strong> is above sea level.
17: . . . one cubic centimeter
18: . . . typical cloud height
19: The sun must, in total, supply 2,300 J to
evaporate <strong>and</strong> lift the gram of water, <strong>and</strong>
only 50 J of the 2,300 J is kept as potential
energy.
20: . . . heat through air resistance <strong>and</strong> collision
with the ocean surface
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.