Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 222
Holding solar back is its intermittency 95 <strong>and</strong> high up-front cost. Intermittency
can be solved by battery storage, but this can double the cost <strong>and</strong>
require maintenance <strong>and</strong> periodic battery replacement. Additionally—as
for many of our renewable options—all of our society’s dem<strong>and</strong>s 96 are
not well met by electricity generation.
95: ...lowcapacity factor that is weatherdependent
96: . . . like transportation <strong>and</strong> industrial
processing
Sizing up a PV installation is fairly straightforward. Having first determined
how many kWh per day are to be produced, on average, divide
this by the kWh/m 2 /day value for the site, 97 which is essentially the
number of hours of full-sun 98 equivalent, <strong>and</strong> tends to be in the 4–6 hour 98: 1,000 W/m 2
ballpark. This says how many kilowatts the array should produce in full
sun (peak Watts). For instance, if only 10 kWh/day are needed, 99 <strong>and</strong>
the region in question gets 5 kWh/m 2 /day, the system needs to operate
at a peak power of 2 kW p , costing about $6k to purchase <strong>and</strong> install (grid
tied). Inflating by 20% offsets unaccounted losses 100 to better match real
conditions.
97: . . . either annual or monthly
99: . . . because you are careful about energy
expenditures
100: ...hot, dirty panels <strong>and</strong> conversion
efficiencies
Solar thermal energy is another way to run a traditional steam-based
power plant, using relatively low-tech mirrors <strong>and</strong> pipes to concentrate
solar energy into a heat-carrying fluid that can later make steam. Effective
efficiencies are relatively low, 101 but on the bright side, the low-tech nature
makes it fairly cheap, <strong>and</strong> the technique can accommodate some degree
of thermal storage for use some hours into the evening. Anything 102
starting from solar input has the potential to be a major player, given the
∼100,000 TW scale of solar energy incident upon the earth.
101: 3% of solar energy hitting the plant
area ends up as electricity
102: ...eveniftheefficiency is modest or
low
13.10 Problems
1. If we had two monochromatic (single-wavelength) light sources—a
green one at λ 0.5 μm <strong>and</strong> a near-infrared one at λ 1.0 μm—
each emitting photons at an energy rate of 1 W, 103 how does
the number of photons emerging per second from each source
compare? Is it the same number for each because both are 1 W
sources, or is it a different number—<strong>and</strong> by what factor, if so?
103: Hint: recall that 1Wis1J/s.
2. Overhead sunlight arrives on the surface of the earth at an intensity
of about 1,000 W/m 2 . How many photons per second strike a solar
panel whose area is 1.6 square meters, if the typical wavelength is
λ 0.5 μm?
3. Using the setup in Problem 2, how many photons enter your pupil
every second if you look directly at the sun? When doing so, your
pupil restricts to a diameter of about 2 mm.
4. The dimmest stars we can see with our eyes are thirteen orders-ofmagnitude
104 dimmer than the intensity of the sun. Building off
of Problem 3, how many photons enter your eye per second at this
edge of detectability?
104: 10 −13 times
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.