Solar Energy

Availability of Solar Energy

The Sun is the primary source of life on Earth. With the exception of bacteria deep in the ocean that use the energy from hydrothermal vents and organisms that eat those bacteria, every living thing on Earth depends on sunlight to survive. Plants use photosynthesis to grow, and photosynthesis requires sunlight.

Therefore, any animal that consumes plants also depends on the Sun, as does the predator of that plant-eating animal, and so on up the food chain.

Similarly, most of the energy sources humans use to generate electricity come, ultimately, from the Sun (the exceptions are tidal, geothermal, and nuclear power). Windmills depend on the Sun, as wind fundamentally results from uneven heating of the Earth's surface due to sunlight. Hydro power depends on the Sun because rivers would not flow without the Sun powering the water cycle, evaporating water, and precipitating it at higher elevations.

Even fossil fuels depend on the Sun, as they originally came from plants, with thanks to photosynthesis and the Sun. Least surprising of all, solar power depends on the Sun for its power.

Sunlight plays such an important role on Earth because it dominates the energy flowing into the terrestrial atmosphere. Without the Sun, Earth would be a cold, dark planet, unsuitable for life.

Availability of Solar Energy

Sunlight is a form of energy, and so the amount of sunlight that reaches Earth per unit time can be measured as power in Watts. Because all life ultimately derives its energy from sunlight, knowing the amount of solar power that reaches us is crucial — it sets an upper bound for life and industry on our planet.

Happily, with some simple geometry and knowledge of the total solar output, it's easy to calculate.

Thus, our first question is: how much sunlight reaches Earth (in Watts)?

Assume: the power output of the Sun is approximately \(\SI{3.85e26}{\watt}\), the Sun is about \(\SI{1.5e11}{\meter}\) from the Earth on average, and the Earth has a radius of about \(\SI{6.37e6}{\meter}\).

Hint: the power output of the Sun is distributed equally in all directions as sunlight.

                 

Availability of Solar Energy

The total power consumption of humans on Earth is approximately \(\SI{e13}{\watt}\), which is orders of magnitude less than the amount of sunlight that the Earth intercepts!

The energy flowing from the Sun to Earth truly dwarfs the amount of energy flowing through our buildings and vehicles. It should therefore be possible to meet all of our energy needs from sunlight. In fact, if we could collect all of the incoming energy from the Sun, we'd need less than \(\SI{1}{\hour}\) to satisfy the global energy demand for an entire year!

Collecting all of the sunlight that reaches Earth is infeasible, but luckily we don't need to collect all of it. Over the rest of this quiz, we will investigate how much collection area is required to meet the energy demand of different countries under different conditions.

Availability of Solar Energy

To figure out how much collection area we need, we first need to know the energy flux (power per unit area) of sunlight that reaches Earth's surface. To calculate this value, we need to consider two things:

First, we'll need the energy flux reaching Earth, which we calculated in the last question.

Second, we'll need the approximate transmittance value of sunlight through the atmosphere. Some sunlight reaching Earth will be reflected or absorbed by the atmosphere, so not all of it is able to reach Earth's surface. Here is the transmittance spectrum of Earth's atmosphere:

This means that \(0\%\) of light with a wavelength of \(\SI{1.4}{\micro\meter}\) will be transmitted through the Earth's atmosphere, while about \(90\%\) of light with a wavelength of \(\SI{1.6}{\micro\meter}\) would be transmitted through. The bands of low transmittance correspond with specific species in the atmosphere that absorb at those wavelengths - light with a wavelength of \(\SI{1.4}{\micro\meter}\) is absorbed by water, for example.

Given that sunlight primarily has wavelengths ranging from \(\SI{0.3}{\micro\meter}\) to \(\SI{2.5}{\micro\meter},\) what is the energy flux of sunlight reaching the Earth's surface?

                 

Availability of Solar Energy

Now that we have an idea about how much sunlight reaches Earth's surface, we need to propose a way to collect it. Let's imagine a generic solar collector, which is able to convert \(25\%\) of the sunlight incident on it into electricity. We will learn about specific mechanisms for converting sunlight to electricity in later chapters, but for now we will not worry about the details of how our solar collector works.

If the central American country of Costa Rica wants to meet their entire electricity demand of \(\SI{1}{\giga\watt}\) (\(\SI{1e9}{\watt}\)) using solar power, how much collection area would be required (in \(\si{\meter\squared}\))? To answer this question, you can assume that the energy flux calculated from the previous question is always available in Costa Rica.

Availability of Solar Energy

The required area we calculated is much less than the total area of Costa Rica \((\sim\SI{5.1e4}{\kilo\meter\squared}\), or \(\SI{5.1e10}{\meter\squared})\), and is also much less than the total built-up area of Costa Rica \((\sim\SI{500}{\kilo\meter\squared}\), or \(\SI{5e8}{\meter\squared})\), which refers to the area covered with buildings and structures.

Therefore, if that was truly the required collector area, it should be possible for Costa Rica to meet their entire electricity demand with solar energy. Of course, possible doesn't necessarily mean realistic. That's still a huge amount of collector area, and deploying enough solar collectors to cover that area would be an extraordinary endeavor.

However, the collector area we calculated doesn't consider all the relevant factors. The approach for the previous problem assumes that we have a constant solar flux, regardless of time, cloud cover, or our position on the planet, but this isn't true in real life! We'd really need more collector area, because you can only collect solar energy while the sun is shining, which is at most about half the time for a particular location.

Availability of Solar Energy

For locations far from the equator, a collector oriented horizontally on the Earth's surface won't be able to collect the full solar flux. Because the Sun never appears directly overhead at far Northern and far Southern latitudes, the solar flux reaching a collector there would be weaker.

Instead of assuming a constant solar flux (in \(\si[per-mode=symbol]{\watt\per\meter\squared}\)) it is useful to know the solar energy available per unit area per day, e.g., in \(\si[per-mode=symbol]{\kilo\watt\hour\per\meter\squared\per\day},\) called the daily solar resource. If \(I_\textrm{surf}\) is the solar flux normal to the incident sunlight at the Earth's surface while the Sun is shining, what is the expression for daily solar resource as a function of latitude angle \(\phi\)?

Ignore the Earth's tilt relative to its orbit around the Sun.

                 

Availability of Solar Energy

With a latitude of about \(10^{\circ}\) North, Costa Rica would have a daily solar resource of about \(\SI[per-mode=symbol]{7.5}{\kilo\watt\hour\per\meter\squared\per\day}\), rather than the \(\SI[per-mode=symbol]{24}{\kilo\watt\hour\per\meter\squared\per\day}\) we used to calculate the previous required collector area. That means that to meet all electricity needs from solar power, Costa Rica would require about 3.2 times as much collector area as previously calculated.

Costa Rica is close to the equator, so it has a large solar resource. What about countries further from the equator? The European country of Estonia has similar electricity consumption to Costa Rica: total consumption is about \(\SI{1.25}{\giga\watt}\), or about \(\SI[per-mode=symbol]{1.1e4}{\giga\watt\hour} / \text{year}\). Estonia sits at a latitude of about \(60^{\circ}\) North.

How much collector area of our \(25\%\) efficient solar collector would be required to meet Estonia's electricity needs (in \(\si{\meter\squared}\))?

Availability of Solar Energy

Even though they have similar demand for electricity, Estonia would require much more collector area due to its Northern latitude. However like Costa Rica, the total collector area is still a small fraction of Estonia's total land area (\(\sim \SI{4.5e4}{\kilo\meter\squared}\)) and is less than Estonia's built-up area (\(\sim \SI{250}{\kilo\meter\squared}\)). So in principle, Estonia could also meet all of its electricity demand with solar power even though it has a lower solar resource.

This highlights the promise and the challenge of solar energy: there's a lot of it, but it’s dilute. The energy flow from the Sun is large enough to meet all electrical demand, but the flux is low enough that collecting enough solar energy for each country would require many square kilometers of collector area.

You should also keep in mind that the analysis in this quiz doesn't consider the effect of clouds on the solar resource. In cloudy areas the solar resource will be much lower than the value given by the expression we came up with, and there isn't a good way to know the real solar resource of an area besides measuring it directly. Also, sunlight is available only during the daytime and with good weather, so to actually meet all electrical demand with solar energy, you’d need a way to store the energy.

Through the rest of this course, we will look at solar energy, how we can convert solar energy to more useful forms, and ways of making those conversion processes more efficient.

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