10 Renewable Overview

We now understand that the path human civilization has traveled to this pointa path paved by fossil fuels cannot lead very much farther before a new path must take over. One distinct possibility is a trek back toward a low-tech existence, but most people would consider such a development to be a failure. What would success look like, then?

Sec. D.5 (p. 404) in the Appendices takes a look at the big picture of long-term human success, but for present purposes we will focus on the critical issue of energy: where could we get enough energy to replace the prodigious one-time gift of fossil fuels?

This chapter is very brief, only setting the stage for upcoming chapters that go into alternative energy sources in greater detail. At the end of this effort, Chapter 17 summarizes the potential of all the energy resources. For now, we describe the origins and scales of Earth’s energy inputs, and finish with a reminder of how much energy we get from these sources today.

10.1 The Players

Before launching into detailed attributes of energy sources beyond fossil fuels, it is helpful to list the cast of characters.

(The remnant of a fallen tree called a nurselog-provides nutrition for a row of new trees, arranged in a colonnade. Photo credit: Tom Murphy)

• Hydroelectric energy (Chap. 11) traps water from a river behind a dam, forced to flow through a turbine¹ that spins a generator to make electricity.
• Wind energy (Chap. 12) spins a turbine² that makes electricity via a generator.

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• Solar energy (Chap. 13) can provide direct heat or make electricity via photovoltaic (PV) panels or in a utility-scale solar thermal installation.
• Biological energy (Chap. 14) can range from food to firewood, or biofuels. These are generally a source of thermal energy, via burning, able to drive heat engines.
• Nuclear Fission (Chap. 15) relies on mining a finite supply of radioactive elements in the Earth’s crust whose fission (splitting) generates heat that can make steam to run a heat engine and generator to make electricity.
• Nuclear Fusion (Chap. 15), if successful, would use abundant hydrogen resources from water to build helium nuclei-a process that would release heat to make steam for running a heat engine and generator to make electricity.
• Geothermal energy (Chap. 16) originates in Earth’s hot interior, and can be used for heating or to make steam to run a heat engine and generator to make electricity.
• Tidal Capture (Chap. 16) is very similar to hydroelectricity, but based on trapped tidal basins instead of dammed rivers.
• Ocean Currents (Chap. 16) behave much like wind, and can be used similarly to produce electricity, but underwater.
• Waves (Chap. 16) bring energy to shorelines that can drive specialized generators to make electricity.

One prevalent theme connects most of these entries: lots of electricity, often by way of heat engines and/or generators. Indeed, alternatives to fossil fuels tend to excel at electricity production. But as we saw in Fig. 7.2 (p. 105), electricity makes up only 38% of energy demand in the U.S., and only 17% of the energy delivered to the four end-use sectors.³ One lesson is that current energy uses that are not electricity-based-like transportation and industrial processing⁴ - will be more difficult to replace by the alternatives above.

10.2 Alternatives vs. Renewables

Before going further, we should clarify the difference between “alternative” and “renewable” resources.

Definition 10.2.1
Alternative Energy is a non-fossil source of energy. Solar, wind, and nuclear would be examples.

Definition 10.2.2
Renewable Energy is a source of energy that is replenished by nature, so that its use may be sustained “indefinitely,” without depletion. Solar energy, for instance is not “used up” by placing a panel in the sunlight.

The sun will continue to shine no matter how many solar panels we set out. Wind is replenished daily by the sun heating the land and driving air currents. Solar energy drives the hydrological cycle, refilling the reservoirs behind hydroelectric dams. Plants grow back to replace harvested ones again thanks to the sun. Ocean currents and waves are also driven by the sun, via wind.

Nothing, of course, lasts forever, but the sun will continue to operate in its current mode for billions of years more, and this is long enough to count as indefinite, for our purposes. Table 10.1 classifies various sources as to whether they are alternatives or renewables, along with justifications. The items with asterisks are technically not renewable, but last long enough that we can treat them as such in a practical sense (see Box 10.1).

Table 10.1: Energy classification. Asterisks indicate non-replenished, but long-lasting sources.

166 finite supply in ground Sun generates rain and refills reservoirs Sun generates daily by heating Earth surface Sun will last billions of years

Resource Chapter Alternative? Renewable? Reason Petroleum 8 No No Natural Gas 8 No No finite supply in ground finite supply in ground Coal 8 No No Hydroelectric 11 Yes Yes Wind 12 Yes Yes Solar 13 Yes Yes Biomass (wood) 14 Yes Yes Nuclear Fission 15 Yes No Nuclear Fusion 15 Yes Yes* Geothermal 16 Yes Yes* Tidal Capture 16 Yes Yes* Ocean Currents 16 Yes Yes Waves 16 Yes Yes Sun grows more finite supply of fissile material in ground billions of years of deuterium; not tritium/lithium finite, but large; rate-limited can drive Moon away eventually Sun/wind-driven Sun/wind-driven

Just because a resource is renewable does not mean it is limitless.⁵ We only have so much land, nutrients, and fresh water to grow biomass, for example. Cutting trees down faster than they grow back would result in depleting the resource-possibly permanently if the land is altered severely enough that trees do not grow back. Installing turbines throughout the ocean to capture ocean currents⁶ would eventually create enough impediment to the flow that it could stop altogether.

Box 10.1: About Those Asterisks...

The items sporting asterisks in Table 10.1 deserve additional explanation as to why they are not technically renewable, even if the depletion timescales are extremely long.

Capturing all available tidal energy would end up accelerating the moon’s egress from Earth⁷, eventually causing loss of the resource.⁸

About half of the geothermal energy store represents a one-time deposit of heat left over from the collapse/formation of the earth, the other half coming from radioactive decays of elements ultimately tracing to ancient astrophysical cataclysms.⁹(5) For both the formation and radioactive contributions, the supply is not replenished after its use, although the timescale for the radioactive decays to fade away is billions of years.

Nuclear fusion needs deuterium and tritium.¹⁰ Roughly one out of every 10,000 hydrogen atoms is deuterium, so ocean water (H2O) will have enough deuterium to last billions of years. Tritium, however, is not found naturally and must be synthesized from lithium, in finite supply. Details will follow in Chapter 15.

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10.3 Renewable Energy Budget

Notice that all of the unqualified¹¹ “Yes” entries in Table 10.1 originate from the sun. For that matter, fossil fuels represent captured ancient solar energy, stored for all these years. The sun sends energy toward the earth at a rate of 1,360 $W/m^2$. Multiplying this by the projected area¹² of the earth (R≈ 1.28 x $10^14m^2$) results in 174,000 TW of solar power intercepting the earth. This number absolutely dwarfs the 18 TW societal energy budget of all humans on Earth. Figure 10.1 shows graphically what happens to this energy input.

174,000 TW (100%) solar input 29.3% atmospheric reflected reflection 22.6%

Figure 10.1: Energy inputs to the earth, ignoring the radiation piece (since that is an output channel). About 70% of incoming solar energy is absorbed by the atmosphere and land, while about 30% is immediately reflected back to space (mostly by clouds). About half of the energy absorbed at the surface into evaporating water, while goes smaller portions drive winds, photosynthesis (land and sea), and ocean currents. Additional non-solar inputs are geothermal and tidal in origin [^63][^64][^65].

Example 10.3.1 Solar Input

Because we will encounter solar power flux many times in this textbook, this is a good opportunity to spell out some key numbers and concepts.

First, sunlight arriving at the top of Earth’s atmosphere delivers energy at a rate of 1,360 Joules per second per square meter (1,360 $W/m^2$), which is known as the solar constant ⁴.

Treating Earth as a sphere of radius R, it has surface area $4πR^2$, but the sun doesn’t “see” the whole surface at once. In fact, from the vantage point of the rays of sunlight intercepting Earth, what matters is the projection of Earth,¹³ which just looks like a disk of area $πR^2$. Averaging the solar input across the entire planet therefore reduces the 1,360 $W/m^2$ by a factor of 4 to 340 $W/m^2$.

Not all the sunlight arriving at the top of the atmosphere makes it to the surface, so in practice, a typical location will receive an average¹⁴ of about $200 W/m^2$. This is a number that comes up often as a typical insolation, so is worth remembering.

Clouds and ice (mostly) reflect almost 30% of incoming sunlight, leaving 123,000 TW to be absorbed by land, water, and atmosphere in various forms (see Table 10.2). Virtually all of the energy hitting the surface goes to direct thermal absorption,¹⁵ much of which then flows into evaporation of water-the starting point of the hydrological cycle. A tiny portion of the absorbed energy gives rise to wind, some of which will drive waves. An even smaller portion contributes to photosynthesis and supports essentially all life (biology) on the planet. And finally, a tiny fragment of the absorbed energy drives ocean currents. Table 10.2 tracks where the incoming solar energy goes, in several stages, also listing non-solar geothermal and tidal contributions. For comparison, the current energy scale of human activity is approximately 18 TW, while (total) human metabolism,¹⁶ is about 0.8 TW.

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Table 10.2: Earth’s energy input budget. Symbols O, , and represent Sun, Earth, and Moon, respectively. The second group breaks out the solar input into three pieces that add to the total in the row above. The third group all comes from absorbed energy-mostly at Earth’s surface. The last group is not from radiant solar energy, so that percentages are in parentheses as they do not belong to the solar budget [[^63] [^64] [^65]].

Category total solar input surface absorption Power (TW) 174,000 83,000 47.9 % solar 100 source reflection to space 51,000 29.3 atmos. absorption 40,000 22.6 evaporation 44,000 25.4 wind 900 0.5 O absorp. photosynthesis 100 0.06 ocean currents 5 0.003 → → → surf. geothermal tides 44 (0.025) 3 (0.0018) Ө (,0 → → surf. → → surf. Comments the next 3 inputs come from here heats surface; evaporates H2O, powers life, wind, etc. from clouds, ice; uncaptured energy heats atmosphere, some to wind from surface absorption; hydrological cycle from absorptions above, also makes waves fuels biology (life) on the planet moves water around half original heat, half radioactive decays gravitational; mostly from Moon, some from Sun

Example 10.3.2 Solar Heating

How much would a black table¹⁷ warm up sitting in full sun for ten minutes?

A nice round-number approximation of full overhead sunlight is that it delivers $1,000 W/m^2$ to the ground. If we situate a table whose top surface area is $1 m^2$, has a mass of 20 kg, and a specific heat capacity of 1,000 J/kg/°C under full sun, we can proceed as follows.

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The table will absorb 1,000 J per second,¹⁸ and therefore receives 600,000 J over the course of ten minutes. Multiplying the specific heat capacity by the table mass means the table absorbs 20,000 J for every 1°C of temperature rise, and therefore would climb 30°C in 10 minutes, in this case. That’s a little unrealistically high, because a real table would also have cooling influences from the air and infrared radiation. But the main point is to show how absorbed sunlight heats things up-like the Earth.

Box 10.2: Making New Fossil Fuels

We know from Chapter 8 that fossil fuels get their energy from ancient photosynthesis trapped in buried plant matter.¹⁹ We also now have a figure for how much solar power goes into photosynthesis: 100 TW.

We can compare this to the power that goes into making new fossil fuels right now by noting that the entire fossil fuel resource contains roughly²⁰ $10^23J$ (page 127), and formed over something like 100 million years, or about $3 x 10^15$ seconds. Dividing the two gives a power of about $3 x 10^7 W$, or 30 MW.²¹

Three neat insights come out of this. First, we currently burn fossil fuels at a rate of about 15 TW, which is 500,000 times faster than they are being replaced! It’s like short-circuiting a battery in a dramatic explosion of power. Imagine charging a phone for 2 hours and discharging it 500,000 times faster: in 0.014 seconds! Now look at the extravagant lights of Las Vegas: should we be proud of the blaze of glory or appalled?²²

Secondly, out of the total 100 TW photosynthetic budget on Earth, only 30 MW gets captured as fossil fuels, which is one part in three-million. Therefore, the chances that any given living matter on the planet today eventually ends up converted to fossil fuels is exceedingly slim.

Finally, if we only used fossil fuels at a rate of 30 MW,²³, then we could consider fossil fuels to be a renewable resource, as the sun/geology will slowly make more!(5) So whether or not something is renewable also relies on the rate of use not exceeding the rate at which it is replenished.

10.4 Renewable Snapshot

Table 7.1 (p. 106) already gave an account of the mix of energy use in the U.S., including many of the renewables. This section revisits those numbers, in slightly more detail.

Source hydroelectricity geothermal wind wood E biofuels solar qBtu TW thermal equiv. % of renewables % of total 2.77 0.093* 24 2.7 2.49 0.083* 22 2.5 2.36 0.079 21 2.3 2.28 0.076 20 2.3 0.92 0.031* 8 0.9 waste (incineration) 0.49 0.016 4 0.5 0.21 0.007 2 0.2 total 11.52 0.382 100 11.4 170

Table 10.3: U.S. Renewable energy consumption in 2018. The last column compares to the 101.3 qBtu total U.S. consumption in 2018 [^34]. Asterisks denote thermal equivalent conversions. While the second column of numbers would be more naturally expressed in GW, the choice of TW is deliberate to emphasize how small renewable usage is compared to the available resource.

hydro 24.0%
biofuels 19.8%
wood 20.5%
wind 21.6%
solar 8.0%
waste 4.3%
geothermal 1.8%

Figure 10.2: Same info as Table 10.3 in pie chart form.

In 2018, roughly 11% of energy in the U.S. came from renewable resources. Table 10.3 lists the contributions from each, the data coming from the Annual Energy Review published by the U.S. Energy Information Administration for 2018. As introduced in Box 7.2 (p. 106), the EIA adopts the practice of assigning a thermal equivalent for each source, in qBtu, even if the source had nothing to do with a thermal process. The rationale is to put everything on the same footing as fossil fuels, for more direct quantitative comparisons. In doing so, they implicitly use the average thermal-to-delivered energy efficiency for fossil fuels of 37.5%.²⁴ In other words, it takes 100 units of thermal fossil energy to produce 37.5 units of useful work. If, then, a solar panel delivers 37.5 units of energy over some amount of time, it will be called 100 units of “input” (thermal equivalent), even though it only delivered 37.5 units.²⁵

Four forms dominate Table 10.3 (and Figure 10.2), each roughly equal in contribution. Lumping wood and biofuels into a generic “biomass” puts this aggregate category in the clear lead, accounting for nearly half of our renewable energy.²⁶

As noted, the entries in Table 10.3 are in qBtu of thermal equivalent, and these have been converted to TW, for easy comparison to Table 10.2.28 A key take-away is how tiny the renewable energy numbers are compared to the natural flows in Earth’s energy budget.

10.5 Upshot: Our Path Forward

We are now ready to plunge into learning about renewable energy resources. The topics are arranged according to ease of understanding the associated physics, which will be new to many students. So while solar is the most potent of the resources, its chapter follows those of hydroelectricity and wind, since its scheme for generating electricity²⁷ is likely the least intuitive of the three. Biologically-derived energy comes next sharing its direct sunlight origin with solar. Following a foray into nuclear energy, a number of minor contributors that are unlikely to be important are relegated to a single chapter of misfits, for completeness.

After this, we will be in a position to assess the entire landscape of alternative energy options (Chapter 17). The book will then take a turn away from physics and address how all this new information might fit into future plans at societal and personal levels.

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10.6 Problems

1. Based on what you already know or suspect about the alternative energy sources listed in Section 10.1, which ones do you suspect3 are pollution free (no emissions, no waste)?
2. Based on what you already know or suspect about the alternative energy sources listed in Section 10.1, which ones do you suspect31 have no negative environmental impacts? Explain your reasoning.
3. Which of the truly renewable (“Yes” without asterisk) entries in Table 10.1 are limited (finite) in terms of the scale32 we could achieve on Earth (explain the nature of the limit), and which are not limited (and why)?
4. Which four entries in Table 10.1 do not ultimately trace entirely to solar energy input to Earth?
5. If, for some terrible reason, the sun ceased shining and humans managed to survive for 1,000 years longer,[^33] what options would be left for obtaining energy? 34
6. About 30% of the 1,360 $W/m^2$ solar power arriving at Earth is immediately bounced back without a trace. Of the part that remains, when distributed/averaged around the whole sphere, what is the average energy deposition rate per square meter into the earth system?
7. Based on the numbers in Table 10.2, Figure 10.1, and in the text, what fraction (in percent) of all biological activity on Earth do (all) humans represent, from a metabolic energy standpoint?
8. Based on the numbers in Table 10.2, Figure 10.1, and in the text, what fraction (in percent) is human societal energy production (all activities; fossil fuels, etc.) compared to all biological activity on the planet?
9. What fraction (in percent) of the solar energy that is absorbed by Earth’s surface goes into evaporation (the hydrological cycle; refer to Table 10.2, and Figure 10.1)?
10. If we add up the five smallest pieces in Table 10.2, what fraction (in percent) does this set of energy flows represent in comparison to the total solar energy absorbed by the earth system?
11. The percentages of absorption and reflection in Figure 10.1 represent averages over weather conditions. On a clear day with the 30: Don’t worry about correctness, as this is an opportunity to think and gauge current understanding. 31: Don’t worry about correctness, as this is an opportunity to think and gauge current understanding. 32: not how long it can last; how much power is available 33: It’s nearly impossible to imagine that survival is at all realistic in this dire situa- tion. 34: face area account for projected vs. total sur-

172 sun overhead, a solar panel has access to more light than the 48% depicted reaching the ground. If we can also capture the portion that on average is reflected by the ground and clouds,35 what might we expect for the rate of energy reaching the ground (in $W/m^2$) if the input at the top of the atmosphere is 1,360 $W/m^2$? 12. Similar to Example 10.3.2, how much warmer would you expect a 10 cm deep puddle of water36 to get after an hour in full sun, if the water absorbs all the energy and does not lose it to the environment? 13. Comparing Table 10.2 and Table 10.3, what is the most striking mismatch,[^37] in terms of large potential vs. small contribution to U.S. energy consumption? 14. In one day, a typical residential solar installation might deliver about 10 kilowatt-hours of energy. Meanwhile, a gallon of gasoline contains about 37 kWh of thermal energy. But the two ought not be directly compared, as burning the gasoline inevitably loses a lot of energy as heat. Correcting the solar output to a thermal equivalent,[^38] how many gallons per day of gasoline could it displace? 15. The U.S. occupies about 2% of Earth’s surface area, thus collecting only part of the 83,000 TW absorbed at the surface. Compare the amount of solar power received by the U.S. to the total renewable power in Table 10.3.39 By what factor are we “underutilizing” the solar input, under the simplifying assumption that we could use all of it? 35: Recall, it’s a clear day; no clouds. 36: Water has a density of 1,000 kg per cubic meter and a specific heat capacity of 4,184 J/kg/°C. Make up whatever area you want; the answer should be the same for any pick. 37: In other words, for those sources that can be matched within the tables, which stands out as the most underutilized relative to its input numbers? 38: the text. Use the 37.5% factor discussed in 39: origin since it’s almost all solar in ultimate