Notation - Energy and Human Ambitions on a Finite Planet

This list describes several symbols that are commonly used within the body of the book.

푐 Speed of light in a vacuum inertial frame: ².^99792458 ^× ¹⁰⁸ ^m/^s ^≈ ³ ^× ¹⁰⁸ ^m/^s
휀 Efficiency; typically 0 ≤ 휀 ≤ 1; unitless
푔 acceleration due to gravity: 9.8 m/s² or ^≈10 m/s²
ℎ Planck’s constant: ⁶.⁶²⁶ ^× ¹⁰−³⁴ ^J · ^s
^푘^B Boltzmann’s constant: ¹.³⁸ ^× ¹⁰−²³ J/K
^푁^A Avogadro’s number: ⁶.⁰²² ^× ¹⁰²³ particles per mole
^Δ푄 Change in thermal energy, in Joules
^푅^⊕ Radius of Earth: 6,378 km
^푅 Radius of Sun: 695,700 km
^푟^⊕ Earth–Sun distance (1 AU): 149.6 million km
^휎 Stefan-Boltzmann constant: ⁵.⁶⁷ ^× ¹⁰−⁸ ^W/K/m²
^Δ푆 Change in entropy, in J/K
^Δ푇 Change in temperature, typically in ◦^C or Kelvin (K)
^Δ푊 Change in energy—work performed, in Joules

1Scale Factor Prefixes¶

Factor	Letter	Prefix	Factor	Letter	Prefix
10-21	z	zepto	1021	Z	zetta
10-18	a	atto	1018	E	exa
10-15	f	femto	1015	P	peta
10-12	p	pico	1012	T	tera
10-9	μ	nano	109	G	giga
10-6	μ	micro	106	M	mega
10-3	m	milli	103	k	kilo

2Greek Letters, with Pronunciation¶

Character	Name	Character	Name
α, A	alpha AL-fuh	ν, N	nu NEW
β, B	beta BAY-tuh	ξ, Ξ	xi KSIGH
γ, Γ	gamma GAM-muh	ο, Ο	omicron OM-uh-CRON
δ, Δ	delta DEL-tuh	π, Π	pi PIE
ϵ, ε, E	epsilon EP-suh-lon	ρ, P	rho ROW
ζ, Z	zeta ZAY-tuh	σ, Σ	sigma SIG-muh
η, H	eta AY-tuh	τ, T	tau TOW (as in cow)
θ, Θ	theta THAY-tuh	υ, Υ	upsilon OOP-suh-LON
ι, I	iota eye-OH-tuh	φ, Φ	phi FEE, or FI (as in hi)
κ, K	kappa KAP-uh	χ, X	chi KI (as in hi)
λ, Λ	lambda LAM-duh	ψ, Ψ	psi SIGH, or PSIGH
μ, M	mu MEW	ω, Ω	omega oh-MAY-guh

3Glossary¶

3.0.1AC¶

alternating current. 77, 215

4AER¶

Annual Energy Review. 102, 103, 105–107, 109, 170

5alpha decay¶

(훼) happens when a nucleus emits an alpha particle, otherwise known as a He ⁴ nucleus. 243, 422, 435

5.0.1alpha particle¶

(α) is a ⁴He (helium) nucleus, ejected from a larger nucleus in an alpha decay It therefore consists of two protons and two neutrons. 243, 245, 422# Amp

(A) is short for Ampere. 77, 293, 422, 425

5.0.2Ampere¶

(A, or Amp) is the SI unit of current, defined such that one Ampere is the same as one Coulomb per second (1 A = 1 C/s). 77, 422

5.0.3a.m.u.¶

atomic mass unit. 241, 246–248, 253, 254, 265, 376, 422, 432, 433, 435

5.0.4Annual Energy Review¶

is compiled by the U.S. EIA, capturing energy use and trends for all sources and sectors [34]. 102, 170, 422

6Astronomical Unit¶

(AU) is a unit of distance, equal to the average Earth–Sun distance of 149.6 million kilometers (1.⁴⁹⁶ ^× ¹⁰¹¹ m). 56, 422

7asymmetric risk¶

describes a condition where given the choice to pursue action B for fear of some future condition instead of the normal action A, the downside of being correct about the threat and not taking action B is far more disastrous than being wrong about the threat and pursuing route B unnecessarily. 345, 351

8atomic mass unit¶

(a.m.u.) is defined so that a single neutral carbon atom, consisting of 6 protons, 6 neutrons, and ⁶ electrons has exactly 12.00000 a.m.u. In other units, it is 931.4941 MeV or ¹.⁶⁶⁰⁵⁴ ^× ¹⁰−²⁷ kg. This unit sometimes goes by the name: Dalton. 241, 376, 422, 433

9AU¶

Astronomical Unit. 56, 206, 420, 422

10Avogadro’s number¶

is $N_A = 6.022 \times 10^{23}$ , pertaining to one mole of particles (e.g., atoms, molecules). 375, 376, 381, 433# band gap

is the energy difference between the conduction band and the valence band, determining how much energy is needed to promote an electron out of an atom and into conduction. 203, 204, 223

10.0.0.1barrel¶

(bbl) is a unit of volume used primarily for petroleum. It is exactly 42 U.S. gallons, amounting to 159 L of volume. A commonly used measure of energy is barrels of oil equivalent (b.o.e.), amounting to 6.1 GJ of combustion energy. 112, 120, 126, 129–131, 135, 141, 211, 266

10.0.1beta decay¶

(β) happens when a nucleus emits either an electron (β⁻) or a positron (β⁺). 243, 245, 265, 435, 438### Betz limit

is a theoretical maximum amount of kinetic power that can be removed from wind without slowing the wind too much. It computes to 19/27, or 59%, and is independent of technology [71, 72]. 188, 189, 195

10.0.2Big Bang¶

is the name given to the start of the universe, about 13.8 billion years in the past. 9, 55, 239, 257, 392, 394, 396

10.0.2.1biofuel¶

describes a liquid chemical fuel derived from biologically grown plants: algae, sugar, corn, rapeseed, etc. The two most common forms are ethanol and biodiesel. 165, 227, 230, 231, 428

10.0.2.2biomass¶

is a generic term for biological matter, but in the energy context usually means firewood or dung that may be burned for thermal energy. 170, 227, 229–231

10.0.3birth rate¶

quantifies the number of births per 1,000 people per year, typically. Numbers tend to be in the 5–30 range. 38, 426

10.0.3.1blackbody¶

is a term describing the radiative qualities for thermal emission of light (infrared radiation for “normal” temperatures, becoming visible for very hot objects). A perfect blackbody is not reflective (i.e., “black” at the wavelengths of interest) and emits energy as a function of wavelength according to the Planck spectrum. 145, 199–201, 203, 223, 434, 438

10.0.4boiling water reactor¶

is a type of nuclear fission reactor in which water surrounding the fuel rods acts both as a moderator and as the means of transporting heat away from the nuclear fuel. 255, 256

11Boltzmann constant¶

is a fundamental constant of nature associated with thermodynamics. In SI units, it has a value of $k_B = 1.38 \times 10^{-23}$ J/K. 89, 199, 381# breeder reactor

is a nuclear fission reactor that transforms non-fissile nuclei into ones that are fissile by means of neutron capture and subsequent radioactive decay. 250, 262, 264, 296, 423

12breeding¶

see breeder reactor. 259

13British thermal unit¶

(Btu) is a unit of energy in the Imperial unit system, defined as the amount of energy required to heat one pound of water by 1◦F. It is equivalent to 1,055 Joules. 75, 423, 427, 435, 437

13.1Btu¶

is short for British thermal unit. 75, 97, 98, 335, 372, 423

14Calorie¶

(Cal, or kcal) is a unit of energy, defined as the amount of energy required to heat one kilogram (1 kg, 1 L, 1,000 cm³ ) of water by 1◦C. It is equivalent to 4,184 Joules, and is the exact same

thing as a kilocalorie. Note the capital C differentiates it from the calorie, which is 1,000 times smaller, making this the dumbest unit convention around, and strongly favoring the use of the equivalent kcal instead. 73

14.0.1calorie¶

(cal) is a unit of energy, defined as the amount of energy required to heat one gram (1 g, 1 mL, 1 cm³ ) of water by 1◦C. It is equivalent to 4.184 Joules. 73, 85, 177, 194, 424, 431

14.0.2capacity factor¶

is the fraction of energy delivered by an installation compared to what it would deliver if operating continuously at peak operating (“nameplate”) capacity. 176, 179, 180, 182, 183, 190, 191, 196, 212, 216, 217, 226, 256, 267, 279, 281, 282, 288

14.0.3caprock¶

is a geological feature of impermeable rock that can trap oil, gas, or steam below it. 120, 278 carrying capacity

refers to the limiting population that can be supported long-term by the environment. No consensus exists for Earth’s carrying capacity for humans, though standards of living have a large influence. 34, 432

14.0.4CFL¶

compact fluorescent light. 21

14.0.5chain reaction¶

is a self-feeding process that keeps itself going. In the context of nuclear fission, neutrons released by the fission precipitate the next fission event, and so on. 251, 252, 255, 262, 425, 432

14.0.6charge¶

is a measure of the degree to which a particle or object is influenced by electromotive forces. Electric charge can be positive or negative, so that like charges repel and opposites attract. The unit for electric charge is the Coulomb. 77, 240, 241, 246, 395, 425, 427, 429, 433

14.0.7Chart of the Nuclides¶

is a Periodic Table on steroids, listing the properties of every known nuclide including mass or energy, abundance (if stable), half life (if unstable), decay mode, neutron cross section, nuclear spin, and other salient properties; see https://people.physics.anu.edu.au/~ecs103/chart/. 240–242, 244, 245, 248, 251, 253, 259, 266, 270

14.0.8chemical energy¶

is energy stored in chemical bonds, like gasoline or wood that might be burned, or in the food we eat. 70, 117, 121, 182, 227, 228, 234, 379, 395, 396

15climate sensitivity parameter¶

relates a change in radiative forcing to the net temperature change once all the feedback mechanisms have acted. The units are ◦C per W/m² , and a typical value is 0.8. 147, 160

16coefficient of performance¶

(COP) refers to the energy gain by a heat pump, usually in the context of heating rather than cooling. It is identical to 휀heat, as defined in Eq. 6.11 (p. 95). 97, 425

17compound¶

describes a particular combination of elements that construct a particular molecule. For instance, H2O is the compound we know as water. 376, 379, 432

18concentrated solar power¶

(CSP) refers to a form of solar thermal (ST) energy, employing troughs or “power towers” or any technique that focuses solar power to create high temperatures, often then used to generate electricity. 220, 425, 436

18.0.0.1conduction band¶

is the energy level a step up from that of electrons in the valence band. Electrons in the conduction band are very loosely bound and freely wander about the crystal, hopping from one atom to the next, and therefore able to contribute to a current. 202, 203, 422, 435, 438

18.0.0.2confinement¶

in the context of fusion refers to the trapping and holding of a high-temperature plasma, usually by magnetic means. 265

18.0.1conservation of energy¶

says that energy is never created or destroyed, only shifting from one form to another. 70, 91–93, 95, 246, 393, 394, 425

18.0.2conservation of mass-energy¶

extends conservation of energy to include mass, so that the combined mass-plus-energy of a closed system is never created or destroyed, only shifting from one form to another (mass-energy exchange via $E = mc^2$ ). 246#### control rod

is used in a nuclear fission reactor to absorb neutrons so that the chain reaction does not get out of control and cause a meltdown. 251, 255, 256, 432

18.0.2.1COP¶

coefficient of performance. 97, 99, 335, 424

18.0.3Coulomb¶

(C) is the SI unit of electric charge. An electron has a charge of ⁻1.⁶ ^× ¹⁰−¹⁹ C and a proton has a charge of ⁺1.⁶ ^× ¹⁰−¹⁹ C. 77, 422, 424, 427

18.0.4coupled¶

refers to the tight connection often seen between energy/resource use and economic scale (as measured, for instance, by GDP). 18, 425

18.0.5critical mass¶

is the mass of fissile material (assumed to be in spherical form) above which a self-sustained chain reaction will occur. Below this, the material poses no danger. Right at critical mass, the material will limp along in a slow chain reaction. Above this threshold—super-critical—an exponential runaway detonation will occur, and is the basis of nuclear weapons. For U 235 , critical mass is 52 kg (a bit smaller than a volleyball), and for Pu ²³⁹ , it is 10 kg, and about the size of an American softball. 262

18.0.6CSP¶

concentrated solar power. 220, 424, 436

19current¶

is a measure of charge flow, expressed in the SI unit of Amps. 77, 85, 202, 203, 205, 422, 425, 436

19.0.1D–D fusion¶

uses deuterons (²H nuclei) as the fuel for fusion, achieving an energy density of 137 million kcal/g. 265# death rate

quantifies the number of deaths per 1,000 people per year, typically. Numbers tend to be in the 5–30 range. 38, 426

20decay chain¶

refers to a consecutive series of radioactive decays. 244, 245

21decoupling¶

is the notion that economic activities need not incur a large energy or resource cost, breaking the tendency for economic scale to be tightly coupled to physical goods. 20

21.0.0.1demographic transition¶

refers to the process in which an undeveloped country initially having high birth rate and high death rate transitions to low death rates followed by low birth rates as medical and resource conditions improve. 39, 44

21.0.0.2deuterium¶

is an isotope of hydrogen, in which the nucleus (called a deuteron) contains one proton and one neutron. 248, 265, 266, 272, 274, 299, 426

21.0.1deuteron¶

is the nucleus of deuterium, consisting of one proton and one neutron. 265, 425, 426

21.0.2dietary energy factor¶

is the quantitative energy impact of a set of dietary choices compared to a vegetarian diet. A typical American diet has a dietary energy factor around 2, meaning it takes twice as much energy as would a vegetarian diet. This term is not in universal use. 339–341, 349, 428

21.0.2.1differential equation¶

is an equation that relates functions and their derivatives. The subject is often sequenced after calculus within a curriculum. 33, 34

21.0.3doping¶

is a process by which deliberate impurities are introduced into a semiconductor in order to change its properties with respect to transport of electrons or holes. 202, 431

21.0.4doubling time¶

is how long it takes a system or collection to double its amount under conditions of growth, such as in exponential growth. See also the rule of 70. 2, 6, 23, 31, 32, 405

21.0.5D–T fusion¶

combines a deuteron ( ²H nucleus) and a triton ( ³H) as the fuel for fusion, achieving an energy density of 81 million kcal/g. 265, 267### duty cycle

refers to the percentage of time something is “active.” For example, a refrigerator may be on 40% of the time to maintain internal temperature, in which case its duty cycle is 40%. 88, 334

21.0.6Ecological Economics¶

is a field that builds economic theory on top of the notion that the planet offers finite resources and flows. A principle aim is that of a steady-state economy capable of indefinite planetary compatibility. 323, 324

21.1EER¶

energy efficiency ratio. 97–99, 427, 430

22EIA¶

Energy Information Administration. 7, 75, 102, 103, 106, 107, 131, 170, 215, 422, 426

23Electric Power Monthly¶

(EPM) is compiled by the U.S. EIA, capturing electricity production and usage at the state level from all energy sources [85]. 215, 427

24electromagnetic radiation¶

refers to any transport of energy by electromagnetic waves, which include light, ultraviolet, infrared, X-rays, microwaves, gamma rays, and radio waves. 10, 198, 397, 426, 431, 435

25electromagnetic spectrum¶

refers to the sweep of wavelengths or frequencies of electromagnetic radiation, including light, ultraviolet, infrared, X-rays, microwaves, gamma rays, and radio waves. 79, 392

25.0.0.1electron¶

is a fundamental particle typically found in the outer parts of atoms, surrounding the nucleus. Electrons have negative charge equal and opposite to that of protons, but are 1,836 times lighter than the proton, at 0.511 MeV. 77, 78, 198, 202, 239, 244, 245, 255, 395, 422, 423, 425, 426, 429, 430, 433–435, 438

25.0.1electron-volt¶

(eV) is a unit of energy, defined as the energy (work) it takes to push a charge of one fundamental charge unit (see entry for Coulomb) through an electric potential of one Volt. 1 eV is equivalent to ¹.⁶ ^× ¹⁰−¹⁹ Joules. 78, 198, 223, 248, 428, 432

25.0.2element¶

pertains to a single atom on the Periodic Table. For instance, hydrogen, helium, and carbon are all elements. 376, 379, 424, 432

25.0.3energy¶

is defined as the capacity to do work. The SI unit is the Joule. 68, 73, 77, 174, 334, 379, 423–425, 427, 431, 434, 437, 438

25.0.4energy density¶

describes how concentrated energy is in a substance, quantified as energy per unit mass. In chemical contexts, anything around 10 kcal/g or higher is considered energy–dense, while substances at about 1 kcal/g or lower are poor. Carbohydrates and proteins are middling, around 4 kcal/g, while fat is 9 kcal/g, and therefore among the more energy–dense substances. 121, 122, 175, 228, 230, 231, 236, 237, 254, 256, 264, 277, 290, 380, 398, 425, 426, 428

25.0.5energy efficiency ratio¶

(EER) refers to the energy gain by a heat pump, usually in the context of cooling rather than heating. Its units are odd, defining how many British thermal units (thermal energy) may be moved per Watt-hour of input energy, but relating to $\varepsilon_{cool}$ (defined in Eq. 6.10 (p. 95)) by a simple numerical factor: EER = 3.41 $\varepsilon_{cool}$ . Sometimes seen as SEER to represent a seasonal average EER value. 97, 98, 426# energy intensity

measures the energy use of a society relative to its economic scale. A typical value may be about 5 MJ/$. 19, 336

26energy trap¶

refers to a phenomenon in which energy shortage motivates aggressive pursuit of alternative energy schemes, but that pursuit requires substantial energy investment—forcing an even more acute but voluntary energy shortage, which is politically difficult. 132, 301, 310, 311

27enriched¶

28see enrichment. 258, 262¶

29enrichment¶

refers to the process of increasing the concentration of a particular isotope within a sample of an element. Usually, this term is applied to the concentration of U ²³⁵ from its natural 0.72% to 3–5% for power plants or >20% (typically ∼85%) for weapons. 258, 427

30entropy¶

is a measure of how many ways a system can be configured for some fixed energy level. The entropy of a closed system cannot decrease. 90, 396, 420

31Environmental Economics¶

is an offshoot of neo-classical economics that adds a layer of pricing to capture “externalities,” or environmental costs not normally included in market price. 323

32EPM¶

Electric Power Monthly. 215, 426

32.0.0.1EROEI¶

Energy Returned on Energy Invested: a measure of how profitable an energy source is in terms of energy, expressed as a ratio. For instance, a 9:1 EROEI means 9 units were extracted or produced for an investment of 1 unit, leaving a net gain of 8 units of energy. 1:1 is break-even, deriving no net energy benefit. 231, 235, 236, 278, 295, 297, 301, 302, 310, 311, 315, 339

32.0.1estimated total resource¶

is an educated extrapolation of proven reserves trying to characterize the amount of resource that may be ultimately found and extracted. 127, 131, 258

32.0.2ethanol¶

(C2H5OH) is a liquid alcohol frequently produced as a biofuel having an energy density of ∼7 kcal/g. 108, 230, 297, 377, 423

32.0.2.1eV¶

electron-volt. 198, 203, 248, 427, 432

32.0.2.2exponential growth¶

happens when the rate of growth—as a percentage or fraction—is constant. 2, 4, 31, 33, 61, 319, 426, 434

32.0.2.3feedback¶

is the response of a system when a change is made that itself influences the change: either counteracting it as in negative feedback or amplifying it as in positive feedback. 145, 147, 424

32.0.3fill factor¶

is a generic term describing the fraction of total area occupied. For instance a polka-dot pattern of circles on a piece of fabric might have a fill factor of 15%. 189

32.0.4fissile¶

describes a nucleus that is prodded into fission by a (slow) thermal neutron. The three fissile nuclides of interest are ²³³U, ²³⁵U, and ²³⁹Pu. 255, 259, 262, 423, 425, 428### fission

is a nuclear process in which a heavy nucleus splits into two lighter nuclei. Only $^{233}$ U, $^{235}$ U, and Pu²³⁹ are usually considered as accessible nuclides that are fissile in the presence of slow (thermal) neutrons. 85, 239, 249, 264, 289, 296, 423-425, 428, 432# flexitarianism

is the practice of pursuing dietary choices based on quantitative assessment of energy costs in an effort to keep the dietary energy factor low, without enforcing complete strictness, enjoying the occasional deviation on special occasions or just to avoid being a pain to others. 342

33fossil fuel¶

refers to an energy source buried in the ground, in the form of coal (solid), petroleum (liquid), or natural gas (gaseous). Fossil fuels represent ancient solar energy captured in living matter, processed and stored underground over millions of years. 7, 22, 27, 31, 61, 103, 104

34fracking¶

is slang for hydraulic fracturing, a technique used to extract “tight” oil and gas resources locked up in less permeable rock formations. High-pressure fluids are used to create cracks in the rock that the allow oil and/or gas to flow. 120, 124, 128, 130, 232

35frequency¶

characterizes the number of cycles per second in a periodic phenomenon (often in wave phenomena). The units are Hertz, or 1/s. 79, 198, 426, 430, 434, 436

36fuel rod¶

is a long cylinder having a high-enough concentration of fissile material to be used in a nuclear fission reactor. 255, 256, 260, 263, 272, 423

428

36.0.0.1fusion¶

is a nuclear process in which two light nuclei merge to form a larger nucleus. Repulsion of the charges in the nuclei make it exceedingly hard to achieve, requiring temperatures of many millions of degrees. 85, 239, 249, 265, 289, 299, 395, 425, 426, 437

36.0.0.2galaxy¶

is a collection of stars held together by mutual gravitational attraction, generally numbering in the billions of stars. 9, 54, 55, 312, 394, 438

36.0.1gamma decay¶

(훾) is when a nucleus in an energetically excited state emits a high-energy photon. 244, 429, 435 gamma ray

(훾) is a high-energy photon, as may be generated by a gamma decay or by annihilation of an electron and positron. 244, 251, 255, 434, 435

36.0.1.1GDP¶

Gross Domestic Product, effectively representing the total monetary flow of goods and services within a society, typically over a one year period. 18, 24, 39, 425

37generator¶

converts mechanical motion (rotation, typically) into electrical current, generally by the relative motion of wire loops and a strong magnetic field. 89, 99, 164, 165, 175, 184, 185, 190, 250, 279, 280, 282, 285, 430, 436

37.0.1geothermal¶

refers to thermal energy within the earth, both from the original heat of formation and from radioactive decay. 85, 99, 108, 166, 275

37.0.2GHG¶

greenhouse gas. 146, 151, 152, 155, 160, 161, 429

37.0.3Gppl¶

is a short-hand unit for giga-people, or billion people. 32, 37

38gravitational potential energy¶

is the energy stored in a mass, 푚, lifted a height, ℎ, above some reference in the presence of gravity, 푔 ^≈ 10 m/^s 2 . The energy amounts to 푚 푔 ℎ, and will be in Joules if the inputs are in kg, m, and s. 66, 69, 70, 77, 89, 167, 173, 174, 177, 184, 275, 280, 283, 395, 396, 438

39Green Revolution¶

refers to the modernization of agricultural practices worldwide beginning around 1950, when fossil fuels transformed both fertilization and mechanization. 31, 37, 123, 124, 234

40greenhouse gas¶

(GHG) absorbs infrared radiation and acts as a thermal blanket in a planetary atmosphere. H2O, CO2, O3, and CH⁴ are powerful greenhouse gases. 11, 12, 144–146, 151, 429

41grid tied¶

refers to a photovoltaic system connected to the local electrical utility grid, enabling export of solar production by day and use of utility electricity by night. 213, 222

42half life¶

is the time after which half a sample of radioactive nuclei will have undergone radioactive decay. After 푁 half-life periods, the remaining fraction will be ¹/² ^푁. 242, 243, 257, 259, 261, 262, 270, 276, 424, 435

43heat capacity¶

is the amount of energy it takes to raise an object’s temperature by 1◦C. The specific heat capacity is the heat capacity divided by mass, becoming an intrinsic property of the material. Water’s

specific heat capacity is 4,184 J/kg/◦C, intimately tied to the definition of the kilocalorie. 74, 85, 99, 147, 153, 168, 194, 271, 277, 372, 401

43.0.0.1heat engine¶

is a device that converts thermal energy into another form, usually mechanical motion. Automobile engines are a common example, as are power plants that create steam from a thermal source that itself drives a turbine and generator. 89, 92, 165, 239, 267, 276, 277, 286, 294, 298, 348, 396, 433, 436

43.0.1heat loss rate¶

as used in this book is the power per ^Δ푇 (in ◦C) required to maintain a temperature differential. Units are W/◦C, and typical houses might be a few hundred W/◦C. 87, 99, 100, 334

43.0.1.1heat of fusion¶

is the energy barrier associated with either forming (fusing) or melting a solid from a liquid. In the case of water (ice), the heat of fusion is 334 J per gram. 152, 153

43.0.2heat of vaporization¶

is the energy barrier associated with turning a liquid into gas. In the case of water going to water vapor, the heat of vaporization is about 2,250 J per gram. 177

43.0.3heat pump¶

is a device that moves thermal energy from a cold environment to a hotter one, against normal flow. Some energy input is required to drive this reverse flow, but thermodynamic principles permit a small amount of input energy to drive a larger amount of thermal energy transfer. 85, 95, 297, 335, 427, 430

43.0.4heating seasonal performance factor¶

(HSPF) refers to the energy gain by a heat pump in the context of heating, but in the same units as the EER so that HSPF is COP times 3.41, numerically. 97, 98, 430

43.0.5heavy oil¶

refers to oil that is very viscous—closer to tar than to gasoline. Heavy oil is more difficult to extract, process, and obtain gasoline via refinement. 131

43.0.6Hertz¶

(Hz) is the SI unit for frequency, and is equivalent to cycles per second, or 1/s. 198, 428

43.0.7hockey stick¶

is a term used to describe plots that suddenly shoot up after a very long time of relative inaction. Plots of human population, atmospheric CO2, energy use, all tend to show this characteristic—which resembles an exponential curve. 31, 115

44hole¶

in the context of semiconductors is the absence of an electron—or an electron vacancy. When another electron fills the hole, it leaves behind another hole, and it is as if the hole moved effectively like a positive charge able to roam through the crystal. 202, 204, 426, 435

45HSPF¶

heating seasonal performance factor. 97–99, 430

46HST¶

Hubble Space Telescope. 59

47hydrocarbon¶

is a chain of carbon and hydrogen atoms such as the alkanes (methane, ethane, propane, butane, octane, etc.) having chemical formula C푛H2푛+2, where ^푛 ⁼ ¹ for methane, 2 for ethane, 8 for octane, etc. 119, 121, 131, 229, 436

48hydrological cycle¶

is the solar-driven process by which evaporation of water from the surface (bodies of water or moist land) forms clouds, and the clouds deliver rain back to the surface. 166, 168, 177

48.0.0.1infrared radiation¶

is the property that all objects glow in light, or electromagnetic radiation. For objects that are not “red hot,” the emission is invisible to the human eye, at longer wavelengths than the visible spectrum. The power radiated obeys the Stefan–Boltzmann law. 10, 84, 143, 147, 151, 161, 169, 396, 397, 423, 429, 435, 437

48.0.1insolation¶

is the annual average solar flux reaching flat, level ground for a particular location. A typical number is 200 W/m², but can range from half that at high latitudes to about 350 W/m² for arid areas at lower latitudes. 168, 178, 189, 206–208, 228, 276, 285### inverse function

is a mathematical operation that “undoes” its counterpart, like the square root undoes the square, or the natural logarithm undoes the exponential. 5, 32, 367, 370

48.0.1.1isotope¶

is what we call atoms that have various nuclear configurations for the same element. That is, variants of a nucleus having the same number of protons but differing numbers of neutrons, and therefore differing mass number. See also nuclide. 240, 242, 252, 261, 266, 296, 375, 376, 426, 433, 437

48.0.1.2ISS¶

International Space Station. 58–60

48.0.2Jevons paradox¶

is named after early economist William Stanley Jevons, and describes the backfire of efficiency improvements leading to increased usage of the associated resource due to greater demand for the more attractive, efficient technology. Also called the rebound effect. 23, 435

48.0.3Joule¶

(J) is the SI unit of work or energy, and is equivalent to Newtons times meters (N·m), or kg · m2/s 2 . 19, 69, 159, 309, 371, 420, 423, 424, 427, 429, 431, 432, 434, 435, 437, 438

49junction¶

describes an interface between two semiconductors that have different doping. Junctions are the basis of photovoltaic, diodes, light emitting diodes (LEDs), transistors, and many light detectors. 202, 204

49.0.1kcal¶

kilocalorie. 74, 85, 99, 118, 121, 122, 136, 140, 228–230, 233, 236, 237, 246, 253, 254, 258, 265, 277, 290, 334, 335, 339, 340, 380, 398, 423–428, 431

49.1Kill-A-Watt¶

is the name of a relatively inexpensive device that can measure instantaneous power in Watts and accumulated energy in kWh of electrical appliances. The name is a pun on units. 334

50kilocalorie¶

(kcal) is a unit of energy, equivalent to 1,000 calories, defined as the amount of energy required to heat one kilogram (1 kg, 1 L, 1,000 cm³ ) of water by 1◦C. It is equivalent to 4,184 Joules. 73, 84, 254, 334, 339, 424, 430, 431

51kilowatt-hour¶

(kWh) is a unit of energy, constructed as a power (kilowatts) times time (hours). It is equivalent to 3,600,000 Joules, or 3.6 MJ. 72, 159, 172, 209, 214, 226, 343, 401, 402, 432

52kinetic energy¶

is the energy of motion, given by ¹ ²푚푣² for a mass, 푚, at velocity, 푣. If input units are kg and m/s, the resulting unit will be Joules. 69–71, 89, 174, 184, 185, 223, 275, 282, 284, 395, 396, 437

52.0.0.1kWh¶

kilowatt-hour. 76, 159, 214, 272, 334, 335, 337, 338, 342, 348, 398, 431, 438

52.0.1LED¶

light emitting diode. 21, 29, 78, 83, 431

53life-cycle CO² emission¶

is an assessment of how much CO² is released from an energy source when considering the entire enterprise—including manufacture/construction, operation, etc. See the Wikipedia page on List of life-cycle greenhouse gas emissions. 181, 194, 218, 221, 264

53.0.1liquefied natural gas¶

(LNG) is cryogenically-cooled natural gas (methane) at −160◦C that can be stored much more compactly than the gaseous form, making it suitable to transport. 432

53.0.1.1LNG¶

53.0.1.2liquefied natural gas. 121, 432¶

53.0.2logistic¶

describes a mathematical model in which rate of growth depends on how close the population is to the carrying capacity. The resulting population curve over time is called the logistic function, or more informally, an S-curve. 34

53.0.3macro-economics¶

concerns itself with the allocation of goods and services across the marketplace, optimizing supply and demand, aiming to minimize surplus or deficits. 323, 324, 433

53.0.3.1mass number¶

(퐴) is simply the total number count of protons and neutrons (nucleons) in a nucleus. For example, a carbon atom having 6 protons and 6 neutrons has 퐴 ⁼ 12. 240, 431

53.1meltdown¶

refers to a failure mode of nuclear fission reactors, in which the chain reaction becomes uncontrolled due to too many neutrons triggering new fission events (as may happen if control rods are absent or insufficiently deployed). 262, 263, 425

54MeV¶

is a mega-electron-volt, or 10⁶ eV. In Joules, it is equivalent to $1.6 \times 10^{-13}$ J. Nuclear masses are often expressed in MeV/ $c^2$ terms, where 1 a.m.u. is equivalent to 931.4941 MeV. 78, 246–248, 253, 265, 422, 427, 433, 435# micro-economics

concerns itself with the production of goods, including raw resources, marketing, and distribution. 323, 324, 433

55micron¶

(휇m) is 10−⁶ meters, or a micro-meter. 198, 200, 438

55.0.1moderator¶

in the context of nuclear fission is a material used to slow down neutrons speeding out from the break-up so that they can become thermal neutrons and stimulate subsequent fission events in a chain reaction. Light atoms like water are a good choice for absorbing the neutron impacts. 251, 255, 256, 423

56molar mass¶

is the mass of one mole of an element or compound. The molar mass for carbon, for instance, is 12 grams. The number is often found on a Periodic Table, in addition to the proton number for the element. 121, 138, 241, 379, 380

56.0.0.1mole¶

is a number of atoms or molecules, tuned so that one mole of the carbon-12 isotope is exactly 12.000 grams. It takes ⁶.⁰²² ^× ¹⁰²³ atoms for this to happen, which is called Avogadro’s number. 78, 83, 375, 376, 378, 422, 432

56.0.0.2negative feedback¶

involves a reaction to some stimulus in the direction opposite the stimulus, performing a corrective action and leading to stability. Systems in equilibrium must have negative feedback keeping them there. 33, 123, 147, 428, 433

56.0.0.3neo-classical economics¶

is the prevailing economic regime practiced today, driven by supply and demand, fueled by growth, market investment, and focus on micro-economics and macro-economics. 323, 427

56.0.0.4neutrino¶

is a fundamental particle associated with the weak nuclear force that has almost no mass, travels near the speed of light, and interacts so weakly with matter that it could pass through light-years of rock before being likely to hit anything. Neutrinos from the sun stream through our bodies constantly, day and night, since Earth is transparent to them. 243, 244, 438

56.0.1neutron¶

is one of two basic building blocks of atomic nuclei, the other being the proton. Neutrons have no electric charge, and a mass of 939.565 MeV, or 1.008665 atomic mass unit (a.m.u.). Neutrons are made up of three quarks: 1 up and 2 down. 240, 243, 244, 255, 299, 375, 376, 395, 422–426, 428, 431–433, 435, 437, 438

56.0.2Newton¶

(N) is the SI unit of force, and is equivalent to $\text{kg} \cdot \text{m/s}^2$ . 68, 371, 431, 438# nuclear binding energy

is the energy associated with the strong nuclear force that holds a nucleus together against charge repulsion. Typical levels are 8 MeV per nucleon. 247, 248

57nuclear energy¶

derives from reconfiguring the nuclei of atoms, releasing tremendous thermal energy that can be harnessed in a heat engine. 103, 104, 239

58nucleon¶

is either of the two building blocks of a nucleus, meaning that it is either a proton or a neutron. 240, 247, 248, 251, 376, 432, 433, 437

59nucleus¶

is at the center of an atom, composed of protons and neutrons and spanning ∼ 10−¹⁵ m. The vast majority (99.97%) of an atom’s mass is in the positively charged nucleus, which attracts a cloud of negative-charge electrons to complete the neutral atom. 239, 375, 376, 422, 423, 425–429, 431–433, 435, 437

60nuclide¶

is any bound arrangement of protons and neutrons. Every nucleus of every isotope is one of the possible nuclides, designated, for instance as C12, C-12, or C 12 . 240, 242, 243, 424, 428, 431, 435

61overshoot¶

occurs when the negative feedback in a system is delayed. After surpassing the equilibrium, oscillation may ensue. 36

62parts per million¶

(ppm) is a unit used to measure small contributions. One ppm is 0.0001%. 61, 139, 141, 434

62.0.0.1parts per million by mass¶

(ppmm) is a parts per million measure in terms of fractional mass. For instance, a gram is is 1 ppm^m of a metric ton (1,000 kg). 141, 258

62.0.1parts per million by volume¶

(ppmv) is a parts per million measure in terms of fractional volume occupied. For instance, a cubic millimeter (1 휇m, or micro-liter) is 1 ppm^v of a liter. 140–142

62.0.2payback time¶

is how long it takes to recuperate an investment by removing a chronic cost. For example, spending $1,000 to no longer pay an annual $100 charge has a payback time of 10 years. 215, 226

63photon¶

is the smallest indivisible particle of light: a minimum quantum packet of energy. Each photon has a well defined energy, which can also be expressed as a wavelength or frequency. 21, 70, 78, 79, 198, 199, 202, 227, 243, 244, 251, 394–396, 429

63.0.1photosynthesis¶

is the process by which living matter captures sunlight and stores some of it as chemical energy. Effectively, it takes CO² out of the atmosphere, combines the carbon with water to make sugars, releasing oxygen back into the air. 227, 395

63.0.2photovoltaic¶

(PV) is a semiconductor technology by which light directly drives an electrical current by interacting with electrons in the material. 165, 197, 201, 217, 218, 239, 267, 289, 292, 315, 350, 429, 431, 435

63.0.3Planck spectrum¶

describes a mathematically precise spectrum of light emission from a blackbody, fully defined by the temperature of the blackbody. 145, 199–201, 423, 436, 438

63.0.4Planck’s constant¶

is a fundamental constant of nature associated with quantum mechanics and the world of the very small. In SI units, its value is $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$ . 79, 198, 199### plasma

is a gas hot enough to strip electrons from atoms to create a highly-ionized medium, such as the gas comprising the sun. 265, 267, 268, 392, 393, 395, 425, 437

64positive feedback¶

involves a reaction to some stimulus in the same direction as the stimulus, thus amplifying the effect. Positive feedback leads to an unstable, runaway process—like exponential growth. 33, 123, 147, 428

65positron¶

is an elementary particle of anti-matter, and specifically an anti-electron, having the same mass and opposite charge as the electron and will annihilate with an electron into gamma rays. 243–245, 255, 423, 429

66power¶

is the rate of energy, or change in energy per change in time. The units are Joules per second (J/s), or Watts (W). 7, 10, 11, 30, 43, 71, 73, 77, 86, 110, 118, 146, 151, 171, 176, 187, 205, 280, 334, 335, 368, 373, 431, 435–438

67ppm¶

parts per million. 61, 139, 141, 433, 437

68predicament¶

describes a seemingly intractable situation: more than a problem, but possibly a tangled set of interconnected problems. Predicaments require responses rather than tidy solutions. 332, 436

68.0.0.1proliferation¶

is used to describe widespread distribution of dangerous nuclear materials, which becomes difficult to control if they exist in abundance due to increased reliance on nuclear energy. 239, 260, 262, 264, 269, 296, 297

68.0.1proton¶

is one of two basic building blocks of atomic nuclei, the other being the neutron. Protons have positive charge, equal and opposite to that of the electron. Protons have a mass of 938.272 MeV, or 1.0072765 a.m.u.. Protons are made up of three quarks: 2 up and 1 down. 77, 240, 243, 244, 375, 376, 395, 422, 425–427, 431–433, 437, 438

68.0.2proven reserve¶

pertains to the amount of resource known to exist, having been discovered and surveyed to estimate the economically recoverable amount. 126, 127, 131, 257, 258, 267, 269, 428

68.0.2.1PV¶

photovoltaic. 165, 197, 201, 205, 217, 220, 221, 267, 269, 281, 292, 293, 434

68.0.3qBtu¶

is short for a quadrillion (1015) British thermal units, and is equivalent to ¹.⁰⁵⁵ ^× ¹⁰¹⁸ Joules. 28, 75, 103–105, 170, 214, 229, 230, 234, 236, 277

68.0.4R/P ratio¶

or reserves-to-production ratio is a means to assess time remaining for a resource of quantity R units, being used (produced) at a rate of P units per year. The result is years available at the present rate, absent discovery of additional resources or change in rate of use. 126, 129, 131, 133, 136, 267

68.0.4.1radiation¶

is a broad term that can can describe light (e.g., electromagnetic radiation, infrared radiation, gamma rays) or particles from radioactive decay or cosmic origin. High-energy radiation of any form can cause damage to materials and biological tissues (DNA being perhaps most critical). 263

68.0.5radiative forcing¶

is used to describe the areal power (in W/m² ) of absorbed solar energy and infrared radiation to space. In equilibrium, a balance exists so that the net radiative forcing is zero. 146, 147, 151–153, 155, 160, 424# radioactive

describes a nucleus, or nuclide that is unstable and will undergo radioactive decay with some half life. 241, 257, 260, 261, 263, 268, 276, 296, 297, 299, 429

69radioactive decay¶

involves a change in the nucleus of an atom, most commonly in the form of alpha decay, beta decay, or gamma decay. 239, 242–244, 262, 275, 297, 423, 425, 429, 435, 437

70rebound effect¶

describes the counterintuitive process by which efficiency improvements lead to greater use of the resource as the enhanced appeal and lower cost results in more widespread adoption and use. Also called the Jevons paradox. 23, 431

71recombination¶

is when an electron in the conduction band of a semiconductor finds a vacancy (hole) for it to settle into. By disappearing from the conduction band, it is no longer available to contribute to current, and the energy it had becomes unrecoverable. 202, 204

is the process by which crude oil—as it comes out of the ground—is separated by approximate hydrocarbon chain length. In order of lighter/shorter to heavier/longer chains, crude oil yields propane and butane, gasoline (around octane), kerosene, diesel, heating oil, lubricating oil, and tar. 119, 430

71.0.1renewable¶

forms of energy are not necessarily depleted by their use. In other words, the resource is replenished naturally at some rate. The sun will still shine and wind will still blow even if we harness some of the energy. Firewood will grow back, but at a limited rate. 103, 104, 106

71.0.2response¶

is an appropriate reaction to a predicament, which may fall well short of a solution, but still represents a reasonable compromise approach. 332, 434

71.0.2.1rule of 70¶

tells us that the time it will take a system or collection to double in size is 70 divided by the percentage growth rate. The time units depend on how the time over which percentage growth is expressed—like 2% per day or 2% per year, for instance. The rule works most accurately for smaller growth rates, under 10%. 2, 5, 6, 28, 31, 405, 426

71.0.2.2R-value¶

describes the thermal resistance, or insulating quality of a wall or similar barrier. It is an inverse to the U-value, numerically 5.7/푈. Units are ◦^F ·ft² · hr/Btu, and larger numbers translate to better insulation. 87, 438

71.0.2.3sea level rise¶

is one of the inevitable consequences of climate change, as land-bound ice melts and ocean water thermally expands. 151, 155

71.0.3sector¶

refers to a domain of activity, typically dividing into residential, commercial, industrial, and transportation. 104, 165, 193, 337

71.0.4semiconductor¶

is a material poised between being a good conductor of electrical current and an insulator (not passing current). Silicon is the most commonly used semiconductor. 201, 202, 426, 430, 431, 435

72SI¶

Système International. 68, 71, 85, 88, 422, 423, 425, 427, 430, 431, 433, 434

72.0.1solar constant¶

measures 1,360 W/m², and is the power flux of the sun at the top of Earth’s atmosphere. It is not technically a constant, but is very stable. 11, 144, 167, 203, 206, 211# solar system

refers to our own star, the sun, and the planets that surround it, including Earth. 54

73solar thermal¶

(ST), also called concentrated solar power (CSP), typically refers to troughs or “power towers” or any technique that focuses solar power to create high temperatures, often then used to generate electricity via a heat engine and generator. 165, 197, 219, 221, 424, 436

74spectrum¶

describes a distribution, often associated with light. In this context, a light spectrum specifies how much light is present as a function of wavelength or frequency. The Planck spectrum is a good example. 145, 200, 434

74.0.1ST¶

solar thermal. 219–221, 269, 424, 436

74.0.1.1Stefan–Boltzmann constant¶

( $\sigma$ ) has a value of $5.67 \times 10^{-8} \text{W/m}^2/\text{K}^4$ and is used in the Stefan–Boltzmann law relating to infrared radiation. 10, 144, 199, 437### Stefan–Boltzmann law

says that the power emitted from a surface of area, $A$ , and temperature, $T$ will be $P = A\sigma T^4$ , where $\sigma$ is the Stefan–Boltzmann constant. 10, 144, 199, 431, 437### stoichiometry

amounts to the counting of atoms and balancing formulas in chemical reactions to reflect the survival of every atom in a reaction: none created or destroyed. 377, 378

74.0.2strong nuclear force¶

is the force that binds nucleons together in a nucleus, overcoming the electrical repulsion of protons. 240, 245, 247, 395, 433, 438

74.0.2.1substitution¶

refers to interchangeability between goods and services, so that an unavailable or inferior resource can be replaced by an alternative, possibly superior one. 21

74.0.3terraforming¶

is the speculative idea of transforming the atmosphere and environment of a planet hostile to human life into one that is suited to human needs. 60, 61

74.0.4Therm¶

is a unit of energy defined as 100,000 British thermal units, and is equivalent to ¹.⁰⁵⁵ ^× ¹⁰⁸ Joules. 76, 335, 337, 348

74.0.5thermal energy¶

is the energy of heat, and is really just randomized kinetic energy (motion) of atoms and molecules vibrating and zipping around. 70, 71, 84, 86, 89, 99, 165, 194, 203, 227, 246, 275, 277, 294, 334, 335, 373, 395, 396, 401, 420, 423, 427, 429, 430, 433

74.0.5.1thermal equivalent¶

is a construct used to compare thermal energy sources like coal, oil, and natural gas to sources like solar, wind, and hydroelectricity, which do not derive from thermal sources. Usually in the context of electricity production, multiplying by about 2.7 puts non-thermal sources into thermal-equivalent terms. 106–108, 170, 256, 279

75thermal expansion¶

describes how materials expand, or swell, as temperature increases. Typical rates of expansion are in the range of 5–100 ppm per ◦C. 155

76thermal neutron¶

is a neutron whose kinetic energy (speed) is no greater than it would naturally possess based on the temperature of its surroundings. Sometimes it is called a “slow” neutron because it is not traveling faster than thermal jostling would establish. 250, 428, 432

77tokamak¶

is the name of a donut-shaped chamber in which high-temperature plasma can be confined, and potentially used to generate fusion. 267

78transmutation¶

describes the transformation of a nucleus into a different one, usually via neutron absorption possibly followed by radioactive decay. 259, 268

79tritium¶

is an isotope of hydrogen, in which the nucleus (called a triton) contains one proton and two neutrons. 265–268, 299, 438

79.0.0.1triton¶

is the nucleus of tritium, consisting of one proton and two neutrons. 265, 426, 437

79.0.0.2turbine¶

is essentially fan blades on a rotating shaft, which can be compelled to move by a flow of air, water, or steam through the blades. 89, 99, 164, 175, 185, 190, 250, 279, 280, 282, 295, 430

79.0.1universe¶

refers to the entirety of our physical realm, including all galaxies. 9, 54, 55, 257, 312, 392, 423

79.0.2U-value¶

describes the insulating quality of a wall or similar barrier, in terms of how many Watts move through each square meter of surface area for each 1°C difference in temperature across the barrier. Units are W/m²/°C, and smaller numbers mean better insulation. The U-value is an inverse measure to the R-value, numerically $5.7/R$ . 87, 436### valence band

is the energy level of outer electrons bound to an atom. Valance electrons stay home, as opposed to electrons in the conduction band. 203, 422, 425

79.0.2.1Volt¶

(V) is a unit of voltage, or electric potential, and can be thought of as the electrical analog to gravitational potential energy, and is also somewhat like pressure in a fluid system. 77, 198, 427, 438

79.0.3voltage¶

is a measure of electric potential energy, expressed in units of Volts. 77, 438

79.0.4Watt¶

(W) is a unit of power, defined so that 1 W is 1 J/s (one Joule per second). 7, 18, 21, 43, 71, 77, 118, 169, 196, 267, 309, 371, 431, 434, 438

80watt-hour¶

(Wh) is a unit of energy, constructed as a power (watts) times time (hours). It is equivalent to 3,600 Joules, or 0.001 kWh. 73, 77, 97, 110, 176, 427, 438

81wavelength¶

measures the length of a wave from crest to crest or trough to trough, and can apply to waves in water, air (sound), or electromagnetic waves (light). The symbol 휆 (lambda) is often used to denote wavelength. The units are length (m), often expressed in microns (휇m). 79, 144, 198, 283, 394, 426, 431, 434, 436

82weak nuclear force¶

joins gravity, electromagnetism, and the strong nuclear force as one of nature’s four fundamental forces, responsible for beta decays and neutrino interactions. 244, 245, 433

83Wh¶

watt-hour. 73, 97, 98, 110, 175, 176, 438

84Wien law¶

describes the wavelength for which the Planck spectrum is at maximum brightness. It is roughly 2.9 mm divided by the blackbody temperature, in Kelvin. 199

85work¶

is a mechanical expression of energy, defined as a force (Newtons) times distance (meters) through which the force acts (along the same direction). The resulting unit is the Joule. 68, 84, 89, 174, 248, 379, 427

Appendices

Appendix D - Alluring Tangents