1. Energy, Electricity, Efficiency, Power, Work, Manufacturing and Engines

Ampere (amp or A)—“The number of electrons passing a given point in the circuit per unit time is called the current. Current is measured in amperes . . . One amp corresponds to the flow of 6.24 × 1018 electrons per second.”

Amperes = volts / ohms

For ohms, see resistance.

1 ampere = 1 coulomb/sec

A device’s rating in amperes may be multiplied by the available voltage (as I write, residential U.S. voltage is often 115 V) to determine its power consumption in watts. See the equation under power.

Battery—See fuel cell.

“Big five” materials—Cement, paper, steel, plastics and aluminum, whose joint manufacture (ca. 2015) emitted 56% of the world’s industrial carbon dioxide. see here.

British Thermal Unit—see here.

Coulomb—A unit of electrostatic charge. “Comprises approximately 6 million million million electrons.”

Current—“A movement or flow of electricity.” “The movement of charges past a particular reference point.”

Efficiency—“The ratio of output to input.” “The efficiency of an ideal machine is 1.0 (100%). However, all real machines have efficiencies of less than 1.0.” “When the rate of work is constant, either work or power can be used to calculate the efficiency. Otherwise, power should be used.” For the generation of electric power with traditional steam turbines, be it from nuclear or fossil fuel, about ⅔ of the heat input accomplishes no direct work. Hence one could say that steam turbines are only about ⅓ efficient. Efficiency in manufacturing has to do with how much thermodynamic work must necessarily be accomplished to create a specific material, and how much more work than that minimum is actually being (“wastefully”) done; further, efficiency reflects how much of the input material and the manufactured material are wasted during processing, as in the “trim scraps” cut off of paper in a printing plant. High heating values of fuels can be considered the light of efficiencies. From the table of Calorific Efficiencies beginning here we see that a pound of gasoline will give up 5.1 times more combustion energy than a pound of green cottonwood. To reduce climate change one should obviously strive for maximum efficiency and minimum greenhouse emissions.

Electricity—“A form of energy that consists of mutually attracted protons and electrons . . .” “Any manifestation of energy conversion of charge that results in forces in the direction of motion those charges carry.” “The electron theory states that all matter is made of electricity.” “Electricity cannot be generated . . . It can, however, be forced to move.” Of course we talked about electricity generation all the time. By this we meant the generation of power.

Energy—Since in and of itself it cannot be measured, energy is a relative term. A high-temperature system has more energy than a low-temperature system. One common definition is the ability to do work. “Energy is a measurement of power over a period of time. It shows how much power is used, or generated, by a device, typically over the period of an hour . . . It is measured in watt-hours (Wh) and kilowatt-hours (kWh).” As it happens, energy is also measured in calories, joules, British Thermal Units, curies, etcetera.

Energy flow—An attempt to total up all various energy expenditures in the manufacture, packaging, shipping, preparation, consumption and disposal of a certain item. Thus the energy flow for a food item would include the energy units (such as BTUs) in its planting, fertilization, harvesting, cooking, waste collection, etcetera. “An important concept underlying the measurement of energy flows throughout an economy is the ‘conservation of embodied energy’ . . . , which states that energy burned or dissipated by a process is passed on, embodied in the products of that process.”

Embodied energy—(i) “The energy required to produce a material from its raw form, per unit mass of material produced. The energy is usually measured as the low heating value (see here) of the primary fuels used plus any other primary energy contributions. These energy requirements are dominated by two main steps: (i) harvesting and (ii) refining.” (ii) Another definition is: Manufacturing energy + use energy.

Manufacturing energy—The energy needed to manufacture a product. More or less equivalent to embodied energy, (i). For instance, the power used to fabricate a refrigerator’s parts and then assemble them.

Use energy—The energy expended by using the product. For instance, the power consumed by running a refrigerator over its working lifetime, or “use phase.”

Erg—A unit of work, comparable to joules, but dimensionally more confusing, and now thankfully not much met with. Often used in older literature to express radioactivity, solar energy, etc. 1 erg = 1 gram per square centimeter per second per second. Or, to be more definitionally regressive:

1 erg = 1 dyne-cm = 1 g-cm2/sec2

1 dyne = 1 g-cm/sec2

Here are some values visually estimated from their placement on a bar graph “Range of Energies”: “Earth’s annual energy from Sun,” more than 1032 ergs; H-bomb, more than 1024 ergs; first atomic bomb, more than 1020 ergs; fission of a uranium nucleus, about 10−4 ergs.

1 erg = 9.4805 × 10−11 BTUs = 7.3756 × 10−8 foot-pounds = 1 × 10−7 joules = about 0.012 roentgens [See section 3, here.]

1 erg-sec [nowadays more correctly written erg/sec or “erg per second”] = 1.3410 × 10−10 horsepower = 1 × 10−7 watts

1 erg per square centimeter per second [erg/cm2-sec]= 1 × 10−3 watts per square meter

Exajoule—See joule.

Exergy—A word often employed by Prof. Timothy Gutowski of MIT in his writings on manufacturing and use efficiencies. I avoided it in Carbon Ideologies. In this section it may be worth introducing: “Exergy of a material flow represents the maximum amount of work that could be extracted from the [energy] flow considered as a separate system as it is reversibly brought to equilibrium with a well-defined environmental reference state . . . [I]n exergy analysis, work and heat are not equivalent, as they are in First Law analysis.” A detailed understanding of specific exergies would obviously assist the fight against climate change.

Foot-pound [ft-lb]—The amount of energy required to lift a 1-pound object 1 foot. The non-metric (and nearly obsolete) counterpart of a joule. If a weight of 7 lbs is lifted 2 ft, then the work done is 14 ft-lbs.

1 ft-lb = 1.356 J = 0.001285 BTU

Ft-lbs ought to be distinguished from lbm [pounds-mass] and lbf [pounds-force]. “The units of pounds-mass and pounds-force are as different as the units of gallons and feet, and they cannot be canceled” in standard dimensional analysis.

Fuel cell—“An electrochemical device in which the chemical energy of a conventional fuel is converted directly and usefully into low-voltage direct-current electrical energy . . . In a battery, the chemical energy is in the cell. Fuel cells keep converting [by combustion] with the addition of oxygen and fuel,” which is usually a carbon-dioxide-emitting hydrocarbon (see here), but can be clean hydrogen. “For short periods, conventional batteries are generally superior to fuel cells, which come into their own when electrical energy is required over long periods.”

Gigawatt [GW]—A billion watts.

1 GW = 109 watts = 106 [= 1 million] kilowatts = 56,884,000 BTUs per minute

Horsepower [hp]—Originally based on the amount of work an “average” horse could do, this archaic unit continued in my day to be applied to motors. (“The real thermal efficiency of an average horse, even at heavy, continuous work, is probably not more than 6 to 10 per cent,” based on BTUs in of horse feed and BTUs out of work, and counting BTUs out of digestion and other metabolic processes as waste. “Under laboratory conditions” it might be 20 percent.) “You may assume that 1 HP equals 3 ft lbs of torque at 1750 rpm (a common motor speed).”

1 hp = 33,000 ft-lb in 1 minute (or per minute, or / min) = 550 ft-lb/sec = 0.7068 BTU/sec = 42.408 BTUs/min = 745.70 watts [absolute]* = 0.7457 kilowatts = 76.0404 kg-m per sec

1 horsepower [U.S.] = 1.0139 metric horsepower

Internal combustion engine—[Sometimes abbreviated ICE.] “A machine for converting chemical energy to mechanical energy by burning a fuel with air in a confined space and expanding the products of combustion, extracting energy as work.” There are two kinds. Gasoline engines are of the spark ignition type, oil engines of the compression ignition type.

Joule [J]—One of several units of work. “The practical unit of electrical energy.” Also, as it happens, “a unit of mechanical energy,” since it can be defined as 1 newton [1 kilogram being accelerated at 1 second per second] for a distance of one meter. As Prof. Gutowski wrote me: “Pick an orange up off the table and raise it over your head. The work you do is about one joule.”

1 J = 1 watt-second = [1/3.6 million or 2.778 × 10−7] kilowatt-hours = 0.0002388 [= 2.388 × 10−4] kilocalories = 0.7376 ft-lbs = 3.725 × 10−7 hp-hrs = 0.000948067 [= 9.48 × 10−4] BTUs = 6.242 × 1018 electron-volts.

One milli[joule]= 0.001 joule/kg. Obsolete.

One megajoule [MJ] = 1 million J = 948.067 BTUs

Energy content of a fuel [see high heating value, here]: 1 MJ/liter [a common metric way of expressing it] = 2.78 × 108 BTUs/gal

1 kJ/kg = 0.4299226 BTUs/lb

1 GJ/kg = 429,922.6 BTUs/lb

One gigajoule [GJ] = 109 [= 1 billion] J = 1 million kJ = 948,067 BTUs

1 ton of TNT = 4.184 GJ = 3,966,712 BTUs

One kilajoule [kJ or KJ] = 1,000 [103] joules = 0.9481 BTUs

One terajoule [TJ] [= 1 trillion] = 1012 joules = 948.1 MBTU [million BTUs]

Therefore, 1 metric ton of greenhouse emissions per TJ of combusted fuel [a typical formulation in non-American greenhouse gas inventories] converts to 1 pound of emissions per 430,955 BTUs.

One petajoule [PJ] = 1015 [= 1 quadrillion] joules = 9.481 × 1011 BTUs

“One petajoule is enough to run the Montréal subway system for a year” (ca. 2009).

Total Canadian energy consumption, 2009: 7,650 PJ.

One exajoule [EJ] = 1018 [= 1 quintillion] joules = 9.481 × 1014 [or 0.9481 quadrillion = 948,000,000,000,000] BTUs = 0.948 quads.

365.93 EJ was the amount of energy used by the entire planet in 1991.

1 EJ consumed in a year is equivalent to 1.902 billion BTUs/min (or 33.45 billion watts), used without letup for that year.

One very rough conversion from EJ per year to million barrels of oil per day: Divide by 2.23.

Kilowatt [kW]—A thousand watts. “The term kilowatt . . . indicates the measure of power which is all available for work.”—American Electricians’ Handbook, 2002.

1 kW = 1,000 watts = 56.884 BTUs/minute = 3,413.04 BTUs/hour = 44,254 foot-pounds/minute = 1.341 hp = 3,600 million J/hr (or 1,000 J/sec)

Since ⅔ of the energy combusted in a traditional fossil fuel power plant is lost, 1 kW takes 170.652 carbon BTUs to generate. See next page.

Kilowatt versus kilowatt-hour—The first is a measure of power, which means rate of energy consumption, or energy used per unit of time (an hour). The second, in spite of its name, lacks a time dimension, because it expresses the absolute amount of energy that has been, will be or would be used in that unit of time. A physics textbook from 1971 explains it more mathematically: “The amount of energy used during a certain operation or process is frequently expressed as the product (power) × (time). For example, the amount of energy generated by a 1-kW power plant operating for 1 hr is 1 kW-hr.” In other words, 1 kWh, for instance, = 1 kW × 1 hour = [56.884 BTUs/minute] × 60 minutes = 3,413.04 BTUs. The time units cancel out. This anti-intuitive distinction figures in conversion calculations relating to the tables in Carbon Ideologies.

Kilowatt-hour [Kwh or KWH or kWh]—Power consumption, not measured in kilowatts per hour. Prof. Anna Mummert notes: “Comparable to BTU (not BTU/time), ft-lb (not ft-lb/hr).” “The common engineering unit of electrical energy.” “If you play a radio (80 watts) an average of 1 hour a day, then during a month’s time (30 days) it would consume 30 times 80 watt-hours or about 2.4 KWH.” “To store 1 kwhr of energy in a reservoir at 1 m (3.28 ft) requires 367,000 kg of water or 96,900 gal . . .” 2,650 sacks of sand, each weighing 100 lb, falling for 10 ft, will produce 1 kWh.

1 kWh [no time unit given or needed] = 3,413.0 BTUs [or, according to one conversion which I did not follow, 3,412.14 BTUs] = 3,600,000 [or 3.600 × 106] joules [abs] = 3.6 MJ = 2.6552 × 106 foot-pounds = 1.341 hp = 3.6 megajoules [no time unit given or needed].

1 kWh/day = 2.37 BTUs/min.

According to the U.S. Energy Information Administration, to generate 1 kWh [the standard power plant wastage of ⅔ is implied (see text here)], require the following [figures in italics are my conversions*]:

Kilowatt-day [Kwd or KWD]—Power consumption, measured in kilowatts used per day.

1 gram U-235 yields 8 kilowatt-days of energy.

1 langley = 3.69 BTUs/ft2. [See section 7, here]

Megawatt—1 million watts. “The power consumed by roughly a thousand households. It’s the equivalent of 10,000 100-watt lightbulbs.” “An average human body exudes about the same heat as” a 100-watt bulb, “. . . so a megawatt . . . can be compared . . . to the rate of bodily heat emitted by 10,000 people . . .”

1 megawatt-hour [MWh] = 1,000 kWh = 3,413,000 BTUs

Ohm—“The resistance through which the fall of potential is 1 volt when the current [electromotive force; see volt] is 1 amp.”

Power—“Power measures the rate of energy conversion. It is measured in watts . . . It equals volts times current.” [Watt-hours, kilowatt-hours, etc., measure the total amount of energy that was used in a given time.] Power is “the amount of work done [per] unit time. It is a scalar quantity.” “Output power per unit volume is directly proportional to speed. Low-speed motors are unattractive for most applications because they are large and therefore expensive. It is usually better to use a high-speed motor with mechanical speed reduction . . . The efficiency of a motor improves with speed.”

For a given device:

Watts of power = volts × current (amps)

“If you have a mobile phone charger that uses 1.2 amps at 5 volts, you can multiply . . . to work out the number of watts,” in this case 6.

Primary power—Power used to supply primary energy, which is “the energy required to produce a material from its raw form, per unit mass of material produced. The energy is usually measured as the low heating value (see here) of the primary fuels used plus any other primary energy contributions. These energy requirements are dominated by two main steps: (i) harvesting and (ii) refining.”

Quad—A quadrillion BTUs.

Resistance—“The opposition to current flow.” Measured in ohms.

Ohms = volts / amperes

Terawatt—1 trillion watts, or 56,884,000,000 BTUs per minute.

Terawatt-hour [Twh, TWh or TWH]—Power consumption, measured in terawatts [trillions of watts] consumed in an hour.

1 TWh = 1 billion kWh = 3,413,000,000,000 [3.413 trillion] BTUs.

1 TWh = 0.086 mtoe [million tons of oil equivalent]

“However, the primary energy equivalent of nuclear electricity is calculated from the gross generation by assuming a 33% efficiency, i.e. 1 TWh = (0.086 ÷ 0.33) mtoe.” [I suspect this last is an error for 0.086 times 0.33.]

Use phase—See embodied energy: use energy.

Volt—“Voltage is a measure of the ‘pressure’ that is trying to force electrons down the wire. Increasing the voltage across a given load will increase the current through the load.” Or, if you like, “voltage . . . is the electromotive force (EMF) which causes electrons to flow.” More technically, voltage expresses the potential difference [in joules per coulomb] between the sourcepoint and the endpoint of electrical flow. “An electric potential or voltage is the work done on a unit charge to bring it from some specified reference point to another point.” “1 V shall be taken as that emf [electromagnetic force] which will establish a current of 1 A through a resistance of 1 [ohm].”

Volts = power / current

For example, a 48-watt motor operating in a 4-amp current must be running at 12 volts.

Volts = amperes × ohms

Watt [w]—A joule per second. “One watt is produced when one ampere flows at an emf [electromagnetic force] of one volt.” “A watt is not a unit of energy per se; . . . it’s a unit describing how rapidly energy is used.” “Power measures the rate of energy conversion. It is measured in watts . . . It equals volts times current.”

A 100-watt lightbulb consumes 100 watts per second (360,000 joules per hour).

1 watt [absolute] = 0.998 watts [IT] = 1 J [abs] per sec and = 0.000948 BTUs per second = 0.056884 BTUs per minute = 3.413 BTUs per hour = 0.00134 horsepower = 1 × 107 ergs per second

Prof. Anna Mummert inserts here: “The unit watts per second is comparable to joules per second per second, or joules per second per hour.”

Since ⅔ of the energy combusted in a traditional fossil fuel power plant does no useful work, 1 w takes 0.170652 carbon BTUs to generate.

1 kilowatt [kW] = 1,000 watts = 0.2388 kilocalories per second = 1.341 horsepower = 0.9478 BTUs per second = 56.884 BTUs per minute. See also terawatt-hour.

1 terawatt [TW] = 1 trillion watts = 56,884,000,000 BTUs per minute. See also terawatt-hour.

1 watt per square meter = 0.317 BTUs per hour per square foot = 0.005288 BTUs/min/ft2 = 2,777.63 BTUs/yr/ft2

Watts = amperes × volts

[See also kilowatt and megawatt. See section 3E, p. 551, for watts expressed in units relevant to nuclear power.]

Electric goods shop in Dubai

Watt-hour [Wh]—Electricity consumption, measured in watts used in each hour. “A 100-watt bulb burning for 5 hours uses 500 watt-hours or 0.5 KWH of energy.” For discussion, see kilowatt-hour.

1 watt-hour [Wh] = 3,600 J = 3.413 BTU = 0.001341 hp-hr

1 Wh/kg = 1.548 BTUs/lb

Work—“Work is the overcoming of mechanical resistance through a certain distance.” “If a system undergoes a displacement under the action of a force, work is said to be done, the amount of work being equal to the product of the force and the component of the displacement parallel to the force.” More simply put, work is force × distance. But since matter and energy are always conserved, and all energies are mutually convertible, heating a liquid (for instance) is also doing work. “Work is a signed, scalar quantity. Typical units are inch-pounds, foot-pounds, and joules,” not to mention ergs and calories. “Mechanical work is seldom expressed in British thermal units or kilocalories,” but in this book, which focuses on fuel combustion, I have done just that.

For a given explosive, one may calculate the work (“the mechanical equivalent of heat”) it can accomplish, in kilogram-meters (a precursor of joules), by multiplying the heat of explosion, in calories, by 425. According to this procedure, the work of detonating nitroglycerin is 671,500 kg-m, or 3.85 times the work of detonating mercury fulminate (174,250 kg-m).