2. Heat and Refrigeration
Blackbody [or “black body”]—“For theoretical purposes it is useful to conceive of an ideal substance capable of absorbing all the thermal radiation falling on it. Such a substance is called a blackbody.” This concept is useful in solar engineering. “The amount of electromagnetic radiation emitted by a black body depends on its surface temperature. Its intensity distribution is dictated by the laws of quantum mechanics and is a manifestation of a state that, in physics, we call thermodynamic equilibrium[: a] state of a physical system where all the energy inputs equal the outputs.”
1 British Thermal Unit [BTU]—The amount of energy needed to warm a pound of water by 1° Fahrenheit. This is contained in one match tip. “On average, coal contains 25 million BTUs per ton.” Prof. Gutowski wrote me: “The world uses joules and watts for energy and power. The US (alone, as far as I know) uses BTUs and horse power. Even the British don’t use BTUs any more. We tried to make this transition in the 1980s but Reagan killed it. I suppose the machine tool companies complained loudly . . . European readers will find it quaint if you use BTUs . . . In my work I have completely abandoned the BTU but many industries still use it and the Department of Energy does too.” In 2016, so did the U.S. Geological Survey; see high heating value of a fuel. (From a build-your-own-solar-powered-home manual, 1975: “The selection of the BTU as a standard energy unit was made reluctantly . . . The rest of the world has adapted to . . . metric . . . and the United States will undoubtedly follow suit in the next decade.” Plus ça change . . .) I decided to use BTUs because even in 2017 they were comprehended better than metric units by my fellow Americans, who like me were energy wastrels who avoided the themes of Carbon Ideologies.
Note:
1 International Table BTU = 1.055 × 103 joules [J]
1 mean BTU = 1.056 × 103 joules [J]
1 thermochemical BTU = 1.054 × 103 joules [J]
Gutowski notes here: “I use 1 BTU [approx. equals] 1 kJ.”
1 BTU = 778.98 foot-pounds = 0.252 kilocalories = 1,054.8 joules [abs] = 1.0548 kilojoules = 107.56 kg-force meters = 251.98 [mean gram] calories [abs] = 251.996 IT calories. Another conversion, not used here, accepts 1 BTU at 252.16 cal.
1 IT calorie = 1/860 IT watt-hours = 4.187 abs J = 4.187 × 107 ergs
IT = “international”; used before January 1, 1948.* New system is abs = “absolute.”
1 kilocalorie [kcal or food Calorie] = 4,187 [sometimes calculated 4,186] J
1 BTU per minute = 17.579 watts
1 BTU per minute per ft2 = 189.226 watts/m2
Energy content of a fuel: 1 BTU per gallon = 3.597 × 10−8 megajoule [MJ]/liter [the common metric way of expressing it].
1 BTU [IT] per lb = 2.326 × 103 J/kg
1 BTU [thermal] per lb = 2.324 × 103 J/kg
1 MBTU = 1 million BTUs = 1.0551 × 10−3 terajoules (TJ) = 2.931 × 10−4 gigawatt-hours (GWh)
1 Q-BTU = 1 quadrillion BTUs = 1 quad
1 BTU/sec = 1.415 hp
1 BTU/hr = 0.01731 watt/cm2 = 2.930 × 10−4 [or 0.000293] kilowatts = 3.9292 × 10−4 horsepower
1 BTU/hr-ft2 = 3.155 watts/m2
1 BTU per pound (BTU/lb) of a given substance = 2.33 kilojoules per kilogram (kJ/kg).
Caloric or calorific—Refers to the inherent energy of a fuel, ready to be released through combustion. Calorific efficiency can also be expressed as high or low heating value.
Calorie:
1 [thermochemical gram-mean] calorie [cal or gcal]—The amount of heat needed to increase the temperature of 1 gram of water by 1° Celsius. Written with a small “c.”
1 calorie = 4.184 joules = 3.9685 × 10−3 BTU
1 Calorie [food calorie]—The same as a kilocalorie [kcal].
1 Calorie = 1 kcal = 1,000 cal = 1 “food calorie”
And why not use food calorie units to indicate the high heating value of coal or oil? “The availability of ammonia and straight-chain paraffins may permit future production of food from fossil fuels.”
1 kcal = 3.968 BTUs
1 kcal/g = 1,798.7961584 BTUs/lb
1 kcal/kg = 1.7987961584 BTUs/lb
Efficiency of a heat engine [e.g., a steam turbine power plant or an internal combustion motor]—Work output divided by heat input, both of them being expressed in the same units of energy [e.g., BTUs or joules]. Or, more explicitly:
Thermal efficiency = 1 − [heat rejected / heat absorbed].
As Carbon Ideologies often points out, about ⅔ of the energy in a nuclear or fossil fuel steam turbine plant accomplishes no useful work.
Fuel—“Fuels, whether for the furnace, automobile, or rocket, are energy-rich substances and the products of their combustion are energy-poor substances.”
Heat—The temperature-related energy which can be transferred between two objects or systems of different temperatures.
Heat of combustion—A more techno-chemical approach to HHV. Although I avoided using this term in Carbon Ideologies, it may be helpful to introduce it, in case you should come across it while comparing fuel energies. When I was alive, it usually signified kilocalories released or taken in per substance oxidized to water and/or carbon dioxide at constant pressure and 25° Celsius. A negative value implied that heat was given off, as would always be the case for a combusted fuel. [A positive value, not relevant to our purposes, showed that the reaction was endothermic; the substance actually cooled as it oxidized.] Heat of combustion was expressed not in pounds or standard volumes, but in moles. Simply and inadequately put, one mole (now sometimes written “mol”) of a substance (6.023 × 1023 atoms per molecule, or the basic unit of a chemical reaction; a mole of carbon weighs 12 grams while a mole of hydrogen weighs only 1, but those two moles are considered as equivalents) is calculated as the sum of the atomic numbers of its component atoms:
Molar weight of H2, or hydrogen:
(hydrogen’s atomic number = 1.0) × 2 (since as the formula shows a hydrogen molecule exists as 2 atoms) = 2 grams per mole
Of CH4, or methane:
(carbon’s atomic number = 12.0) × 1 (since there is only 1 carbon atom in the formula), + (hydrogen’s atomic number = 1.0) × 4 (since the formula shows that 4 of them are present) = 16 g/mole
C4H10, or butane:
(12.0 × 4) + (1.0 × 10) = 48 + 10 = 58 g/mole
C8H18, or octane:
1,307.53 (12.0 × 8) + (1.0 × 18) = 96 + 18 = 114 g/mole
The heats of combustion of these substances are:
Hydrogen: −68.32 kilocal per mole [= kcal/2 grams]
Methane: −212.80
Butane: −687.98
Octane: −1,307.53
Thus, to convert methane’s combustion heat back to a more familiar form (see next entry), one would multiply [212.80 kcal/mole] × [1 mole/16 grams] × [453.5 grams/lb] × [0.04163 lbs/cu ft] × [3.968 BTUs/kcal] = 996.34 BTUs per cubic foot.
For a discussion of molar ratios in climate change computations, see mole in section 12.
High heat[ing] value of a fuel = HHV (in BTUs/lb) = 14,544C + 62,028(H − O/8) + 4,050S
C = carbon content [in %]
H = hydrogen content
O = oxygen content
S = sulfur content
(“I never use the term hhv in my studies. My colleagues and I at the USGS used Btu as the measure of the heat content of coal. From a quick check on the Internet the terms seem to be comparable.”—Robert Finkelman, United States Geological Survey, 2016.)
The high heating value is also called the gross calorific value. This is the energy emitted in combustion. [See heat of combustion.] In many countries, among them Bangladesh, the GCV is expressed in kJ/kg.
1 BTU/lb = 2.326 kJ/kg
1 J/kg = 0.0004299226 BTU/lb
1 kJ/kg = 0.4299226 BTU/lb
1 MJ/kg = 429.9226 BTUs/lb
1 GJ = 429.9226 million BTUs/lb
1 kcal/kg = 1.7987961584 BTUs/lb
For HHVs of many fuels, see the table of Calorific Efficiencies beginning here.
Low heating value [LHV], or net calorific value (sometimes known as recovery heat), is the fraction of emitted energy which actually warms the target material. There are several reasons why HHV and LHV are not the same; one is that a frequent product of combustion is water, which then absorbs some heat. [LHV is measured “in the absence of water condensation.”] According to the International Energy Agency, “for coal and oil, net calorific value is usually around 5% less than gross and for most forms of natural and manufactured gas the difference is 9–10%.” In the Argonne National Laboratory’s 2010 list of LHVs and HHVs of various fuels I note a spread closer to 10%. Since combustion energies are sometimes expressed only in HHVs, I have used only those in this book even though the LHVs are more realistic.
Quad—A quadrillion BTUs = 1015 BTUs = 1.055 × 1018 joules. [See section 1 beginning here.] “Roughly the energy contained in 200 million barrels of oil.”
1 quad = 1.054 exajoules*
Rankine Cycle—A mathematically idealized description of the compression, heating, vaporization, superheating, expansion, condensation and then recompression of water in the “closed loop” of a steam turbine power plant. Heat losses in the condenser stage explain much of this system’s typical inefficiency (30–40%). [A counterpart model for an internal combustion engine is called the Otto Cycle.]
1 Refrigeration ton [U.S.]—“Represents the amount of heat that must be removed from a short ton (909 kg) of water to form ice in 24 h[ours].”
= 3.51 kilowatts = 12,000 BTUs per hour = 12.7 megajoules per hour
A British refrigeration ton (mentioned here only for completeness) = 14,256 BTUs/hr.
Specific heat—Generally speaking, the thermal energy needed to alter the temperature of a given mass of a substance by a given amount. In the units BTU/lbm-°F, the specific heat of water conveniently equals 1.0. Often abbreviated “c,” and expressed in BTU/lbm-°F or J/kg-°C. [For a definition of lbm, see foot-pound in section 1, p. here.]
Some specific heats:
water: 1.0 BTU/lbm-°F
gasoline: 0.53
light oil: 0.50
benzene: 0.41
pure aluminum: 0.23
pure gold: 0.031
Therm—My [natural] gas bill is expressed in this unit. One therm = 105 (100,000) BTUs or 1.055 × 105 joules (= 25,200 kcal).
Thermal efficiency—The LHV divided by the HHV.
The thermal efficiency of natural gas is 84%, of propane 85%.
Thermie—1,000 kilocalories.