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2024-03-18
Don't forget to check your integer type!
Coal ash contains more energy than was gained from burning the coal.
Natural uranium, in a fast-neutron reactor | 28,000 GJ/kg [so 28e9 J/g] |
Hard black coal (IEA definition) | >23.9 MJ/kg |
Hard black coal (Australia & Canada) | c. 25 MJ/kg [so 25e3 J/g and 207.25 g/mol according to https://pubchem.ncbi.nlm.nih.gov/compound/1-Anthrylmethanolate] |
Sub-bituminous coal (IEA definition) | 17.4-23.9 MJ/kg |
Sub-bituminous coal (Australia & Canada) | c. 18 MJ/kg |
Lignite/brown coal (IEA definition) | <17.4 MJ/kg |
Lignite/brown coal (Australia, electricity) | c. 10 MJ/kg |
mass / molar mass = moles
moles * avogadro = number of molecules
number / avogadro = moles
moles * molar mass = mass
1e6 / 6.022140857e24 * 207.25 = 3.4414672e-17 g of coal = 8.603668e-13 J (25e3 J/g * 3.4414672e-17 g)
1 / 6.022140857e24 * 238.02891 = 3.952563e-23 g of uranium = 1.1067176e-12 J (28e9 J/g * 3.952563e-23 g)
1 / 6.022140857e24 * 232.03806 = 3.8530826e-23 g of thorium = 1.0788631e-12 J (28e9 J/g * 3.8530826e-23)
https://pubs.usgs.gov/fs/1997/fs163-97/FS-163-97.html
"2,000 coal samples from the Western United States and approximately 300 coals from the Illinois Basin. In the majority of samples, concentrations of uranium fall in the range from slightly below 1 to 4 parts per million (ppm). Similar uranium concentrations are found in a variety of common rocks and soils, as indicated in figure 2. Coals with more than 20 ppm uranium are rare in the United States. Thorium concentrations in coal fall within a similar 1–4 ppm range"
So at 1 ppm uranium and 1 ppm thorium, a coal power plant releases only (8.603668e-13 / (1.1067176e-12 + 1.0788631e-12)) = 0.3936559286 = 39% of the available fission energy in coal.