Wednesday, September 26, 2012

A hierarchy of energy

kw: references, energy, combustion, fission, fusion, kerr black holes, annihilation

From time to time I find or gather a synthesis of related ideas, and this is as good a place to store them as any. Reading recently about the energy released from matter falling into a spinning black hole, often called a Kerr black hole after the New Zealander who first worked out the math, I sought to place it in the context of more familiar sources of energy. Not that a Kerr black hole is going to be easy to harness as a "source" of energy, but perhaps a sufficiently advanced civilization could do so.

Sundry classifications have been made of speculative levels of civilization, and they frequently hinge on the level of energy use. Here I present one based on energy source. The characteristic figure for an energy source is the fraction of the mass-energy that is made available at each level.

Level 0 would have to be pre-Human, based on what follows. The only source of energy is food energy, a type of slow combustion; overt, external combustion is not used.

The primary energy source of Level 1 civilizations is combustion. The genus Homo began using combustion (very) roughly a million years ago, and that is still the primary source of energy used by the human race, though our fuel supply has changed from time to time. One of our most efficient combustion systems is hydrogen-oxygen, so far primarily used for rocket propulsion. Burning a gram of hydrogen releases about 142 kJ of energy, while also consuming 8 grams of oxygen. By Einstein's energy equation, e=mc², we find that the combustion products must be lighter than the uncombusted gases by 15.8 trillionths of a gram per gram of hydrogen burnt, or 1.75 trillionths of a gram per gram of combined gases. Note that hydrocarbon combustion is somewhat less energy intensive on a gram per gram basis, when oxygen consumption is included.

Some nations are on the boundary of Level 2, in that a large fraction of their total energy is derived by nuclear fission. In the fission of U-235, a large variety of reactions may occur, but on average we find that the fission products and neutrons emitted weigh about 0.2 AMU less than the original uranium nucleus. Thus the mass conversion is about 0.00085 grams per gram of uranium fuel. This is about 490 million times as much energy per gram as hydrogen combustion.

Nuclear fusion has been a holy grail for many. Success in developing economical fusion power would yield a Level 3 civilization. Note, however, that the 4H-to-He system is only about 8 times as powerful as uranium fission, or 0.0071 grams per gram of H consumed. The methods being studied are mostly based on deuterium fusion, which has very little advantage over uranium fission, on a grams released per gram converted basis. If we could, however, capture large fractions of the Sun's energy output (such as by a Dyson sphere), we could sidestep our way to energy use characteristic of this Level, as the Sun uses the 4-hydrogen reaction.

Now we come to Kerr black holes. The theoretical maximum energy that could be extracted is 28% of the rest mass of the infalling matter. Thus, if a Level 4 civilization could harness a rapidly spinning black hole (in the range of 10,000-100,000 rotations per second if it is stellar-sized), 0.28 grams of effective mass-energy per gram consumed is 39 times the energy available from hydrogen fusion.

Is a higher proportion of energy release attainable? Could a Level 5 civilization arise that makes effective use of total annihilation? In the Star Trek civilization, "antimatter generators" produce antimatter fuel for use in starships (at least), moderated by "dilithium" and "rubindium" and other special materials. The matter-antimatter reaction does result in annihilation, but if you are generating the antimatter somewhere, rather than having found an antimatter mine, it may be assumed that you are using energy characteristic of a lower Level to do so.

For those of us on the threshold of Level 2, we find there is no political will, and great public opposition, to expanding energy sources that release large amounts of radioactivity or produce radioactive waste. Thus I favor sidestepping our way to Level 3 by effective use of solar energy. So far, we barely have a bit of a toe in the water on this. The side of earth facing the Sun at any one time intercepts about 64 quadrillion watts of solar energy, at ground level. Total human energy use is presently less than 20 trillion watts, or about 1/3200 of what is available. Of course, paving land and sea with solar cells is a formula for ecological suicide, but covering 0.1% of the total (because much is in darkness at any one time) would be enough to meet all our needs and then some.

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