![]() ![]() ![]() Thus, the entropy of a solar mass black hole is ~10^18 times greater than the entropy of the Sun. For sufficiently large masses it follows that the entropy of a black hole will far exceed that of the matter from which it formed. In contrast, the entropy of a black hole is proportional to its surface area, and hence to the square of its mass. The entropy of ordinary matter is, roughly speaking, proportional to the number of particles, and hence proportional to the total mass. In the absence of any certainty about the nature of dark energy this would be premature. We have avoided discussing the entropy of dark energy. If dark matter consists of particles more massive than the nucleons, then its entropy is smaller than that of ordinary matter. If dark matter consists of particles comparable in mass to the electron, their entropy would be negligible compared with that of the Big Bang photons and neutrinos, but still far larger than that of ordinary matter. If dark matter consists of particles lighter than ~2eV then their entropy would dominate that of the Big Bang photons. The contribution of dark matter to the universe's entropy depends upon the mass of the individual particles involved. ![]() Hence, the entropy of the universe as a whole has increased, as it must. The above results imply that the photon entropy has increased by ~3.5 x 10^86 since recombination, whereas that of ordinary matter has decreased by ~2 x 10^81. ![]() Thus, the formation of structure in the universe has been accompanied by a roughly 3:1 reduction in the entropy of the ordinary matter involved. If all the ordinary matter were now in the form of stars of roughly solar mass, its total entropy would be ~10^81 in these units. The entropy of ordinary matter, after recombination but before star formation, would have been about 3 x 10^81 in these same units. The entropy of the Big Bang photons and neutrinos are about the same, and total 7 x 10^89 in units of Boltzmann's constant. In this Chapter we show that 99.9% of the photons in the observable universe originated from the Big Bang, and there are 10^89 of them. Nevertheless, the entropy of the matter involved does decrease, and this is the origin of orderly structure within the universe. Consequently the second law of thermodynamics is respected, and entropy overall does not decrease. This radiation carries away at least as much entropy as the matter looses. This is provided by some cooling mechanism, and the energy is lost in the form of radiation. Hence, in order to collapse, there must be some mechanism for removing energy from the collapsing matter. In collapsing, matter moves to a state of lower potential energy, and, it turns out, to a state of lower total energy. In Appendix B1 we show that the entropy of matter collapsing under gravity does indeed decrease. It is not immediately obvious how this apparent transition from disorder to order can be reconciled with the second law of thermodynamics, namely that the entropy of the universe should never decrease. We inhabit a planet which is replete with natural order, not least its flora and fauna, including ourselves. And yet here we are, 13.7 billion years later. Rick's Cosmology Tutorial: Chapter 20 Abstract Rick's Cosmology Tutorial: Chapter 20 AbstractĪccording to the Big Bang theory, the universe is supposed to have started in a highly dense and extremely hot state consisting of radiation and particles in random motion, devoid of structure. ![]()
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