barcode for vb Exercise 11.5.1: Entropy of the Sun in .NET Print code 128 barcode in .NET Exercise 11.5.1: Entropy of the Sun

Exercise 11.5.1: Entropy of the Sun generate, create none none for none projectsean 13 generating We have seen in 8 that a typ none none ical photon in the Sun takes 106 y to randomly walk out of the Sun. That means that the Sun contains all the photon energy it generated by nuclear reactions in the last million years. This must all be in the form of photons, since the particles in the Sun have the same total energy today as they had a million years ago.

(a) Calculate from the solar luminosity how much energy the Sun contains in photons. (b) If the average temperature inside the Sun is 105 K, calculate mean energy of each photon. (c) From these two results estimate the number of photons inside the Sun.

(d) From the mass of the Sun, assuming for simplicity that it is composed entirely of hydrogen, calculate the number of protons (hydrogen nuclei) in the Sun. (e) Find the ratio of the number of photons to the number of protons in the Sun. This is a measure of what physicists call the entropy of the Sun.

. ISO Specification just the right energy at a ca rbon nucleus, the impact would cause it to split up into three alphas, but these would not y apart; the extra attraction would hold them together, oscillating about one another, until they eventually emitted a gamma-ray photon and settled back down to a normal carbon nucleus. Experiments soon found the predicted effect. Carbon does have such an excited state, three alpha particles do attract one another more than one might at rst expect, and carbon can form inside stars by three-alpha collisions.

The synthesis of elements beyond carbon then needs only a succession of two-particle reactions: add one helium nucleus to carbon and one gets stable oxygen; combine oxygen and carbon nuclei and one gets stable silicon, and so on. So life seems to hinge on the existence of this one excited state of carbon. This seems to be a small detail of the laws of physics.

If certain fundamental numbers, like the mass of the electron, the unit of electric charge, or the strength of the nuclear force were to have been just slightly different, then life would simply not have been possible: the elemental building blocks would not have been there. Another example of the special nature of the laws of physics is given in the next chapter, where we consider the death of stars by supernova explosions. Some of these are triggered by the collapse of the core of a massive star when it runs out of nuclear fuel.

The collapse releases energy, and this blows the rest of the star apart. These explosions are one of the ways that elements heavier than helium are placed into clouds of interstellar gas, ready to act as seeds for planets and for life in the next generation of stars. It appears that our own Solar System formed from gas enriched by such an explosion, without which we would not be here.

It seems, from theoretical calculations, that it is not easy to blow such stars apart. The energy released by such a collapse is carried away by neutrinos, which leave only just barely enough energy to blow the envelope of the star away. Now, we.

11. Stars at work shall see that this collapse only occurs when the mass of the exhausted core reaches about one solar mass. This mass can be calculated, quite remarkably, from simple fundamental constants of nature: Newton s constant of gravitation G, Planck s constant h, the speed of light c, and the mass of the proton mp . If the proton were a bit more massive, then (as we shall see) the core would collapse when it had less than one solar mass.

Such a collapse would release less energy, and perhaps not enough would be available to blow apart the star. What is more, the collapse causes an explosion only because something halts the collapse, causing a rebound of the infalling material. This something is the formation of a neutron star, which we will also study in 12.

We will see there that the existence of neutron stars depends on the exact strength of the nuclear forces. A small weakening of these forces would have led the collapse to form black holes, with little or no rebound, and the interstellar medium would not have been enriched as much as it has been. This sort of ne-tuning can be found elsewhere, as well, and we will give more examples in the nal chapter.

This has given rise to a point of view about the history of the Universe that is called the Anthropic Principle. The mildest form of this principle holds that, since we are part of life, any universe in which the netuning prevented life from forming would not have had us in it to puzzle over the ne-tuning. Therefore, the ne-tuning is no puzzle; it must be taken for granted from the simple fact that we are here to discover it.

This point of view seems plausible if one believes that there might be many universes , so that the cosmological experiments can be repeated many times, and there is nothing special about ones that happen to produce life on obscure planets. One might imagine a repeating Big Bang, endlessly cycling through expansion and re-collapse (the Big Crunch ). Or one might imagine the Universe to be extremely large, and that different regions of it have different values of such things as the proton mass.

We would then not see such regions because light has not had time to reach us from them since the Big Bang. A more radical version of the Anthropic Principle is more metaphysical: the Universe is ne-tuned to produce life because its purpose is to produce life. Scienti cally, this could be a dead end, since it discourages further questions about the ne-tuning, except possibly to try to nd relations between examples of it that seem rather distant from one another.

I prefer the rst version of the principle, especially since, as we will see in 27, many physicists are working hard now to arrive at a theory of quantum gravity, and this may well predict that our Universe is not the only one, that the values of the fundamental constants are not the only ones that have occurred or will occur. I have not addressed here the other ingredients necessary for life, especially the enormous chain of chemical reactions building upon one another to make the complex molecules of life on the present Earth. It is usually assumed that this happened spontaneously on the Earth, using a combination of catalysts and natural selection to guide the chemistry.

Some astronomers, including Hoyle, have revived the idea of panspermia, which is that life could have spread from one star to another, perhaps propelled by strong mass ows that astronomers observe from some kinds of giant stars, so that it need not have arisen on Earth. That still requires that the complex chemistry take place somewhere in the Galaxy, but it allows biologists to look in environments very different from the early Earth for the very rst steps toward evolution..

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