with the density into 150 g/sm 3 and average molar mass 0.6 (see task ) particle concentration is equal

In reality average molar mass in the center of the sun now somewhat more than 0.6, since

hydrogen is there already strongly burned-out, after becoming helium. However, an order of magnitude n remains the same, and only it to us is necessary.

Photon concentration of blackbody emission at a temperature is equal (see task ) This to three and the more of order is less than the particle concentration. It means, and the role of radiation pressure in interior of the suns is small (see solution of problem ).

It is interesting that, according to the calculations of the models of the internal structure of the sun, in the larger part of its mass the density and temperature T are connected with relationship

. Therefore the relation , found by us for the center of the sun, is characteristic for its depths as a whole. Photons in interior of the suns (and of all stars, except the massive) it is much lessthan protons.

12.4 water density of 1 g/sm³. In this case it is known that in the liquids the molecules almost come into contact with each other. With the densities, the substantially large of water density, existing in interior of the suns, hydrogen atoms are ionized by pressure. As a result the volume ratio, occupied with particles (respectively by atoms and by naked nuclei), decreases s to

, where cm - nuclear size, cm - size of atom. Thus, nuclei will begin to be adjoined and "to interfere with" each other only with the densities

of g/sm³. These are - nuclear densities. They are characteristic for the neutron stars. In principle up to these densities the ionizovannoye substance can remain gas.

Together with the density, the state of aggregation of starry substance is determined by

temperature. Thus, it is known that with a decrease in the temperature of white dwarf the atomic nuclei in his depths must be erected into crystal lattice. So that the atomic nuclei would move freely, i.e., they gasified, it is required that their kinetic energy kT would substantially exceed the Coulomb energy, equal in order of magnitude , where - the average distance between the nuclei. Condition with the use of relationships (for the purely hydrogen plasma) where n - nucleus concentration, it is possible to rewrite in the following form:

or in the numbers

where . For the center of the sun we have , g/sm³ (see the

previous task), so that . Thus, even with the density into 150 g/sm³ substance in the center of the sun because of the high temperature remains gas.

The future it is necessary to accept to the faith. According to the calculations of the models of the internal structure of the sun, the relationship , valid for the center of the sun,

approximately is fulfilled also in the larger part of its depths. Therefore everywhere in interior of the suns, but not only in its center, substance is gas.

12.5 let us calculate the energy, which separates with the nuclear fusion of the atom of helium from four protons. According to Einstein's formula we have , since in the course of this nuclear reaction (more precise, the chain of synthesis reactions - particle of four protons)"disappears" (more precise, 0.7%) mass. Total rest energy of the sun is equal . If the sun wholly consisted of hydrogen, then with its complete transformation into helium energy would be isolated . The time, to which this energy would be sufficient for maintaining the luminosity of the sun at its present level, comprises

years. Coefficient of 5/3 "is unimportant" - the sun wholly does not consist of hydrogen and t. d. In actuality in the time of its life on the main sequence the sun will have time to burn only approximately 10% of its reserves of hydrogen.

Thus, to the sun it is tempered approximately the years of "calm" life on the main sequence, that completely good!

12.6 we will consider that the sun emits blackbody emission with K. The medium energy, which falls to one blackbody photon, equal (see task ), comprises then

eV. Therefore the number of photons, radiated by the sun due to the energy, which separates with synthesis of one - particle, equal

to pcs since with the synthesis - particle of four protons two of them due to - disintegration they are converted into the neutrons, then in this case be born two neutrinos. As a result the number of second-by-second radiated by the sun photons occurs once of more than the number of neutrinos emitted by it.

12.7 substance, akkretsiruyemoye by the sun, with the drop reaches on its surface of planet escape velocity km/s. The desired rate of accretion is determined from the condition of equality to kinetic energy of that falling out for 1 from the substance and the luminosity of the sun:

from where

How will change the duration of year, i.e., the period of revolution of the earth P with a change in the mass of the sun? From the third law of Kepler

we find

From other side, must remain the angular momentum , so that

From these two relationships we find that

from where with we obtain, that . This corresponds to the

decrease of the duration of year on c per year, what clearly it does not occur. It is possible therefore with the confidence to assert that the sun shines not due to the accretion.

12.8 in terms of the values of temperatures it is possible to conclude that the discussion deals with the massive stars, whose luminosity is ensured by N- cycle. It is known that the rate of energy release with reactions N- cycle is approximately proportional . Therefore the unknown relation is equal . Do not be sufficient at the calculator - all it is possible to calculate in the mind, after using the remarkable limit

Actually,

With an increase in the temperature in all to the rate of energy release it grows more than 7!