To illustrate the effect of the chemical composition of a star, we
revert to the problem of the support of the upper layers by the
gas underneath. At a given temperature every independent particle
contributes the same amount of support no matter what its mass or
chemical nature; the lighter atoms make up for their lack of mass by
moving more actively. This is a well-known law originally found in
experimental chemistry, but now explained by the kinetic theory of
Maxwell and Boltzmann. Suppose we had originally assumed the sun to
be composed entirely of silver atoms and had made our calculations
of temperature accordingly; afterwards we change our minds and
substitute a lighter element, aluminium. A silver atom weighs just
four times as much as an aluminium atom; hence we must substitute
four aluminium atoms for every silver atom in order to keep the mass
of the sun unchanged. But now the supporting force will everywhere be
quadrupled, and all the mass will be heaved outwards by it if we make
no further change. In order to keep the balance, the activity of each
particle must be reduced in the ratio ¼; that means that we must assign
throughout the aluminium sun temperatures ¼ of those assigned to the
silver sun. Thus for unsmashed atoms a change in the assigned chemical
composition makes a big change in our inference as to the internal
temperature.
But if electrons are broken away from the atom these also become
independent particles rendering support to the upper layers. A
free electron gives just as much support as an atom does; it is of
much smaller mass, but it moves about a hundred times as fast. The
smashing of one silver atom provides 47 free electrons, making with
the residual nucleus of the atom 48 particles in all. The aluminium
atom gives 13 electrons or 14 particles in all; thus 4 aluminium atoms
give 56 independent particles. The change from smashed silver to an
equal mass of smashed aluminium only means a change from 48 to 56
particles, requiring a reduction of temperature by 14 per cent. We
can tolerate that degree of uncertainty in our estimates of internal
temperature;[4] it is a great improvement on the corresponding
calculation for unsmashed atoms which was uncertain by a factor 4.
Besides bringing closer together the results for different varieties
of chemical constitution, ionization by increasing the number of
supporting particles lowers the calculated temperatures considerably.
It is sometimes thought that the exceedingly high temperature assigned
to the interior of a star is a modern sensationalism. That is not so.
The early investigators, who neglected both ionization and radiation
pressure, assigned much higher temperatures than those now accepted.
_Radiation Pressure and Mass_
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