Environmental Engineering Reference
In-Depth Information
covalent bond energies inmolecules and solids. This large size is, of course, a driving
factor toward the use of fusion reactors on earth.
Returning to the sun, it is believed that the p - p cycle accounts for about 98% of the
suns energy output [10], all occurring in the core. The energy diffuses slowly out to
the outer surface with attendant reductions in pressure and temperature, the latter
from 15 million K to about 5800 K.
The first reaction in the proton - proton cycle at the suns core is [11]
p þ p ! D þ e þ þ u e ;
ð 1 : 10 Þ
where D is the deuteron, the bound state of the neutron and proton, which has mass
2.0136 u. (Themass unit, u,isde
ned as 1/12 of themass of the 12 C nucleus. One u is
10 27 kg). Here,
about 1.67
the energy release is 1.44MeV, which includes
0.27MeV to the neutrino.
This rst proton - proton reaction occurs very frequently in the sun, as the rst step
in the basic energy release process. But this reaction is impossible from the point of
view of classical physics. It should not occur, from the following reasoning. Accepting
the estimated temperature at the center of the sun as 1.5
10 7 K, the thermal energy
1 / 2 k B T
1 / 2 1.38
in the center of mass motion of
two protons would be
¼
10 23
10 16 J
10 7 J
646.9 eV.
(There will more realistically be a distribution of kinetic energies, and energies
higher than 10 keV will frequently be available to colliding protons at 15 million K).
But any such estimated energy is far short of the potential energy k C e 2 /r that is
required classically to put two protons in contact. (Here k C
1.5
¼
1.035
¼
10 9
¼
9
and e
¼
10 19 C). The radius of the proton has been measured and we will take it as
1.6
10 15 m. In this case, the Coulomb energy k C e 2 /r in eV is 9
10 9
10 19 /
1.2
1.6
10 15 )
(2
0.6MeV. This energy is vastly higher than the kinetic energy (see
Figure 1.6). Classically, this reaction will not occur because the two protons will never
come into contact.
This fundamental discrepancy was resolved in the early years of the quantum
mechanics, and in particular by George Gamow [12], an American physicist. The
resolution is that the reaction proceeds by a process of quantum mechanical
tunneling, and the kinetic energies near the solar Gamow peak in the range
15
1.2
¼
27 keVprovidemost of the reactions. We will return to this topic later. The process
is now completely understood, and we will explore it in some detail because it is also
central to experimental approaches to generating fusion energy on earth.
A later and important reaction in the p - p cycle, which we will come back to, is
fusion of two deuterons. The result can be a triton Tplus a proton, 3 He plus a neutron,
or an a ( 4 He) plus a gamma ray (photon). (A triton is one proton plus two neutrons,
and forms tritium atoms similar to hydrogen and deuterium atoms. Tritium, as
opposed to deuterium, does not occur in nature).
-
1.1.1.3 Distribution of Solar Influx for Conversion
The suns energy density varies considerably with differing cloud cover characteristic
of different parts of the world. A summary of this is shown in Figure 1.7a. The
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