Environmental Engineering Reference
In-Depth Information
radiated energy. Using the energy
-
mass equivalence of Einstein,
Mc
2
¼
D
E
;
ð
1
:
6
Þ
D
10
26
W
10
7
s/year
10
34
J/year.
on a yearly basis, we have
D
E
¼
3.82
3.15
¼
1.20
10
17
kg/year. Although
D
M is large, it is tiny in comparison to the much larger mass of the sun, M
10
34
J/year )/c
2
This is equivalent to
D
M
¼
(1.20
¼
1.337
¼
1.99
10
30
kg. Thus, we
nd that the fractional loss of mass per year,
D
M/M, for the sun is
1.337
10
14
/year. This is tiny indeed, so the
radiation is not seriously depleting the suns mass. On a scale of 5.4 billion years, the
accepted age of the earth, the fractional loss of mass of the sun, during the whole
lifetime of earth, taking the simplest approach, has been only 0.036%.
Where does all this energy come from? It originates in the strong force of
nucleons, which is large but of short range, a few femtometers. Chemical reactions
deal with the covalent bonding force, nuclear reactions originate in the strong force,
about a million times larger. The energy is from burning hydrogen to make helium,
in principle similar to burning hydrogen to make water, but the energy scale is a
million times larger.
In more detail, the composition of the sun is stated as 73.5% H and 24.9% He by
mass, so the obvious candidate fusion reaction is the conversion of H into He. The
basic proton
-
proton fusion cycle leading to helium in the core of the sun (out to about
0.25 of its radius) has several steps that can be summarized as
10
17
kg/year
10
30
kg
1.99
¼
6.72
4
He
2e
þ
þ
4p
!
þ
2
u
e
:
ð
1
:
7
Þ
This says that four protons lead finally to an alpha particle (two protons and two
neutrons, which forms the nucleus of the Helium atom), two positive electrons, and
two neutrino particles.
This is a fusion reaction of some of the elementary particles of nature, which
include, besides protons and neutrons, positive electrons (positrons) and neutrinos
u
e
. Positrons and neutrinos may be unfamiliar, but a danger is to become intimidated
by unnecessary details, rather than, in an interdisciplinary
field, to learn and make
use of essential aspects. The important aspect here is that energy is released when
particles combine to formproducts the sumof whosemasses are less than themasses
of the constituents. Furthermore, as we will learn, this reaction can proceed only
when the source particles have high kinetic energy, to overcome Coulomb repulsion
when the charged particles coalesce. In addition, the essential process of quantum
mechanical tunneling, an aspect of the wave nature of matter, allows the reaction to
proceed when the interparticle energies are in the kiloelectron volt (keV) range,
available at temperatures above 15million K. Fromelementary physics, we recall that
the average kinetic energy per degree of freedom in equilibrium at temperature T is
1
=
2
k
B
T
E
av
¼
;
ð
1
:
8
Þ
10
23
J/K. The energy units for atomic
processes are conveniently expressed as electron volts, such that 1 eV
where Boltzmanns constant k
B
¼
1.38
10
19
¼
1.6
