Environmental Engineering Reference
In-Depth Information
where
g
c
is the effective statistical weight of the electron continuous spectrum. For
an ideal plasma, this statistical weight is rather large because the electron number
density
N
e
is small compared with a typical atom number density. This leads to
the conclusion that a remarkable degree of ionization takes place at relatively small
temperatures,
T
J
. However, the probability of atomic excitation is very small at
these temperatures; that is, the number density of excited atoms is small. Hence,
at these temperatures, atoms are either in the ground state or ionized.
1.2.6
Dissociative Equilibrium in Molecular Gases
Equilibrium between atoms and molecules in a molecular gas is maintained by the
processes
X
C
Y
$
XY
.
This equilibrium bears analogy to the equilibrium between discrete and continu-
ous atomic states corresponding to bound and free states of atoms. We can find
the relation between the equilibrium number densities of atoms and molecules
in this case by analogy with the Saha distribution. On the basis of (1.52), one can
express the relationship between the number densities of atoms and molecules in
the ground state as [41]
μ
3/2
exp
,
N
X
N
Y
g
X
g
Y
g
XY
T
D
T
D
(1.54)
N
XY
(
v
D
0,
J
D
0)
2
π
„
2
where
g
X
,
g
Y
,and
g
XY
are the statistical weights of atoms and molecules with
respect to their electron states,
is the reduced mass of atoms
X
and
Y
,and
D
is
the dissociation energy of the molecule.
In contrast to the ionization equilibrium of atoms, in this case most molecules
are found in excited states. Using (1.46) and (1.47), which connect the number den-
sity of molecules in the ground state to their total number density, we can trans-
form (1.54) to the form
μ
μ
3/2
B
T
1
exp
exp
,
N
X
N
Y
N
XY
g
X
g
Y
g
XY
T
„
T
D
T
D
(1.55)
π
„
2
2
where
N
XY
is the total molecular number density.
1.2.7
Laws of Blackbody Radiation
An ionized gas contains excited atoms or molecules that emit radiation, so it is
necessary to examine how the gas interacts with radiation. If the interaction of ra-
diation with a gas is strong, the distance that an individual photon travels before
being absorbed is relatively small. Then we deal with so-called equilibrium radia-
tion [54]. Radiation in a vessel whose walls are at a temperature
T
will be absorbed
