Geoscience Reference
In-Depth Information
Similarly we find n.r/
n.r/
D
n
1
C.R/
"
1
s
T
R
T
1
!
D.r/
#
˛
2
(3.209)
Because q
R
D
1:5kT
R
n
R
(continuous approximation), we can express n
R
in
terms T
R
T
T
R
n.R/
D
n
1
(3.210)
From the condition n.R/
D
n
R
and Eqs.
3.209
and
3.210
we have
T
T
R
D
C.R/
"
1
s
T
R
T
1
!
D.R/
#
˛
2
(3.211)
This is the equation linking
R
and
T
R
. Another equation for these unknowns
follows from the condition that the derivative of
n
is continuous. To derive this
equation we need to find .a;R/,
The radius
R
of the free molecule zone can be now determined from the condition
of the continuity d
r
n.R/. The contribution of the free molecule zone is
s
T
R
T
1
!
a
2
R
2
p
R
2
n
0
D
n
1
C.R/
˛
2
a
2
To find the contribution of the continuous zone we use the equation
s
T
R
T
1
n
R
n
1
.a;R/
D
C.R/
fm
.a/
(3.212)
and
T
1
T.r/
n.r/
D
n
1
Then
n
1
T
1
T
R
n
0
D
T
0
.R/
Next,
.a;R/.T
T
R
/
4ƒR
2
Q
4ƒR
2
D
T
0
.R/
D
