INFICON Composer Gas Concentration Controller User Manual
Page 44
2 - 2
IP
N 07
4-
28
9L
Composer Operating Manual
[6]
In practice, the exact value of
L
is unimportant. Composition is computed from
knowledge of the mixture's frequency relative to the frequency of the pure gas
as follows. Let:
[7]
[8]
[9]
Applying equations 7, 8, and 9 into equations 3 and 4 yields,
[10]
[11]
If we define the speed of sound in the majority, or carrier, gas as
C
2
[12]
and apply equations 9 and 10 into equation 4 we get:
[13]
Since the speed of sound in a fixed resonator is directly proportional to the
frequency of resonance, we define a ratio:
[14]
Where
f
and
f
2
are the resonant frequencies of the mixture and pure gas,
respectively.
f
C
2L
-------
=
m
M
1
M
2
--------
=
g
γ
1
γ
2
-----
=
h
1
γ
2
-----
=
M
M
2
m 1
–
(
)x 1
+
{
}
=
γ 1
=
γ
2
g h
–
(
) 1 h
–
(
)
{
}
x 1 g
–
(
)
g h
–
(
)
+
{
}
--------------------------------------------------
+
C
2
γ
2
RT
M
2
-------------
=
c
2
c
2
2
h
g h
–
(
) 1 h
–
(
)
x 1 g
–
(
)
g h
–
(
)
+
-------------------------------------------
+
1 m 1
–
(
)x
+
[
]
1
–
=
λ
C
C
2
------
2
f
f
2
----
2
=
=