INFICON Composer Gas Concentration Controller - Manual (Page 43)

2 - 1
IP
N 07
4-
28
9L
Composer Operating Manual
Chapter 2
How the Instrument Works
2.1 Speed of Sound and Gas Composition
The speed of sound, C , in an ideal gas is equal to:
[1]
where:
= 1.4 for Air [2]
T = Kelvin temperature
R = Universal Gas Constant = 8.3143 x 10
7
erg / (Mole K)
M = Molecular Weight (AMU)
Equation [1] may be expanded for binary mixtures by modifying the Specific
Heat Ratio and molecular weight to account for the Mole Fraction of component
two,
x , as follows.
[3]
[4]
So the speed of sound of the mixtures, CM , is:
[5]
which holds for any ideal mixture; that is, a mixture that is formed without
change in volume.
The Instrument System determines the speed of sound by precisely
determining the gasses’ fundamental resonant frequency in a fixed chamber of
length L. At resonance, a standing half wave exists in the Resonant Chamber,
so the speed of sound and frequency are related as follows:
C
γRT
M
---------- =
γ
C
p
C
v
------
Heat Capacity at Constant Pressure
Heat Capacity at Constant Volume
--------------------------------------------------------------------------------------- = =
γ 1
x
γ
1
1 –
--------------
1 x –
γ
2
1 –
-------------- +
1 –
+ =
M xM
1
1 x – ( )M
2
+ =
C
M
γRT
M
---------- =