User Manual

2 - 1
IPN 074-289L
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,
C
M
, 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–
--------------
1x–
γ
2
1–
--------------+
1–
+=
MxM
1
1x–()M
2
+=
C
M
γRT
M
----------=