1 8 6 D O C . 3 9 P R O P A G A T I O N O F S O U N D
We now proceed to the calculation of by considering cyclic-adiabatic changes
in volume of a partially dissociated gas. Let be the volume, the density of the
partially dissociated gas which we subject to small time-dependent changes ( ,
, , etc.). Then,
, (9)
where is the atomic weight of , the sum total of associated and non-associ-
ated -atoms in moles. It is then easy to derive from (9) the following relation:
. (10)
We can write the equation of state of our gas in the form
(11)
where is the number of moles , the number of moles of the dissociated -
gas, such that
. (12)
From (11) and (12) follows
,
or taking into account (12) and the constancy of :
. (13)
We still have to find two relations that allow us to express and in terms of
; then our calculation of is finished, thanks to (10). Since the process is adi-
abatic, we have for each time element
π
Δ
---
V ρ
ΔV
Δρ Δp
Vρ mn const. = =
m J n
J
π
Δ
---
Δp
Δρ
------ -
1⎛
ρ⎝
-- -
p
Δ(pV)
ΔV
----------------⎞
–
⎠
= =
[p. 383]
pV RT n1 n2), + ( =
n1 J2 n2 J
n 2n1 n2 + =
Δ(pV) R n1 n2)ΔT + ( RT( Δn1 Δn2) + + =
n
Δ(pV) R n1 n2)ΔT + ( RTΔn1 – =
ΔT Δn1
ΔV
π
Δ
---