D O C . 3 9 P R O P A G A T I O N O F S O U N D 1 8 7
where is the sum of the heat capacities of the dissociated and nondissociated
parts, is the heat of dissociation per mole (under constant volume). Therefore,
with the accuracy desired by us, the equation
(14)
also holds. Furthermore, we have to consider the chemical reaction that takes place
during the time element . For this we have to make a hypothesis about the dy-
namics of the decay reaction, which then, in turn, has to be checked through acous-
tic observations. The simplest assumption from a formal point of view—but by no
means from a kinetic point of view—is that the reaction is one of first order, i.e.,
that
molecules decay per units of time and volume. This hypothesis assumes that the
collisions of the molecules are not the immediate cause of the decay, because it
might be possible that molecules of a specific (internal) energy have a certain prob-
ability of decay like, say, radioactive atoms. Or else it might be possible that the
radiation causes the decay of the molecules, an opinion recently advanced with
great emphasis by J. Perrin. If the decay would be caused by the collision of two
molecules or one molecule with an atom , we would have to use in place
of the above expression
or
respectively, where has to be imagined as independent of the concentrations.
We can cover all of these possibilities by retaining the expression but allow-
ing to possibly be dependent on the concentrations of the two kinds of mole-
cules.
For the velocity of recombination we have to put, correspondingly,
C dT D dn1 – dV, –p =
C
D
0 CΔT DΔn1 – p dV + =
dt
κ1-----1V
n
J2
[4]
J2
[p. 384]
J2 J
κ1⎝
n1
V⎠
----⎞
-
⎛
2
κ1⎝
n1
V⎠
----⎞
-
⎛
n
----⎞,⎠2-V
⎝
⎛
κ1
κ1----
n1
V
-
κ1