1 8 8 D O C . 3 9 P R O P A G A T I O N O F S O U N D
.
Consequently, we obtain for the time element the relation
or
(15)
here is the constant of the mass action law which obeys the well-known
relation
. (16)
In order to benefit from equation (15) we apply it to a state which only infinitesi-
mally deviates from a state of equilibrium. We get, because of (16) and (12) and by
again using the symbols , , , , , referring to the equilibrium state
(state of rest):
.
Assuming that the variables , and go through cyclical transitions and
complexifying them into quantities with the factor , we can put after execution
of the differentiation in the fourth term
. (17)
κ2⎝
n2
V⎠
----⎞
-
⎛
2
dt
V κ1----
n1
V
- κ2⎝
n2
V⎠
----⎞
-
⎛
2
– dt dn1 – =
κ1
κ2
-----n1
n22
V
------- –
1
κ2
-----
dn1
dt
--------.
– =
κ1
κ2
----- κ =
1
κ
-- -
dκ
dT
------ -
D
RT
2
--------- - =
κ1 κ2 κ n1 n2 V
0
κDn1
RT
2
-------------ΔT
κ
4n2
V
--------⎞
+
⎝ ⎠
⎛
Δn1
1
κ2
-----
dΔn1
dt
------------
n2
V⎠
----⎞
-
⎝
⎛
2
ΔV + + + 0 = =
ΔT Δn1, ΔV
ejω t
0
κDn1
RT
2
-------------ΔT
κ
4n2
V
--------
jω⎞
κ2
-----⎠ - + +
⎝
⎛
Δn1
n2
V⎠
----⎞
-
⎝
⎛
2
ΔV + + =