794 ) 
> "Co, 
Enter Zoot fooylT-TEr, | 7 dT+RTX P Ine thT Sy = 
5 ww oe 5) 
= =P F017 [Er vrt Sen fee T-Tp af ttre TED wen + 
+ RT Ev, ners Af ERN 
on the other hand equation (2) requires that: 
| 
Ur + B, So te TR 5 . > tee EA (5) 
for the equilibrium, where the velocity = 0. 
If PF, were the same function as in equation (11) of the preceding 
paper, this would lead to: 
ye); + RTS ry, 4 RT Lv, lne, = viert LRT ZV, + RTZyylnc,, (9) 
and this equation is in conflict with the undoubtedly valid 
equation (7) as in general the specific heats of the reaction products 
and of the reacting substances are not equal and the constants of 
entropy do not oceur in the latter equation. This observation is not 
new. It is namely at bottom identical with the argumentation on p. 
45—51 in Mr. pe LANGEN’s Thesis for the doctorate’), that the 
omission of the pure functions of the temperature from the formuta 
for the thermodynamic potential for chemical reactions brings us in 
collision with Van ’r Horr’s equation. For the latter is imme- 
diately obtained by differentiation from (7), whereas differentiation 
from (9) yields the equation of p. 46 of Mr. pr LANGEN’s Thesis for 
the doctorate, which is in opposition to it. Mr. pr LANGEN coneludes 
from this that the kinetic gas theory and thermodynamics are here in 
contlict. 
But this conclusion cannot be maintained. For it has been over- 
looked that for the kinetic derivation of the thermodynamic potential 
of a mixture of chemicaliy interacting substances, we shall have to 
take BonrzMANN’s*) “kritische Räume” into consideration, and that 
when the heat of reaction varies with the temperature, terms must 
appear which are dependent on the difference of the specific heats*). 
What the relation must be between these terms and the temperature 
and the specific heats, could only be revealed by a perfectly developed 
kinetic theory, which could at the same time give an account of 
the value of the specific heat of the different substances. So at present 
thermodynamics leads us further in this respeet, though it naturally 
') Groningen 1907. 
2) Gastheorie Il Abschnitt VI. 
3) loc. cit. p. 199. 
