526 Prof. W. McF. Orr on Clausius’ 
which is of course the same as that which it would do in the 
indefinitely slow expansion. 
In some instances, however, is there such an obscurity and 
inversion of ideas, as it seems to me, on this point, that 
Verdet *, followed by Jamin and Bouty +, in the endeavour 
to prove Clausius’ theorem for irreversible cycles, classifies 
such cycles in several types, one of which consists of “ those 
in which the body expands without developing a quantity of 
sensible energy equal to the work of its elastic force, that is 
to say, where the pressure which it has to overcome is sensibly 
inferior to its own pressure and virtually reverses the pre- 
ceding argument.” 
Objections to treating some problems of Chemical Equilibrium 
by Method of Entropy, Thermodynamic Potential, or 
Available Energy. 
23. The view held by Bertrand and urged here as to the 
conception of entropy constitutes to some extent an objection 
to the application of the principle of the Increase of Entropy, 
whether by Gibbs’ method of Thermodynamic Potential or 
von Helmholtz’s of Free, or Available, Hnergy, to a certain 
class of chemical problems, viz., those which deal with the 
internal equilibrium of a phase. The conception, as a 
measurable quantity, of the Thermodynamic Potential or of the 
Available Energy of a given state requires us to suppose that 
that state can be obtained in a reversible way from a certain 
standard state of equilibrium. The method then implies that 
we can conceive the possibility of passing by reversible 
processes to states wherein the bodies concerned are not in 
chemical equilibrium: as a specific instance, the usual treat- 
ment of the question of equilibrium in a gas system requires 
us to suppose that the various gases can diffuse into each 
other through semipermeable membranes in proportions other 
than those appropriate to the equilibrium state, for the 
reversible way in which the gases are supposed to be mixed 
or to have their relative concentrations altered is by being 
passed through such membranes. 
It may be held that this method is only competent to 
decide which of two or more given possible states of equilibrium 
is the most stable. 
* Théorie Mécanique de Chalew, Hiuvres, tome 7, Art. 164, p. 188. 
+ Cours de Physique, ii. 2° fascicule, p. 189. 
