in the gaseous and the
liquid state are the same--which we may call the supposition of the
identity of the two conditions of aggregation--then the heat which is
given out by the condensation at constant T is due to the potential
energy lost in consequence of the coming closer of the molecules which
attract each other, and then it is equal to a(1/v_l - 1/v_v). If a should
be a function of the temperature, it follows from thermodynamics that it
would be equal to (a - T.da/dT)(1/v_l - 1/v_v). Not only in the case of
liquid and gas, but always when the volume is diminished, a quantity of
heat is given out equal to a(1/v1 - 1/v2) or (a -T.da/dT)(1/v1 - 1/v2).

Associating substances.

If, however, when the volume is diminished at a given temperature, and
also during the transition from the gaseous to the liquid state,
combination into larger molecule-complexes takes place, the total
internal heat may be considered as the sum of that which is caused by
the combination of the molecules into greater molecule-complexes and by
their approach towards each other. We have the simplest case of possible
greater complexity when two molecules combine to one. From the course of
the changes in the density of the vapour we assume that this occurs,
e.g. with nitrogen peroxide, NO2, and acetic acid, and the somewhat
close agreement of the observed density of the vapour with that which is
calculated from the hypothesis of such an association to
double-molecules, makes this supposition almost a certainty. In such
cases the molecules in the much denser liquid state must therefore be
considered as double-molecules, either completely so or in a variable
degree depending on the temperature. The given equation of state cannot
hold for such substances. Even though we assume that a and b are not
modified by the formation of double-molecules, yet RT is modified, and,
since it is proportional to the number of the molecules, is diminished
by the combination. The laws found for normal substances will,
therefore, not hold for such associating substances. Accordingly for
substances for which we have already found an anormal density of the
vapour, we cannot expect the general laws for the liquid state, which
have been treated above, to hold good without modification, and in many
respects such substances will therefore not follow the law of
corresponding states. There are, however, also substances of which the
anormal density of vapour has not been stat