vided the initial
condition be properly chosen, and provided we take care, even more than
in the former method, that there is no influx of heat. Those conditions
being fulfilled, we may, simply by adiabatic expansion, not only lower
the temperature of some substances down to T3, but also convert them
into the liquid state. This is especially the case with substances the
molecules of which contain few atoms.

Let us imagine the whole net of isothermals for homogeneous phases drawn
in a pv diagram, and in it the border-curve. Within this border-curve,
as in the heterogeneous region, the theoretical part of every isothermal
must be replaced by a straight line. The isothermals may therefore be
divided into two groups, viz. those which keep outside the heterogeneous
region, and those which cross this region. Hence an isothermal,
belonging to the latter group, enters the heterogeneous region on the
liquid side, and leaves it at the same level on the vapour side. Let us
imagine in the same way all the isentropic curves drawn for homogeneous
states. Their form resembles that of isothermals in so far as they show
a maximum and a minimum, if the entropy-constant is below a certain
value, while if it is above this value, both the maximum and the minimum
disappear, the isentropic line in a certain point having at the same
time dp/dv and d^2p/dv^2 = 0 for this particular value of the constant.
This point, which we might call the critical point of the isentropic
lines, lies in the heterogeneous region, and therefore cannot be
realized, since as soon as an isentropic curve enters this region its
theoretical part will be replaced by an empiric part. If an isentropic
curve crosses the heterogeneous region, the point where it enters this
region must, just as for the isothermals, be connected with the point
where it leaves the region by another curve. When c_p/c_v = k (the
limiting value of c_p/c_v for infinite rarefaction is meant) approaches
unity, the isentropic curves approach the isothermals and vice versa. In
the same way the critical point of the isentropic curves comes nearer to
that of the isothermals. And if k is not much greater than 1, e.g. k <
1.08, the following property of the isothermals is also preserved, viz.
that an isentropic curve, which enters the heterogeneous region on the
side of the liquid, leaves it again on the side of the vapour, not of
course at the same level, but at a lower point. If, however, k is
greater,