196
VIII
EVAPORATION OF LIQUIDS
Hence its kinetic energy
the space u and have the velocity u.
is mu²/g; this is attained by the force P-p acting upon its
centre of mass through the distance u/2, so that an amount of
work (P-p)u/2 is done by the external forces. From this
follows the equation P-p= mu/g; or, since m = ud, m² =
P-p=mu/g;
gd(P-p).
Now the problem which evaporation places before us is to
find the relations between these quantities for all possible
values of them. Two of the eight quantities T1, T2, T, p, d,
u, m, and P, namely T, and T₂, are independent variables; so
also are any two of the others. The other six are connected
with these by six equations. Of these we have already given
three; in order to solve the problem completely we have to
find, from theory or experiment, three more. But if we choose,
as in the experiments, T, and P as the independent variables,
and consider only evaporation in the narrower sense, we are
no longer interested in T₂, and the problem resolves itself into
representing two of the quantities T, p, d, u, m as functions
of T₁ and P. But now the functions to be determined do not
apply only to the case of evaporation between parallel walls;
they hold good for any vapour which arises from a plane
element of a liquid, and exerts upon it a pressure P.
For we
can imagine such evaporation taking place as if we allowed a
piston to rest upon the surface at temperature T₁, and at a
given instant removed it from the surface with velocity u.
The result of this experiment must be singly determined by
T, and u. But the two above-mentioned functions give us one
possible result, and hence this result is the only possible one.
Thus the quantities relating to an element of the evap-
orating surface are completely determined by two of them,
and the assumption upon which the experiments were based
is justified; on the other hand, our discussion shows that the
experiments, even if they had been successful, would not have
completely solved the problem.
We can assign limits to the quantities in question if we
make use of the two following assertions which, according to
general experience, are at any rate exceedingly likely to be
(1) If we lower the temperature of one of several
liquid surfaces in the same space while the others remain at
the original temperature, the mean pressure upon these surfaces
correct.