300
XIX
ADIABATIC CHANGES IN MOIST AIR
We may use
of entropy between the initial and final states.
the equation obtained until the temperature falls to the freezing-
point; then we pass to-
Stage 3, in which the air contains ice, as well as vapour
and liquid water. Now the temperature will not at once
fall any further with further expansion, for the latent heat
developed by the freezing water will, without any lowering of
temperature, yield the work necessary to overcome the external
pressure. But the latent heat will not be spent in this work
alone, but also in evaporating a portion of the water already
condensed. For since during the expansion the volume
increases without fall of temperature, at the end of the pro-
cess there will be more aqueous vapour than before, and the
weight of ice formed will be less than that of the liquid water
initially present. Letv again denote that portion of μ which
exists as vapour, σ the portion existing as ice, and let q be
the latent heat of fusion of 1 kilogramme of ice. T, e, r are
constants. Since then ɗT = 0, we need only supply the air with
the heat XARTdv/v, the water which is evaporated with the
heat rdv, and the water which is frozen with the heat-qdo.
Hence the whole of the mixture is supplied with the heat
dv
v
dQ =λART+ rdv — qdo.
-
As before we put dQ = 0, divide by T, and integrate, and
thus get
0 = XAR log
vo
+7(v − 1) − 1 (0 −0。).
The division by T was only necessary to make the right-hand
member a difference of entropy. By the aid of the character-
istic equation and of equation (a), we can eliminate v and v,
and introduce the pressure p. The equation then shows us
how the quantity σ of ice formed varies with the change of
pressure. But the details of the process are of less interest
to us than the limits within which it takes place. Hence we
let the index 0 refer to the state when the mixture just
reached the temperature 0°, in which therefore ice was not
present, and where σ = 0. The index 1 refers to the state
in which all the water is just frozen, in which therefore the