302
XIX
ADIABATIC CHANGES IN MOIST AIR
equation we get the Po, which occurs in the equations of the
third stage. If now we determine from equation III the final
pressure p₁ of the third stage, this pressure and the tempera-
ture 273° constitute the p。 and T, in the equations of the
fourth stage. It will frequently happen that the temperature
down to which the first stage holds, lies below the freezing-
point; then we pass on at once to the fourth stage, the second
and third disappearing. After we have in this way determined
the coefficients and limits of validity of all the equations, we
may employ them to determine for any desired p the corre-
sponding T, and vice versa. These calculations can only be
performed by successive approximations, and it will be advisable
to take the necessary approximate values from the table. When
we have determined p and T for any state, its remaining pro-
perties are easily deduced. The density of the mixture follows
from the corresponding characteristic equation. The equation
(a) gives the quantity of vapour, and thus also that of the
water condensed. We may
often need to know the differ-
ence of height h, which corresponds to the different states
Po and P₁, on the assumption that the whole atmosphere is in
the so-called adiabatic state of equilibrium. The exact solu-
tion of the problem is given by the laborious evaluation of the
integral
Po
h = vdp,
Pi
but as in this particular respect an exact determination is
never of any special use, we may always use the convenient
diagram here given.
B. If we were here concerned with one mixture of one
determinate composition, i.e. with only one value of the ratio
μλ, we could exactly represent the formulæ deduced by a
diagram showing directly the adiabatic changes of the mixture,
starting from any state whatever. We could use pressure and
temperature as coordinates of a point in a plane, and could
cover the plane with a system of curves connecting all those
states which can pass adiabatically into each other. Then it
would only be necessary from a given initial state to follow
the curve passing through the corresponding point, in order