XIX
299
ADIABATIC CHANGES IN MOIST AIR
temperature T as the mixture; but the pressure p of the
mixture is the sum of the partial pressures P₁ =
RT
of the
v
air, and
P₂ =e of the water vapour.
The equation
ᎡᎢ
p =λ = + e,
-
or (p − e)v=λRT
v
is now the characteristic equation of the mixture. The amount
of heat necessary to produce the changes dT and dv is for the
air as before
dv
dQ₁ = x(c,dT + ARTds),
but the amount of heat to be supplied to the water in order
to produce the change dT, and at the same time to increase
the amount of water-vapour by dv, while pressure and volume
suffer corresponding changes, is
vr
dQ₂ = Td+μcdT.
T
(17) + μecaT.
The equation is deduced by Clausius in his Mechanische
Wärmetheorie, vol. i. part vi. § 11. c is the specific heat of
liquid water and r the external latent heat of steam, both being
measured in heat units. Hence the whole amount of heat to
be supplied is
dQ=λ(cdT + ART")+Td()+
+μcdT.
Here again we put dQ = 0, divide by T, and integrate. From
the integral equation we eliminate v and by means of the
characteristic equation and equation (a), and obtain
T
0 = (λc₂+µc) log++λAR log
R
Po 0
P-
e
Το
-
+RTp-e To Po-co
R₁
(II).
The quantity equated to zero again represents the difference