Page 170 - Advanced Thermodynamics for Engineers, Second Edition

7.5 THE CLAUSIUS–CLAPEYRON EQUATION 157

Pressure, p

Critical point

Water Steam
1 2
Liquid Vapour
Liquid + vapour

Specific volume, v
FIGURE 7.4
Change of phase depicted on p –v diagram.

The left hand side of Eqn (7.19c) is the rate of change of entropy with volume at constant
temperature.
If the change of phase of water, from, say, liquid to steam is considered, then this takes place at
constant pressure and constant temperature, known as the saturation values. Hence, if the change of
phase between points 1 and 2 on Fig. 7.4 is considered

vs s 2 s 1
¼ ; (7.76)
vv T v 2 v 1
which, on substituting from Eqn (7.19c) becomes

vp s 2 s 1
¼ (7.77)
vT v v 2 v 1
If there is a mixture of two phases, say steam and water, then the pressure is a function of
temperature alone, as shown in Section 8.4. Thus

dp s 2 s 1
¼ : (7.78)
dT v 2 v 1

vh
Now ¼ T; and during a change of phase both Tand p are constant, giving h 2 h 1 ¼ T(s 2 s 1 ).
vs
p
Thus
h 2 h 1 dp
¼ T (7.79)
v 2 v 1 dT