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Section 7.2
One-Component Phase Equilibrium

Y Figure 7.1
The H O phase diagram at low
2
S H 2 O and moderate pressures. (a)
Caricature of the diagram. (b) The
diagram drawn accurately. The
R vertical scale is logarithmic. (For
the H O phase diagram at high
2
pressures, see Fig. 7.9b.)

(a)

(b)

definite T and P. Recall that the water triple point is used as the reference temperature
for the thermodynamic temperature scale. By definition, the water triple-point temper-
ature is exactly 273.16 K. The water triple-point pressure is found to be 4.585 torr. The
present definition of the Celsius scale t is t/°C T/K 273.15 [Eq. (1.16)]. Hence
the water triple-point temperature is exactly 0.01°C.
The melting point of a solid at a given pressure P is the temperature at which
solid and liquid are in equilibrium for pressure P. Line AD in Fig. 7.1 is the solid–
liquid equilibrium line for H O and gives the melting point of ice as a function of pres-
2
sure. Note that the melting point of ice decreases slowly with increasing pressure. The
normal melting point of a solid is the melting point at P 1 atm. For water, the nor-
mal melting point is 0.0025°C. The ice point (Secs. 1.3 and 1.5), which occurs at
0.0001°C, is the equilibrium temperature of ice and air-saturated liquid water at 1 atm
pressure. The equilibrium temperature of ice and pure liquid water at 1 atm pressure
is 0.0025°C. (The dissolved N and O lower the freezing point compared with that of
2 2
pure water; see Sec. 12.3.) For a pure substance, the freezing point of the liquid at a
given pressure equals the melting point of the solid.
Along line OA, there is equilibrium between solid and vapor. Ice heated at a pres-
sure below 4.58 torr will sublime to vapor rather than melt to liquid. Line OA is the
vapor-pressure curve of the solid. Statistical mechanics shows that the vapor pres-
sure of a solid goes to zero as T → 0 (Prob. 23.42), so the solid–vapor line on a P-T
phase diagram intersects the origin (the point P 0, T 0).