Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

What happens if gfgg? Obviously the two phases are not in equilibrium

at that moment. The second law requires that (dG)T,P(gfgg) dmf0.

Thus,dmfmust be negative, which means that some liquid must vaporize

until gfgg.Therefore, the Gibbs function difference is the driving force

for phase change, just as the temperature difference is the driving force for

heat transfer.

Chapter 16 | 809

EXAMPLE 16–7 Phase Equilibrium for a Saturated Mixture

Show that a mixture of saturated liquid water and saturated water vapor at

120°C satisfies the criterion for phase equilibrium.

Solution It is to be shown that a saturated mixture satisfies the criterion

for phase equilibrium.

Properties The properties of saturated water at 120°C are hf503.81 kJ/kg,

sf1.5279 kJ/kg · K, hg2706.0 kJ/kg, and sg7.1292 kJ/kg · K (Table

A–4).

Analysis Using the definition of Gibbs function together with the enthalpy

and entropy data, we have

and

Discussion The two results are in close agreement. They would match

exactly if more accurate property data were used. Therefore, the criterion for

phase equilibrium is satisfied.

96.8 kJ>kg

gghgTsg2706.0 kJ>kg 1 393.15 K 21 7.1292 kJ>kg # K 2

96.9 kJ>kg

gfhfTsf503.81 kJ>kg 1 393.15 K 21 1.5279 kJ>kg # K 2

The Phase Rule

Notice that a single-component two-phase system may exist in equilibrium

at different temperatures (or pressures). However, once the temperature is

fixed, the system is locked into an equilibrium state and all intensive prop-

erties of each phase (except their relative amounts) are fixed. Therefore, a

single-component two-phase system has one independent property, which

may be taken to be the temperature or the pressure.

In general, the number of independent variables associated with a multicom-

ponent, multiphase system is given by the Gibbs phase rule,expressed as

(16–20)

where IV the number of independent variables,Cthe number of com-

ponents, and PH the number of phases present in equilibrium. For the

single-component (C1) two-phase (PH 2) system discussed above, for

example, one independent intensive property needs to be specified (IV 1,

Fig. 16–19). At the triple point, however, PH 3 and thus IV 0. That

is, none of the properties of a pure substance at the triple point can be var-

ied. Also, based on this rule, a pure substance that exists in a single phase

IVCPH 2

T

WATER VAPOR

LIQUID WATER

100 °C

150 °C

(^200) .°C
..
FIGURE 16–19
According to the Gibbs phase rule, a
single-component, two-phase system
can have only one independent
variable.
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