Thermodynamics

What happens if g f g g ? Obviously the two phases are not in equilibriumat that moment. The second law requires that (dG) T, P (g f g g ) dm f 0.Thus, dm f must be negative, which means that some liquid must vaporizeuntil g f g g . Therefore, the Gibbs function difference is the driving forcefor phase change, just as the temperature difference is the driving force forheat transfer.Chapter 16 | 809EXAMPLE 16–7Phase Equilibrium for a Saturated MixtureShow that a mixture of saturated liquid water and saturated water vapor at120°C satisfies the criterion for phase equilibrium.Solution It is to be shown that a saturated mixture satisfies the criterionfor phase equilibrium.Properties The properties of saturated water at 120°C are h f 503.81 kJ/kg,s f 1.5279 kJ/kg · K, h g 2706.0 kJ/kg, and s g 7.1292 kJ/kg · K (TableA–4).Analysis Using the definition of Gibbs function together with the enthalpyand entropy data, we haveandg f h f Ts f 503.81 kJ>kg 1393.15 K2 11.5279 kJ>kg # K296.9 kJ>kgg g h g Ts g 2706.0 kJ>kg 1393.15 K2 17.1292 kJ>kg # K296.8 kJ>kgDiscussion The two results are in close agreement. They would matchexactly if more accurate property data were used. Therefore, the criterion forphase equilibrium is satisfied.The Phase RuleNotice that a single-component two-phase system may exist in equilibriumat different temperatures (or pressures). However, once the temperature isfixed, the system is locked into an equilibrium state and all intensive propertiesof each phase (except their relative amounts) are fixed. Therefore, asingle-component two-phase system has one independent property, whichmay be taken to be the temperature or the pressure.In general, the number of independent variables associated with a multicomponent,multiphase system is given by the Gibbs phase rule, expressed asIV C PH 2(16–20)where IV the number of independent variables, C the number of components,and PH the number of phases present in equilibrium. For thesingle-component (C 1) two-phase (PH 2) system discussed above, forexample, one independent intensive property needs to be specified (IV 1,Fig. 16–19). At the triple point, however, PH 3 and thus IV 0. Thatis, none of the properties of a pure substance at the triple point can be varied.Also, based on this rule, a pure substance that exists in a single phaseWATER VAPORT100°C150°C200°C.LIQUID WATERFIGURE 16–19According to the Gibbs phase rule, asingle-component, two-phase systemcan have only one independentvariable.