The Gibbs phase rule, which determines how many intensive variables (e.g., temperature, pressure) can be varied independently, is:
$$
F = C - P + 2,
$$
where \(F\) is the number of degrees of freedom, \(C\) is the number of components and \(P\) is the number of phases. In a single-phase region, heat may be added isobarically to increase the temperature:
$$
\Delta H = nc_p(T_2 - T_1) = Q,
$$
where \(Q\) is the amount of heat added, \(c_p\) (kJ/[kmol K]) is the constant-pressure heat capacity, \(n\) is the number of moles, and \(T_1\) and \(T_2\) (K) are the initial and final temperatures. For isothermal processes, changes in the specific volume (L/mol) accompany phase changes; heat must be added or removed for these phase changes to take place.
In a two-phase region, the amount of each phase can be determined from:
$$
\frac{n_H}{n_H + n_L} = \frac{H - H_L}{H_H - H_L}
$$
where \(n_H\) (mol) is the amount of the higher-energy phase, \(n_L\) (mol) is the amount of the lower-energy phase, \(H\) (kJ/mol) is the specific enthalpy of the system, \(H_H\) (kJ/mol) is the specific enthalpy of the saturated high-energy phase and \(H_L\) (kJ/mol) is the specific enthalpy of the saturated low-energy phase. Note that \(H\), \(H_H\), and \(H_L\) must be evaluated at the same temperature and pressure.
Withing the triple point, the amounts of each phase composition is complex [1, 2].
References:
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Revised Release on the Equation of State 2006 for H2O Ice Ih, Report Number IAPWS R10-06(2009), Doorwerth, Netherlands: The International Association for the Properties of Water and Steam. (Jan 13, 2023) www.iapws.org/relguide/Ice-2009.html.
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Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam, Report Number IAPWS R7-97(2012), Lucerne, Switzerland: The International Association for the Properties of Water and Steam. (Jan 13, 2023) www.iapws.org/relguide/IF97-Rev.html.
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J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2012.
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