The Gibbs phase rule, which determines how many intensive variables (e.g., temperature, pressure) can be varied independently, is:
is the number of degrees of freedom,
is the number of components and
is the number of phases.
In a single-phase region, heat may be added isobarically to increase the temperature:
is the amount of heat added,
(kJ/kmol K) is the constant-pressure heat capacity,
is the number of moles, and
(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:
(mol) is the amount of the higher-energy phase,
(mol) is the amount of the lower-energy phase,
(kJ/mol) is the specific enthalpy of the system,
(kJ/mol) is the specific enthalpy of the saturated high-energy phase and
(kJ/mol) is the specific enthalpy of the saturated low-energy phase. Note that
must be evaluated at the same temperature and pressure.
Within the triple point, the amounts of each phase composition is complex [1, 2].
 Revised Release on the Equation of State 2006 for Ice Ih
, Report Number IAPWS R10-06(2009), Doorwerth, Netherlands: The International Association for the Properties of Water and Steam. (Aug 3, 2018) www.iapws.org/relguide/Ice-2009.html
 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. (Aug 3, 2018) www.iapws.org/relguide/IF97-Rev.html
 J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics
, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2012.