Thermodynamic PropertyMethodsThe key thermodynamic property calculation performed in a calculation isphase equilibrium. The basic relationship for every component i in the vaporand liquid phases of a system at equilibrium is:fiv = fil (1)Where:fiv = Fugacity of component i in the vapor phasefil = Fugacity of component i in the liquid phaseApplied thermodynamics provides two methods for representing the fugacitiesfrom the phase equilibrium relationship in terms of measurable statevariables, the equation-of-state method and the activity coefficient method.In the equation of state method:fiv=?ivyi p (2)fil=?ilxi p (3)With:(4)Where:?? = v or lV = Total volumeni = Mole number of component iEquations 2 and 3 are identical with the only difference being the phase towhich the variables apply. The fugacity coefficient ?i? is obtained from theequation of state, represented by p in equation 4. See equation 45 for anexample of an equation of state.In the activity coefficient method:fiv = ?ivyi p (5)fil = xi?ifi*,l (6)Where ?iv is calculated according to equation 4,?i=Liquid activity coefficient of component ifi*,l = Liquid fugac