It has been suggested that a simple cubic equation of state can also be used to describe a solid. However, since in a solid certain molecular contacts are preferred, compared with a fluid (vapor or liquid) in which molecules interact in random orientations, it has also been suggested that different equation-of-state parameters be used for the fluid and solid phases. Assume both the fluid and solid phases obey the equation of state 

with the parameters a_f and a_s, respectively. Develop expressions for the fugacity coefficients of the gas, liquid, and solid. Discuss how you would use such an equation to calculate the vapor-liquid, liquid-solid, vapor-solid, and vapor-liquid-solid equilibria.

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P = RT V a V2