a. For the adiabatic, steady-flow flash process from specified initial conditions of T₁ and P₁ to a specified final pressure P₂ shown here, develop the equilibrium and balance equations to compute the final temperature, the vapor-liquid split, and the compositions of the coexisting phases.

b. Develop an algorithm for the calculation of part (a) using an equation of state. 

c. Use the Peng-Robinson equation of state for a multicomponent mixture to do the calculations for an adiabatic (Joule-Thomson) expansion of a liquid under pressure to produce a vapor-liquid mixture at ambient pressure. The results should include the outlet temperature, the mole fractions of each species in each phase, and the fractions of the outlet stream that are liquid and vapor.

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T₁, P₁ Liquid Vapor Liquid P₂ T₂ = ?