Consider non-ideal liquid phases where the activity coefficient is given by the one-parameter model

The saturation pressure of species 1 is 800 mm Hg, and the saturation pressure of species 2 is 1000 mm Hg.

(a) Write a MATLAB program that uses Newton’s method to compute the azeotrope pressure as a function of the composition of the liquid phase, x₁, for values of A ∈ [1.6, 2.0]. (These are below the liquid–liquid phase separation value of A.) What is the nonlinear algebraic equation you need to solve and the derivative needed for Newton’s method? Your program should automatically plot the azeotrope pressure versus the composition of the liquid phase.

(b) Develop a system of equations that you need to solve to compute the P–x–y diagram for A = 2. In your written solution, include the unknown vector, the residual equations, and the Jacobian for this system.

(c) Use the result from part (b) to write a program that automatically produces the P–x–y and x–y diagrams for this system (where the compositions refer to species 1).

Transcribed Image Text:

In yi = A(1-x₂)²