System of implicit non-linear equations the Newton-Raphson method

2 System of implicit non-linear equations the Newton-Raphson method 

The Newton method can be extended to several variables in order to find the zeroes of n functions/ in n variables x which we lump as the vector x = [x. x ]T, i.e., to solve the system of equations 

Although several examples implementing the Newton-Raphson method for the computation of chemical equilibrium are developed in Chapter 6, we will now present some simple applications that illustrate its basic principles. 

Assuming that AHf are constant, calculate the composition of the solid and liquid coexisting at T = 1600K. 

The variable X referring to mole fractions, equilibrium is achieved when the chemical potentials /i(ln A ) for each element are equal in each phase 

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