General conditions for equilibrium and stability

Let us consider a closed system containing u components and 7 phases. The phases are assumed to be in internal equilibrium and to be open with respect to each other, i.c. the entropy, volume, and mole fractions arc variables for each phase. 

Write the fundamental equation (Equation 1.1.1-1) for each phase  

As the internal energy of the system is a state function, under the conditions a-l 

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