In class, we argued that to describe a mixture with nc components in VLE, we need 2n, thermodynamic variables: T, P, ne - 1 mole-fractions, {x}, and ne 1 mole-fractions, {y}. Then, using the VLE criteria, we were able to show that only ne out of these 2nc variables can be specified independently. In this problem, we will generalize the above results to more than 2 phases to obtain the Gibbs' phase rule, which states that for a mixture with nc components, which are distributed across phases in equilib- rium with one another, nc - + 2 variables can be independently specified. (a) How many thermodynamic variables do we need to describe to describe the above system? What are they? (b) How many constraints, i.e., phase equilibrium criteria, do the above variables need to obey? (c) Using your answers from the above two parts, show that the number of variables that can be specified independently is nc - +2.