[simonsci]

I don't understand why an intensive state is specified by N+1 variable and an extensive state is specified by N+2 variables.

[mjc123]

The intensive state is specified by pressure, temperature, density and composition. P, T and ρ are related by the equation of state, whatever it is, so if you define any 2 of them the third is fixed. The composition is defined by the mole fractions (or weight fractions) of the components. However, since the sum of the fractions must equal 1, you need only define N-1 fractions - the Nth is then fixed. So the number of variables you need to define is N-1+2 = N+1. For the extensive state, you need 2 of P, T, ρ, plus the number of moles of each component (or alternatively, N-1 mole fractions and the total number of moles); that is N + 2 variables.