Conjugate pairs extensive/intensive properties

The fundamental equation for U is in agreement with the statement of the preceding section that for a homogeneous mixture of Ns substances, the state of the system can be specified by Ns + 2 properties, at least one of which is extensive. The total number of variables involved in equation 2.2-8 is 2NS + 5. Ns + 3 of these variables are extensive (U, S, V, and (nj), and Ns + 2 of the variables are intensive (T, P, /.q ). Note that except for the internal energy, these variables appear in pairs, in which one property is extensive and the other is intensive these are referred to as conjugate pairs. These pairs are given later in Table 2.1 in Section 2.7. When other kinds of work are involved, there are more than 2Ns + 5 variables in the fundamental equation for U (see Section 2.7). 

The first term on the right side of Eq. (1.53) orEq. (1.54) represents heat associated with the thermodynamic temperature T. and the remaining terms are the work terms. The pairs of intensive and extensive properties, such as 1 IT and U, or/, and A, are the conjugate properties. 

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