Some Thermodynamic Identities in the Mixture Model Approach

SOME THERMODYNAMIC IDENTITIES IN THE MIXTURE-MODEL APPROACH 

In this section, we consider classification procedures that provide a QCDF that has only two components. A very simple example was treated in detail in Section 5.6. For the purpose of this section, as well as for most of the later applications, we can construct such a two-component system from any of the singlet GMDF s which have been previously introduced. For example, using Xc K) in (5.10), we can regroup the particles with 

Clearly, is the mole fraction of particles having a CN smaller than or equal to K. These may be referred to as particles with low local density (for more details, see Section 5.2). Similarly, Xjj is referred to as the mole fraction of high-local-density particles (i.e., particles for which K K ). In this way, the system is viewed as a mixture of two quasicomponents, L and H. This point of view is called a two-structure model (TSM). In a similar fashion, one can construct TSM s from any other discrete or continuous QCDF. Therefore, the following treatment applies for any TSM, not necessarily the one defined in (5.122) and (5.123). 

Within the realm of TSM s, the following natural question may be asked. Suppose that x and Xh are the mole fractions of the two components how are they expected to respond to variation of temperature or pressure or addition of solute This question has been the subject of many investigations. Here, we shall derive a few identities which will be found useful for later applications. 

Given a two-component system of, say, L and H at chemical equilibrium, we have the condition 

Some Thermodynamic Identities in the Mixture Model Approach 

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