Flory, Orwoll, and VRIJ FOV Model

Au contraire to the empirical equation of Tait for EOS predictions, theoretical models can be used but generally require an understanding of forces between the molecules. These laws, strictly speaking, need be derived from quantum mechanics. However, Lenard-Jones potential and hard-sphere law can be used. The use of statistical mechanics is an intermediate solution between quantum and continuum mechanics. A canonical partition function can be formulated as a sum of Boltzmann s distribution of energies over all possible states of the system. Necessary assumptions are made during the development of the partition function. The thermodynamic quantities can be obtained by use of differential calculus. For instance, the thermodynamic pressure can be obtained from the partition function Q as follows  

The principle of corresponding states can be used to express the pressure, tan-perature, and specific volume in terms of reduced variables. Experimental observations reveal that the compressibility factor, Z Equation (2.24), for different fluids exhibits similar behavior when correlated as a function of reduced temperature, T, and reduced pressure, The reduced variables may be defined with respect to some characteristic quantity. For example, they can be defined as follows with respect to critical temperature and critical pressure  

All fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor, and aU deviate from ideal-gas behavior to about the same degree. 

Corresponding-states correlations of Z based on this theorem are referred to as two-parameter correlations. They require the use of two reducing parameters, and P. These correlations are nearly exact when used to describe noble gases such as argon, krypton, and xenon. When complex fluids were encountered, a three-parameter corresponding states parameter was found to be needed. An acentric factor, o), can be defined as introduced by Pitzer [11]. The acentric factor for a pure substance is defined with respect to its vapor pressure  

The acentric factor is defined as this difference evaluated at r= 0.7  

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