Volumetric functions, molecular similarity

The interrelations of the form of Eqs. 1.6-1 and 1.6-2 are always obeyed in nature, though we may not have been sufficiently accurate in our experiments, or clever enough in other ways to have discovered them. In particular, Eq. 1.6-1 in dicates that if we prepare a fluid such that it has specified values T and V, it wilt always have the same pre.ssure P. What is this alue of the pressure PI To know this we have to either have done the experiment sometime in the past or know the exact functional relationship between T, V, and P for the fluid being considered. What is frequently done for fiuids of scientific or engineering interest is to make a large number of measurement. of P, V, and T and then to develop a volumetric equation of state for the fluid, that is, a mathematical relationship between the variables P, V, and T. Similarly, measurements of U, V, and T are made to develop a thermal equation of state for the fluid. Alternatively, the data that have be eh obtained may be presented directly in graphical or tabular form. (In fact, as will be shown later in this book, it is more convenient to formulate volumetric equations of state in terms of P, V, and T than in terms of P, V, and T, since in this case the same gas constant of Eq. 1.4-3 can be used for all substances. If volume on a per-mass basis V was u.sed, the constant in the ideal gas equation of state would be R divided by the molecular weight of the substance.)... 

Free-volume theory Molecular motion involves the availability of vacancies. The vacancy volmne is the free volume, Vp, of the liquid, approximately the difference in volume of the liquid, Vl, and crystalline, 14, forms. Vp is a function of temperature. D is a constant close to unity. The Williams-Landel-Ferry (WLF) equation uses a similar approach in which is the fraction of free volume at Tg, about 0.025, and Pl and Pc are the volumetric thermal expansion coefficients of the liquid and solid, respectively. 

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