The molecular assumptions of the ideal gas model were relaxed to develop the van der Waals equation of state, by including a attractive term and a hard sphere repulsive term. This equation heuristicaUy illustrates how molecular concepts can be applied to developing an equation of state. In fact, it was shown that the more accurate cubic equations that have been developed since van der Waals s time have the same general form. Alternatively, the virial equation results from a power series expansion of the compressibility factor, either in concentration 1/v) or in pressure. [Pg.254]

The approach used here differs from that in 5.3.1 merely because of the form adopted for the equation of state. For the simple virial equation (5.3.2), we can choose whether we want to use a volume-explicit or a pressure-explicit form. Both forms give the same results for excess properties, and both require about the same computational effort. However for dense fluids, more complicated equations of state must be used often, they are cubic or higher-order polynomials in the volume. That is, most are pressure-explicit, they cannot be converted into volume-explicit forms, and in such cases, we must use the expressions (5.3.14)-(5.3.16) to obtain excess properties. [Pg.199]

In this chapter, we studied equations of state, which relate the measured properties P, v, and T. Examples include cubic equations of state (e.g., van der Waals, Redlich-Kwong, Peng-Robinson), the virial equation (with several specific forms), and the generalized compressibility charts. The Rackett equation allows us to estimate the molar volume of liquids at saturation, while the thermal expansion coefficient and the isothermal compressibility allow us to determine how to correct for the volumes of liquids and solids with temperature and pressure, respectively. [Pg.254]

This form is easier to solve for the required density or volume but is less reliable at the lowest temperatures. If a virial equation is used over a restricted range of the gas phase which includes the ideal gas region, it is usually truncated after the second or third term. When it is truncated after the third term, it becomes cubic in density and can be solved analytically, as described in Section 8.4.2. [Pg.168]

Commonly used EOS models include the ideal, virial, PengRobinson, Soave-RedUch Kwong, and Lee-Kesler. The reduced form of the EOS is particularly significant. Substances with the same reduced properties are in corresponding states. Van der Waal s EOS is a poor predictor of state properties, but the experimental data do correlate well with reduced conditions. Many of the cubic EOS models are based on the van der Waal equation. [Pg.1342]

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