Virial equation of state truncated

At moderate pressures, the virial equation of state, truncated after the second virial coefficient, can be used to describe the vapor phase. As suggested by Hirschfelder, et. al. (1 3) the temperature dependence of the virial coefficients is expressed... 

Semiempirical Relationships. Exact thermodynamic relationships can be approximated, and the unknown parameters then adjusted or estimated empirically. The virial equation of state, truncated after the second term, is an example of such a correlation (3). 

Two gram-moles of nitrogen is placed in a three-liter tank at -150.8 C Estimate the tank pressure using the ideal gas equation of state and then using the virial equation of state truncated after the second term. Taking the second estimate to be correct, calculate the percentage error that results from the use of the ideal gas equation at the system conditions. 

An alternative form of the virial equation of state, truncated after the third virial coefficient is written as... 

Derive equations to calculate component fugacity coefficients in a binary mixture using the virial equation of state truncated after the second virial coefficient. The mixture second virial coefficient is given as... 

At low to moderate pressures, the virial equation of state truncated after the second virial coefficient. 

The pressure virial equation of state was shown in Eq. (1.3-4), and it was shown in an example that A2, the second pressure virial coefficient, is equal to B2, the second virial coefficient. Find an expression for (dS/dP)j- for a gas obeying the pressure virial equation of state truncated at the A2 term. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

An efficient method of solving the Percus-Yevick and related equations is described. The method is applied to a Lennard-Jones fluid, and the solutions obtained are discussed. It is shown that the Percus-Yevick equation predicts a phase change with critical density close to 0.27 and with a critical temperature which is dependent upon the range at which the Lennard-Jones potential is truncated. At the phase change the compressibility becomes infinite although the virial equation of state (foes not show this behavior. Outside the critical region the PY equation is at least two-valued for all densities in the range (0, 0.6). 

Using the truncated virial equation of state with the second virial coefficient B T)... 

Truncating the virial equation of state after the second term yields... 

Bi and are the second virial coefficients of components 1 and 2, and Bi2 is the interaction second virial coefficient. Express the virial equation of state in the following alternative form, truncated after the second virial coefficient ... 

In order to compute f /P or/r/Py,-, by the truncated virial equation of state (see Table 14-8), it is necessary to evaluate the second virial coefficient B. There follows a summary of the formulas needed to evaluate the second virial coefficient for both polar and nonpolar compounds. 

For a given temperature, pressure, and composition, the corresponding density and Z factor given by the equation of state is needed. The vapor root is found by solving the truncated virial equation of state (see Table 14-8) for Z, and for small values of BP/RT, the expression so obtained reduces to Z = 1 + BP/RT, that is,... 

The virial equation of state in Table 4.2 provides a sound theoretical basis for computing P-v-T relationships of polar as well as nonpolar pure species and mixtures in the vapor phase. Virial coefficients B, C, and higher can, in principle, be determined from statistical mechanics. However, the present state of development is such that most often (4-34) is truncated at B, the second virial coefficient, which is estimated from a generalized correlation. - In this form, the virial equation is accurate to densities as high as approximately one half of the critical. Application of the virial equation of state to phase equilibria is discussed and developed in detail by Prausnitz et al. and is not considered further here. 

From the historical point of view and also from the number of applications in the literature, the common method is to use activity coefficients for the liquid phase, i.e., the polymer solution, and a separate equation-of-state for the solvent vapor phase, in many cases the truncated virial equation of state as for the data reduction of experimental measurements explained above. To this group of theories and models also free-volume models and lattice-fluid models will be added in this paper because they are usually applied within this approach. The approach where fugacity coefficients are calculated from one equation of state for both phases was applied to polymer solutions more recently, but it is the more promising method if one has to extrapolate over larger temperature and pressure ranges. 

Clearly there is no point in trying to fit more virial coefficients to experimental data than the uncertainty of the data warrants, so in practice truncated forms of the virial equations of state, often containing no terms higher than 5, are employed in the analysis of data of modest accuracy covering fairly short ranges of pressure. However, gross truncation of the equations causes (17) to be inapplicable and it is not then justifiable to speak of the second virial coefficient without specifying the series to which the coefficient applies. Thus equation (15) can be expressed in the form... 

Obtain the formula for the work done on a sample of gas during an isothermal reversible volume change if it is represented by the truncated virial equation of state ... 

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