Ideal gas and residual properties

The enthalpy and entropy are simple sums of the ideal gas and residual properties, which are evaluated separately. 

Thus, H and S are found from the corresponding ideal-gas and residual properties by simple addition. General expressions for H and S 9 are obtained by integration of Eqs. (6.22) nd (6.23) from an ideal-gas state at reference conditions T0 and P0 to the ideal-gas state at T and P ... 

Combine the ideal gas and residual parts to obtain the absolute properties. 

The actual properties of the mkture are calculated by adding the ideal gas and residual contributions ... 

The most satisfactory calculation procedure for the thermodynamic properties of gases and vapors is based on ideal gas state heat capacities and residual properties. Of primary interest are the enthalpy and entropy these are given by rearrangement of the residual property definitions ... 

The ideal-gas and ideal-solution approaches also differ because they are based on different kinds of experimental data. The residual properties and fugadty coeffidents depend on volumetric data measurements of P, v, T, and x. But the excess properties and activity coeffidents depend on density measurements for calorimetric measurements for h, and phase-equilibrium data for and y,-. Modem modeling tends to rely on volumetric data (equations of state), and a prindpal feature of this chapter has been to establish how excess properties can be computed from residual properties and how activity coefficients can be computed from fugadty coeffidents. But note that such calculations can be performed in either direction that is, at least in principle. 

Figure 6.1 To obtain changes in prop>erties of one-phase mixtures, our basic strategy is to compute deviations relative to some ideality. In route lA (left) the ideality is the ideal gas and the deviations are the residual properties. In route IB (right) the ideality is an ideal solution and the deviations are the excess properties. In addition, we could use the relations in 5.3 to compute residual properties from excess properties and vice versa.

Property changes are readily determined for fluids in the ideal gas state, and these in combination with residual properties are used to compute property changes of real fluids. The computational scheme is suggested in Figure 5, and is based on the following identity ... 

The ideal gas is a useful model of the behavior of gases and serves as a standard to which real gas behavior can be compared. This is formalized by the introduction of residual properties. Another useful model is the ideal solution, which sei ves as a standard to which real solution behavior can be compared. This is formalized by introduction of excess propei ties. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

The most satisfactory calciilational procedure for thermodynamic properties of gases and vapors requires PVT data and ideal gas heat capacities. The primary equations are based on the concept of the ideal gas state and the definitions of residual enthalpy anci residual entropy ... 

In these equations the heat capacity C p is that of the ideal gas state or that of the real gas near zero or atmospheric pressure. The residual properties AS[ and AH] are evaluated at (Plt T,) and AS2 and AH2 at (P2, Tf). Figure 7.28 gives them as functions of reduced temperature T/Tc and reduced pressure P/Pc. More accurate methods and charts for finding residual properties from appropriate equations of state are presented in the cited books of Reid et al. (1977) and Walas (1985). 

Just as the fundamental property relation of Eq. (13.12) provides complete property information from a canonical equation of state expressing G/RT as a function of T, P, and composition, so the fundamental residual-property relation, Eq. (13.13) or (13.14), provides complete residual-property information from a PVT equation of state, from PVT data, or from generalized PVT correlations. However, for complete property information, one needs in addition to PVT data the ideal-gas-state ieat capacities of the species that comprise the system. 

The definition for the residual property isXR =X-Xideal, where X and Xldeal are the actual and ideal gas properties, respectively. Residual volume (FR) is... 

Residual Properties These quantities compare true and ideal gas properties through differences ... 

The graphs are based on the Peng-Robinson equation of state (1) as improved by Stryjek and Vera (2, 3). The equations for thermodynamic properties using the Peng-Robinson equation of state are given in the appendix for volume, compressibility factor, fugacity coefficient, residual enthalpy, and residual entropy. Critical constants and ideal gas heat capacities for use in the equations are from the data compilations of DIPPR (8) and Yaws (28, 29, 30). 

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