Residual thermodynamic functions

Table 1. Compression factor, fugacity coefficient, and residual thermodynamic functions of real fluid Refrigerant 500...

In the present investigation, the compression factor, fugacity coefficient, and residual thermodynamic functions of the real fluid R-500 have been calculated using the BACK equation of state. For this purpose, the experimental data, i.e., critical constants, saturated liquid density, saturation vapor pressure, and the PVT data have been utilized. 

Other five common residual thermodynamic functions and... 

A class of thermodynamic functions called residual properties is given generic definition by equation 132 ... 

One simple universal equation applies to all substances, requiring no substance-specific parameters. However, for most real states, the ideal-gas equation is inadequate, and real-fluid properties are obtained by adding to the ideal-gas equation the contribution of intermolecular potential in the form of deviation functions, also called residual functions. A major objective of Section 4.2 is to derive the deviation functions from the equation of state of the substance. Because the ideal-gas properties are known, to And the deviation function is as good as finding the state function of a real substance. In this way the ideal-gas equation is used universally in all equation-of-state calculations of thermodynamic functions. 

RESTATEMENT OF THE THERMODYNAMIC EQUATIONS IN TERMS OF THE RESIDUAL WORK FUNCTION, A(p, T)... 

The restatement of the equations given in Table 14-2 in terms of the residual work function is presented in Table 14-3. The use of the reformulated form of the equations for the evaluation of the thermodynamic functions is a useful technique which appears to have been suggested first by Benedict et al.6... 

Table 14-3 Statement of the thermodynamic functions of Table 14-2 in terms of the residual work content A...

The thermodynamic functions for the real fluid less the functions for the ideal gas at the same temperature and pressure or volume (the residual functions) are calculated from the following equations. 

At this point we may introduce an important class of thermodynamic functions called residual or departure functions. In this case, the residual Gibbs free energy may be defined as ... 

These mathematical properties have a simple practical result they ensure that the same relationships can be written among all forms of a thermodynamic function, including molar, total, residual, partial molar, or residual partial molar. 

The virial equation can not only describe the PvT behavior of gases, but also the different residual functions. Both forms (Leiden form and Berlin form) are well-suited for this purpose, but most of the thermodynamic functions can be derived easier using the Berlin form, because this form is volume explicit. Volume explicit means that the equation can be solved explicitly for vas a function of T and P. As an example, the calculations of the fugacity coefficient and of the residual function of the enthalpy are shown, using the virial equation in the Berlin form truncated after the second virial coefficient B. 

We noted in 13.2.3 that the fugacity coefficient, in the form RTXnjf, is a residual function, defined ( 13.2.3) as the difference between a real system thermodynamic function and the same function for an ideal gas under the same conditions. 

The Helmholtz energy is convenient as a generating thermodynamic function because its derivatives, with respect to volmne and each of the components moles numbers, yield the pressme and the chemical potentials, respectively. The residual Helmholtz energy is then... 

Latour RA. Jr., Hench L.L. A theoretical analysis of the thermodynamic contributions for the adsorption of individual protein residues on functional zed surface. Biomaterials 2002 23 4633-4648... 

TMA, if it represented a pure length change of an isotropic sample, would give the expansion coefficient (a), shown as a dashed line in Figure 7.38. The volumetric expansion coefficient (dF/dT)p is a second-order thermodynamic function parallel to Cp. Through a should therefore show much the same shape curve as Cp. In reality, creep, relaxation of residual moulding, stresses, complex interplay with heating rate, etc., make this technique semi-empirical. 

Silylene complexes are not only stable with donor substituents but also with simple alkyl residues at silicon. These alkyl complexes still have a sufficient thermodynamic stability, but otherwise are reactive enough to allow a rich and diverse chemistry. Particularly the chlorocompounds 7 and 11 are valuable starting materials for further functionalization reactions the details of these reactions will be discussed in the forthcoming sections. The data for the known compounds are summarized in Table 1. 

Figure 7.28. Residual entropy and enthalpy as functions of reduced properties, (a) Residual entropy, (b) Residual enthalpy. Drawn by Smith and Van Ness (Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York, 1959) from data of Lydersen et al. For illustrative purposes primarily, see text for other sources.]...

---