Entropy departure

The integral in Equation 4.84 can be evaluated from an equation of state3. However, before this entropy departure function can be applied to calculate entropy, the reference state must be defined. Unlike enthalpy, the reference state cannot be defined at zero pressure, as the entropy of a gas is infinite at zero pressure. To avoid this difficulty, the standard state can be defined as a reference state at low pressure P0 (usually chosen to be 1 bar or 1 atm) and at the temperature under consideration. Thus,... 

To calculate the entropy of a liquid or gas at temperature T and pressure P, the entropy departure function (Equation 4.84) is evaluated from an equation of state3. The entropy at the reference state is calculated at temperature T from Equation 4.85. The entropy at the reference state is then added to the entropy departure function to obtain the required entropy. The entropy departure function is illustrated in Figure 4.10. As with enthalpy departure, the calculations are complex and are usually carried out in physical property or simulation software packages. 

Both enthalpy and entropy can be calculated from an equation of state to predict the deviation from ideal gas behavior. Having calculated the ideal gas enthalpy or entropy from experimentally correlated data, the enthalpy or entropy departure function from the reference state can then be calculated from an equation of state. 

FIGURE 1.11 Entropy departure of gases and liquids Zc = 0.27. (Hougen, Watson, Ragatz—Chemical Process Principles, Part II, Wiley, 1959.)... 

The Soave equation is widely used for hydrocarbons and related components over broad ranges of temperature and pressure. It is accurate enough for calculating enthalpy and entropy departures, vapor-liquid equilibria, and vapor density in natural gas processing and many petroleum-related operations. The equation is not very accurate in the critical region and for liquid density calculations. 

Calculate initial molar volume and enthalpy and entropy departure... 

This equation and Fig. 6.6-3 are the bases for the entropy departure plot given in Fig. 

In particular, to obtain numerical values for the enthalpy or entropy departure for a fluid that obeys the Peng-Robinson equation of state, one uses the following procedure ... 

The enthalpy and entropy departures from ideal gas behavior calculated in this way can be used to solve thermodynamic problems in the same manner as the similar functions obtained from the corresponding-states graphs were used in the previous section. 

Using the value of Z found above and Eq. 6.4-30 to calculate the entropy departure from ideal gas behavior, S — (Note that though they are not needed in this problem, the enthalpy departure and other properties can also be computed once the compressibility is known.)... 

Before we proceed with the evaluation of dq)arture functions, and to develop a picture of their magnitudes as functions of pressure, we calculate enthalpy and entropy departure values in the next two Examples for i-butane. 

Typical results with the Pitzer approach and the SRK EoS are presented in Table 9.1 and similar ones are obtained with the PR and vdW-711 EoS. For the latter t = tQ should be used to avoid the pronounced and distorting effect that dt/dT) has on enthalpy and entropy departure values close to the criticd point (Androulakis et al, 1989). 

Eq.9.11.4 can be used along with experimental PVT data for the evaluation of fugacity coefficients through graphical integration. As with the evaluation of enthalpy and entropy departures, however, the integration is carried out by first fitting the Fl tiata to an accurate equation of state. And since such EoS express P =f(V,T), rather than V = f P,T)y direct use of Eq.9.11.4 is not possible. 

Prediction of vapor and gaseous volumes, enthalpies of vaporization and enthalpy and entropy departures with cubic EoS are discussed in Sections 8.10.8,8.14.1 and 9.8.5 respectively. 

For enthalpy and entropy departure values of nonpolar/weakly polar mixtures, the cubic EoS discussed here give reasonable accuracy up to moderate pressures. At higher pressures, the Pitzer-Lee-Kesler approach should be used. 

S.For more details on the estimation of the volumetric behavior and of enthalpy and entropy departure values for gas and liquid mixtures, see Reid et al. 

Define a departure function. Use generalized enthalpy and entropy departure functions to solve first- and second-law problems for systems that exhibit nonideal behavior. 

Like the enthalpy departure function, the entropy departure function can be used to find the entropy change of a real fluid. It is defined as the difference in that property between the real, physical state and that of a hypothetical ideal gas at the same T and P ... 

Finally, we get the entropy departure by inserting these results in Equation (5.47) ... 

Again, Equation (5.54) can be integrated with the appropriate data or equation of state for z. Using the Lee-Kesler equation of state gives results that include a simple fluid term and a correction term. The form of entropy departure using this equation of state is given in Appendix E. 

---