Entropy departure function

The calculation of entropy is required for compression and expansion calculations. Isentropic compression and expansion is often used as a reference for real compression and expansion processes. The calculation of entropy might also be required in order to calculate other derived thermodynamic properties. Like enthalpy, entropy can also be calculated from a departure function ... 

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. 

The ideal gas law is used to calculate the enthalpy and entropy of fluids at low pressure. The principles of thermodynamics can be used to extend these to higher pressure. This is done through the so-called departure functions. For the enthalpy, the departure function is given as follows ... 

This example demonstrates that reliable PVT correlation and constant-pressure heat capacity of an ideal gas are sufficient to determine a variety of thermodynamic properties, as enthalpy, entropy, Gibbs free energy, etc., and built comprehensive charts. This approach will be extended by means of departure functions. 

Any equation of state may be used to generate analytical expressions for residual or departure functions. In the case of PR-EOS the results for enthalpy and entropy are ... 

Lee and Kesler (reference cited) found an accurate representation for compressibility of both gases and liquids by combining BWR-EOS with corresponding states law. They generated departure functions for enthalpy, entropy, fugacity coefficient and heat capacity. Tables are given in Reid et al. (1987), whereas illustrative graphs are presented in Perry (1997). The method is similar to that developed for compressibility. As an example, the enthalpy departure function may be calculated with the relation ... 

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

On a molecular level, we can consider this departure function to represent the change in enthalpy if we could turn off the intermolecular interactions in the real fluid. In this section, we will specifically explore how to calculate changes in enthalpy and entropy using departure functions however, this methodology can be expanded to any property. ... 

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 ... 

Of the following mixture, which do you think has entropy departure function of larger magnitude... 

Develop expressions for the enthalpy and entropy departure functions for a gas that follows the Redlich-Kwong equation of state. 

Repeat Problem 5.32 using the entropy departure function. 

This program calculates departure functions of enthalpy and entropy for a pure species given a known set of dependent properties. You may choose T and P as dependent properties to give... 

In the absence of any data, the maximum of the entropy functional is reached for p(r) = m(r). Any substantial departure from the model, observed in the final map, is really contained in the data as, with the new definition, it costs entropy. This paper presents illustrations of model testing in the case of intermetallic and molecular compounds. 

Recent papers have noted the connection of the FR to Kullback-Leibler distance, or relative entropy which measures the irreversibility of the system and Sevick et al consider a similar property—the departure of the average of the time-averaged dissipation function from zero—as a measure of irreversibility. The effect of system on size on reversibility is discussed in ref. 213. 

We now apply the above results to the energy function E(S, V,n, rit). To explore the effect of entropy fluctuations giving rise to slight departures from... 

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. 

Generally, therefore, these additional functions are connected with the departures from additivity shown by the volume F, the heat capacity and the chemical constant i and the enthalpy H on dilution of the solution. They find their tangible expression in volume contractions, heat effects and anomalous behavior of specific heats. Physically they should be attributed to an excess or deficiency in attraction between the molecules of solvent and solute over the cohesion of identical molecules. Hildebrand has termed solutions in which additional entropy terms such as 2, 3 and 4 are missing, regular solutions (see p. 222). In them the excess and deficiency attractions may be related quantitatively to the heat of dilution, since in the insertion of molecules of one component between those of the other, a heat effect other than zero results because the energy necessary for the separation of identical molecules differs from that obtained in bringing together dissimilar particles. 

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