Enthalpy departure function

Thermodynamic paths are necessary to evaluate the enthalpy (or internal energy) of the fluid phase and the internal energy of the stationary phase. For gas-phase processes at low and modest pressures, the enthalpy departure function for pressure changes can be ignored and a reference state for each pure component chosen to be ideal gas at temperature and a reference state for the stationarv phase (adsorbent plus adsorbate) chosen to be adsorbate-free solid at. Thus, for the gas phase we have... 

To calculate the enthalpy of liquid or gas at temperature T and pressure P, the enthalpy departure function (Equation 4.78) is evaluated from an equation of state2. The ideal gas enthalpy is calculated at temperature T from Equation 4.81. The enthalpy departure is then added to the ideal gas enthalpy to obtain the required enthalpy. Note that the enthalpy departure function calculated from Equation 4.78 will have a negative value. This is illustrated in Figure 4.9. The calculations are complex and usually carried out using physical property or simulation software packages. However, it is important to understand the basis of the calculations and their limitations. 

Simple vapor and liquid enthalpy models may be developed by recognizing that, on a mass basis, vaporization enthalpies and vapor and liquid heat capacities do not vary widely from component to component, and the latter are relatively independent of temperature. Enthalpy departure functions in mass units are first defined as follows ... 

The enthalpy models are actually for the enthalpy departure function. Normally, the molar enthalpy of a phase is found from the ideal gas enthalpy and the enthalpy departure... 

Symbolic determination of enthalpy departure function for the Clausius equation of state... 

The proposed approximation amounts to neglecting the partial derivatives of the enthalpy departure functions, the Q s, with respect to the component-flow rates. As shown in Chap. 14, Q appears in the definition of the virtual value of the partial molar enthalpy. For example, for any component i in the liquid phase on plate j, the virtual value of the partial molar enthalpy is given by... 

The vapor enthalpies were expressed in terms of the enthalpy departure function Q (see Chap. 14) as follows... 

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 ... 

We now need to come up with an expression for the enthalpy departure function so that we can solve Equation (5.47). Since enthalpy departure at a given state is related to the intermolecular forces involved, we will need to use the PvT relation developed in Chapter 4 and then apply the relationships of the thermodynamic web to come up with an expression for the enthalpy departure function. In the development that follows, we will use the generalized compressibility charts and tables discussed in Section 4.4 to develop values for the generalized enthalpy departure function based on corresponding... 

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 ... 

Develop an expression for the enthalpy departure function for a gas that obeys the van der Waals equation of state. Write it in terms of reduced coordinates. 

This question should be completed without doing any calculations. Consider the enthalpy departure function for the following cases. Rank them horn the smallest magnitude to the largest. Explain. 

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