08.01 - The Departure Function Pathway

Demystifying The Departure Function (11min) (uakron.edu)
...a peek inside the magician's hat. The connection from the real fluid to the ideal gas is not really magic. You can look at it as transforming the interaction potential (ie. u(r)) from 0 (ideal gas) to a Lennard-Jones model (real fluid). Alternatively, you can view it as the difference between the real fluid and ideal gas at each density, summed from zero density (where both exhibit ideal gas behavior) to the density of interest. This latter approach is most convenient and makes good use of our new expertise in derivative manipulations and equations of state.

Comprehension Questions:

1. In the diagram of (A-Ac)/RTc, which state represents the closest point to an ideal gas: A, B, C, or D?
2. Write out the departure function pathway in its various steps to compute "U" = (U-U^_Ref).
3. Identify the steps in #2 above as departure function or ideal gas contributions.
4. For propane at 355K and 3MPa, (U-U^ig)= -2572 J/mol. We can compute U^ig(355K)-U^ig(230K)=8000 J/mol. The departure function for liquid propane at 230K, 0.1MPa is (U-U^ig)= -16970 J/mol. Compute the value of "U" at 355K and 3MPa relative to liquid propane at 230, and 0.1MPa using this information.
5. Compare your answer to the value given by PREOS.xlsx.
6. Compare your answer to the value given by the pathway of Figure 2.6c. (Hint: use Eqn. 2.47 to decide whether 355K,3MPa corresponds to a vapor or liquid.)