Summary

The study of departure functions often causes students great difficulty. That is understandable since it involves simultaneous application of physics and multivariable calculus. This may be the first instance in which students have applied these subjects in combination to such an extent. On the other hand, it is impressive to see what can be accomplished with these tools: the functional equivalent of “steam tables” for any compound in the universe (given a reliable equation of state).

When you get beyond the technical details, however, it seems obvious that there is a difference between an ideal gas and a real fluid. As the accountants for energy movements, we need to be able to account for such contributions. Our method is to first add up all the contributions as if everything behaved like an ideal gas, then to compute and add up all the departures from ideal gas behavior. We apply this over and over again. The calculations are greatly facilitated by computers such that the minimum requirement is the knowledge of what calculation is required and which buttons to push. The purpose of this chapter was to turn your attention to developing a better understanding of the subtleties underlying the equations inside the computer programs.

Your understanding of departure functions is reflected in your ability to develop expressions for various equations of state, as well as the mechanics of adding up the numerical quantities. We covered several derivations, especially for the Peng-Robinson model, and you should be able to reproduce that procedure for other models. Obtaining numerical results occasionally requires iteration and careful consideration of the key constraints. For example, an isentropic compression may transition from the three-root region to the one-root region and your awareness of issues like this corresponds directly with your understanding of how the calculations are performed. Try to rewrite the Excel files yourself, to ensure that you fully comprehend them.