In Lecture 4 we introduced Z, the compression factor, a useful parameter that relates the molar volume of a real gas to that expected for ideal behavior. Regions where Z are greater or less than one represent the relative strengths of attractive (intermolecular) forces or repulsive (volume-based) forces. After discussing three general trends of Z vs P plots, we defined the Boyle temperature as that temperature at which the initial slope is equal to zero.
In order to connect this concept to stuff we already know, we saw how to relate a particular equation of state to this Boyle temperature. After manipulating the equation of state so that it fits into the Z=PV/nRT construct, we take the derivative with respect to P, take the limit as P approaches 0 and then see what we get. This procedure was straightforward with the virial equation (expanded in terms of P) but the van der Waals equation (and others) is a little bit more work. Still, a procedure was developed that connects these real gas empirical parameters to measurable and important quantities like the Boyle temperature.
Lastly we introduced van der Waals' Principle of Corresponding States, the hypothesis that a single equation could describe fluid behavior in which material-dependent parameters like a, b and B were not used, instead being expressed in terms of reduced thermodynamic parameters. Of considerable historical importance, this analysis was used to help guide early scientists into cryogenic work and represents a universal equation for substances that do not possess high directionality (e.g. polarity).
Question 09 in hw.1 has a typo: Instead of alpha and beta (the symbols from our previous textbook) that should read beta and kappa.
We will spend perhaps 15 minutes finishing up Chapter 7 on Wednesday [delaying the discussion of fugacity until later] before hopping back to Chapter 2 and Thermodynamics proper.