Chapter 5.3, Problem 50P

The compression factor of a fluid is defined as the ratio $PV/NkT$; the deviation of this quantity from 1 is a measure of how much the fluid differs from an ideal gas. Calculate the compression factor of a van der Waals fluid at the Critical point, and note that the value is independent of a and b. (Experimental values of compression factors at the critical point are generally lower than the van der Waals prediction, for instance, 0.227 for ${\text{H}}_2\text{O}$, 0.274 for ${\text{CO}}_{\text{2}}$, 0.305 for He.)