text: Real gases can be characterized by their difference from ideal. This is done by writing the mechanical equation of state in the form  where , called the compressibility factor, is usually expressed either as a function of pressure and temperature, or density and temperature, and in each case in the limit  or , , the ideal gas value.
  In the second case . Thus for a van der Waals fluid the compressibility factor is , or in terms of reduced variables
  where . At the critical point, , .
  In the limit ,  (for finite ); the fluid behaves like an ideal gas, a point noted several times earlier. Note additionally that the derivative  for , and when  this is . The slope is positive or negative depending on whether  is greater than or less than , and becomes infinitely large negative as  approaches .
  Figure 6 shows a plot of various isotherms of  vs . Also shown are the spinodal and coexistence curves described previously. The subcritical isotherm consists of stable, metastable, and unstable segments, and are identified the same as they were in Fig. 1. Also included are the zero initial slope isotherm and the one corresponding to infinite temperature.
  By plotting  vs  using  as a parameter, one obtains the generalized compressibility chart for a vdW gas, which is shown in Fig. 7. Like all other vdW properties, this is not quantitatively correct for most gases but it has the correct qualitative features as can be seen by comparison with this figure which was produced from data using real gases. The two graphs are similar, including the caustic generated by the crossing isotherms; they are qualitatively very much alike.