text: The equation has been, and remains very useful because:
  * Its coefficient of thermal expansion,  has a simple analytic expression [this is also true of its isothermal compressibility, ] 
  * it explains the existence of the critical point and the liquid–vapor phase transition including the observed metastable states 
  * it  establishes the law of corresponding states 
  * its specific heat at constant volume, , can be shown to be a function of  only, and its thermodynamic properties, internal energy , entropy , as well as the specific heat at constant pressure  have simple analytic expressions [this is also true of enthalpy , Helmholtz free energy , and Gibbs free energy ]
  * its Joule–Thomson coefficient and associated inversion curve, which were instrumental in the commercial liquefaction of gases have simple analytic expressions.
  The equation also plays an important role in the modern theory of phase transitions. It depicts the liquid metals, Mercury and Cesium, quantitatively, and describes most real fluids qualitatively. Consequently it can be regarded as one member of a family of equations of state, that depend on a molecular parameter such as the critical compressibility factor, , or the Pitzer (acentric) factor, , where  is a dimensionless saturation pressure, and log is the logarithm base 10.
  All this makes it a worthwhile pedagogical tool for physics, chemistry, and engineering lecturers, in addition to being a useful mathematical model which can aid student understanding.