Validity
Above the critical temperature the van der Waals equation is an improvement of the ideal gas law, and for lower temperatures the equation is also qualitatively reasonable for the liquid state and the low-pressure gaseous state. However, the Van der Waals model is not appropriate for rigorous quantitative calculations, remaining useful only for teaching and qualitative purposes.
In the first-order phase transition the range of (P, V, T), where the liquid phase and the gas phase are in equilibrium, it does not exhibit the empirical fact that p is constant as a function of V for a given temperature: although this behavior can be easily inserted into the van der Waals model (see Maxwell's correction below), the result is no longer a simple analytical model, and others (such as those based on the principle of corresponding states) achieve a better fit with roughly the same work.
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