[Byrne]

Is there any sort of demonstration one could perform to illustrate the equation's usefulness?  If not, is there a demonstration one could do to determine the critical temperature/pressure of a gas that could be performed in university chemistry lab?

Thanks in advance

[Donaldson Tan]

the saturated pressure/temperature and critical pressure/temperature of many fluids are tabulated. these data are readily available, from any reference books. Try looking for this book for the data you need:

THERMOPHYSICAL PROPERTIES OF FLUIDS
An Introduction to Their Prediction
by Marc J Assael (Aristotle University, Greece),
J P Martin Trusler & Thomas F Tsolakis (Imperial College, UK)

It also contain useful information for your research on VDW equation, and many other equations of state.  This book is concerned with the prediction of thermodynamic and transport properties of gases and liquids. The prediction of such properties is essential for the solution of many problems encountered in chemical and process engineering as well as in other areas of science and technology. The book aims to present the best of those modern methods which are capable of practical application. It begins with basic scientific principles and formal results which are subsequently developed into practical methods of prediction.