The van der Waals equation provides a more realistic model for a real gas. (P+ v2a )(v−b)=RT (i) Sketch a set of representative isotherms on a P−V diaaram showing the behaviour of a van der Waals fluid. (ii) On your P-V diagram mark regions where the fluid would be in a gas phase, a liquid phase and the co-existence of both phases. (iii) Mark the critical point on your P-V diagram. (iv) Describe the properties of the fluid in the neighbourhood of the critical point.