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SOLVED: Calculus can be used to derive a relation between the critical constants and the van der Waals parameters of a gas. The critical point of a van der Waals gas occurs where the isotherm has a flat inflection, which is where dp/dVm = 0 (zero slope) and d2p/dVm2 = 0 (zero curvature). (a) Derive expressions for these first and second derivatives by differentiating the van der Waals equation of state. Hence find expressions for the critical constants in terms of the van der Waals parameters. (
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