The van der Waals equation for 1 mole of gas is given by (p+av-2)(v - b) = RT. In general, curves of p versus vforvarious values of T exhibit a maximum and a minimum at thetwopoints where (δp/δv)T = 0. The maximum and minumumcoalesceinto a single point on that curvewhere(δ2p/δv2)T = 0 inaddition to(δp/δv)T = 0. This point is calledthe \"critical point\"of the substance and its temperature,pressure, and molar volume aredenoted by Tc,pc, and vc,respectively.
   (a) Express a and b in terms of Tcandvc.
   (b) Express pc in termsofTc and vc.
   (c) Write the van der Waals equation in termsofthe reduced dimensionless variables T' ≡ T/Tc , v'≡v/vc , p' ≡ p/pc
This form should involve neither a nor b.
