1. The problem statement, all variables and given/known data Calculate the molar volume using the van der Waals equation of a gas at P=3000psia, T=60F. The critical pressure and temperature, Pc and Tc, are Pc=408psia, Tc=504F. 2. Relevant equations The given van der Waals equations(s): (P+a/Vm^2)(Vm-b)=RT ----(1) Vm^3-Vm^2(b+RT/P)+Vm(a/P)-(ab/P) ----(2) a=(27/64)R^2Tc^2/Pc^2 ----(3) b=(1/8)RTc^2/8Pc^2 ----(4) 3. The attempt at a solution I first determined the constants a and b to be: a=110600psia(ft^3/lb-mol)^2 b=3.168ft^3/lb-mol And since the critical volume Vc=3b: Vc=3(3.168)=9.504ft^3/lb-mol I then basically simplified the cubic equation of state as much as I could and came up with this (leaving the units out for the moment): Vm^3-Vm^2(9.504)+Vm(270.978)-(858.458)=0 Now, I don't know how to solve for the roots of this particular cubic equation. I tried factoring out the term Vm, leaving me with a root equal to zero and a quadratic polynomial. I tried solving for the roots of the quadratic polynomial using the quadratic formula but calculated complex roots which are incorrect, I believe. Does anyone know of a practical method for calculating the molar volume of a real gas using the van der Waals equation of state? Thanks for taking the time to read this.