The "root" Function in MathCAD: the van der Waals Equation

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For an industrial process, it is necessary to introduce 1400 mols of 1,3,5-trihydroxybenzene at a temperature of 560 K and pressure of 150 kPa in a steel cylinder. Calculate the volume of the cylinder using the van der Waals equation, if the a and b constants are known.
The van der Waals formula is a third degree equation for the volume: Higher degree equations are handled by Mathcad with the root function. The syntax is: root(f(x),x). It returns the value of x that makes the function f equal to zero.

Since an iterative algorithm is used for the calculation, an initial guess value is necessary. It must be borne in mind that for a third degree equation there are three solutions and which root is found depends on the initialization value. Of the three roots, only one will have physical meaning; in other words a negative or a complex value for the volume, although mathematically correct, has no physical meaning.

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