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.
The given van der Waals equations(s):
The Attempt at a Solution
I first determined the constants a and b to be:
And since the critical volume Vc=3b:
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):
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.