1. Cubic Equation of State van der Waals
David Bilhartz
Erin Lee
Lauren Carter
Jennifer Loving

2. van der Waals Equation of State
parameters a and b are positive constants ideal gas equation is recovered when a and b are 0

3. Cubic Equation of State
Proposed cubic equations of state are all special cases of:
Where van der Waals equation results when η=b, θ=a, κ=λ=0

4. Cubic Equation of State
Generic cubic equation of state results when the following parameters are set:

5. Cubic Equation of State
Parameters b and a(T) from the previous equation are calculated using:
Where Tc is the critical temperature and Pc is the critical pressure and Tr is the reduced pressure
Tc and Pc can be found in App. B

6. Table 3.1: Parameter Assignments for Equations of State

7. Vapor & Vapor-Like Roots of the Generic Cubic Equation of State
The generic cubic equation of state can be rearranged to solve for the largest root: vapor or vapor-like volume:

8. Vapor & Vapor-Like Roots
The following parameters can be substituted into the previous equation and V=ZRT/P and solved for Z:

9. Vapor & Vapor-Like Roots
Parameters β and q can be solved for using the following equations:
Calculating Z is accomplished by iterating starting with the ideal Z=1
Once Z converges, solve for V using V=ZRT/P

10. Liquid & Liquid-Like Roots of the Generic Cubic Equation of State
When iterating with V=b on the right side of the equation a liquid or liquid-like root results when it converges

11. Liquid & Liquid-Like Roots
Parameters β and q can be solved for using the following equations:
Calculating Z is accomplished by iterating starting with Z=β
Once Z converges, solve for V using V=ZRT/P

12. Isotherms as Given by Cubic Equation of State

13. Example 3.9 (using van der Waals)
Given that the vapor pressure of n-butane at 350 K is bar, find the molar volumes of (a) saturated-vapor and (b) saturated-liquid n-butane at these conditions as given by van der Waals equation

14. Solving for parameters:
Tc = K and Pc = bar from App. B

15. (a) saturated-vapor
Iteration
Converges to:

16. (b) saturated-liquid
Iteration
Converges