Cubic Equation of State van der Waals

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Presentation transcript:

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

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

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

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

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

Table 3.1: Parameter Assignments for Equations of State

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:

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

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

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

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

Isotherms as Given by Cubic Equation of State

Example 3.9 (using van der Waals) Given that the vapor pressure of n-butane at 350 K is 9.4573 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

Solving for parameters: Tc = 425.1 K and Pc = 37.96 bar from App. B

(a) saturated-vapor Iteration Converges to:

(b) saturated-liquid Iteration Converges