# 10: Cubic EOS and Their Behavior II

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Learning Objectives

• Module Goal: To demonstrate thermodynamic quantification using modern cubic EOS.
• Module Objective: To highlight the most often used cubic EOS

• 10.1: Multiple Roots and Cubic Behavior
It comes as no surprise that cubic equations of state yield three different roots for volume and compressibility factor. This is simply because they are algebraic equations, and any nth order algebraic equation will always yield “n” roots. However, those “n” roots are not required to be distinct, and that is not all: they are not required be real numbers, either.
• 10.2: Modern Cubic EOS
First, we can say that the vdW cubic behavior is qualitatively reasonable; and second, we can say that it is capable of describing the continuity between liquid and vapor. Nevertheless, vdW cubic EOS has been proven not to bequantitatively suitable for most engineering purposes. Certainly, it yields unacceptable errors for the quantitative prediction of densities and any other related thermodynamic property.
• 10.3: Redlich-Kwong EOS (1949)
Redlich and Kwong revised the van der Waals EOS by making the attraction parameter “a” of van der Waals a function of temperature.
• 10.4: Soave-Redlich-Kwong EOS (1972)
In 1972, Soave proposed an important modification to the RK EOS — or shall we say, a modification to vdW EOS. Between the time of vdW EOS and Redlich-Kwong’s, a new concept for fluid characterization was being discussed. Pitzer had introduced the concept of acentric factor in 1955.
• 10.5: Action Item

This page titled 10: Cubic EOS and Their Behavior II is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michael Adewumi (John A. Dutton: e-Education Institute) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.