# 9: Cubic EOS and Their Behavior I

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Learning Objectives

• Module Goal: To demonstrate thermodynamic quantification using modern cubic EOS.
• Module Objective: To introduce you to the basis premises of cubic EOS and their behavior

• 9.1: Introduction
In general, any equation of state that is cubic in volume (and Z) and explicit in pressure is regarded as a cubic equation of state. vdW EOS is a cubic EOS, and all the transformations and modifications that it has undergone during the more than one hundred years since its publication are also cubic EOS; or better, they are in-the-van-der-Waals-spirit EOS or of-the-van-der-Waals-family EOS.
• 9.2: The Cubic Behavior
• 9.3: Implications of S-shaped curve (Sub-critical Conditions)
Can we really model the discontinuity? Not really, but we can get around it. van der Waals provided a possible solution in his dissertation on the “continuity of vapor and liquid.” Even though neither cubic equations nor any other continuous mathematical function is able to follow the discontinuity, what they can do is good enough for engineering purposes. The “cubic behavior” can reasonably match the liquid and vapor branches for the real, experimental isotherms.
• 9.4: Action Item

9: Cubic EOS and Their Behavior I 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 conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.