Simplifying the calculation of residual properties using numerical methods

Abstract

The calculation of thermodynamic properties using Residual properties (Rp) is a key element in Chemical Engineering curricula. Traditionally, the derivation of Rp involves solving analytical expressions through partial differentiation and integration of generalized thermodynamics equations combined with specific equations of state (EoS). This method is mathematically demanding, increasing cognitive load and often limiting classroom discussions to simpler EoS for which analytical solutions are readily available in textbooks. To enhance student engagement and reduce the time spent on complex derivations, we propose a simplified approach that numerically evaluates Rp using standard software tools. This approach not only minimizes the mathematical effort, allowing students to focus on thermodynamic concepts, but also extends the applicability to more complex EoS that are not covered in textbooks. By significantly reducing the instructional time required for Rp calculations, this method fosters critical thinking, promotes autonomy, and can be applied to other fundamental thermodynamics topics that traditionally rely on analytical expressions, such as multicomponent solution models.