Reclaiming the Central Role of Equations of State in Thermodynamics

Abstract

An equation of state expresses the characteristic relationship between state variables for a particular thermodynamic system. Knowledge of the equations of state for a given system can be used to derive all its thermodynamic properties. Despite their central role in thermodynamics, the topic of equations of state is poorly addressed in traditional physical chemistry textbooks and in most cases is typically associated with the properties of gases. This approach minimizes the importance of the subject and hinders students from building a comprehensive understanding of classical thermodynamics. The central goal of this article is to present an alternative approach to the derivation, analysis, and discussion of equations of state in physical chemistry courses. The strategy relies on the use of response coefficients (partial derivatives involving the system's thermodynamic variables) and the systematic manipulation of simple thermodynamic relationships. The methodology can be used to derive the equation of state of a wide variety of systems and to analyze the similarities and differences in their thermodynamic behavior.