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.
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