Discovering Pressure–Volume–Temperature Phase Relationships with 3D Models

A central goal of thermodynamics is to describe the interdependence of the pressure, molar volume, and temperature of a system in order to identify which phase is most stable and when phase transitions occur. For a pure substance in a single phase, the behavior of any intensive property is a function of the other two variables. Textbooks, however, are limited to two-dimensional graphs depicting how a property varies as a function of only one other variable (e.g., P vs T), which makes it difficult for students to appreciate the three-dimensional nature of equations of state and phase equilibria as well as the connections between the various 2D representations. We have developed 3D models that simultaneously depict the interdependence of the P, Vm, and T for an ideal gas as well as for a real gas (carbon dioxide). These models are the basis for group exercises in which students discover the broader connections between these properties and learn how two-dimensional phase diagrams and condensation graphs represent different perspectives on the same underlying phase equilibria.