Thermodynamic analysis of anomalous region, critical point, and transition from subcritical to supercritical states: Application to van der Waals and five real fluids

Abstract

All fluids exhibit large property-variations near the critical point in a region identified as the anomalous state. The anomaly starts in the liquid and extends well into the supercritical state, which can be identified thermodynamically using the Gibbs free energy (g). The specific heat, isobaric expansion, and isothermal compressibility parameters governing the transitions are: (cp/T), (vβ), and (vκ), rather cp, β, and κ. They are essentially the second-order derivatives of g and have two extrema (minimum, maximum); only maxima reported ever. When applied to the van der Waals fluid, these extrema exhibit closed loops on the phase-diagram to satisfy d3g = 0 and map the anomalous region. The predicted liquid-like to gas-like transitions are related to the ridges reported earlier, and the Widom delta falls between these loops. Evidently, in the anomalous region, both the liquid and the supercritical fluid need to be treated differently. Beyond the anomalous states, the supercritical fluids show monotonic, gradual changes in their properties. The analysis for argon, methane, nitrogen, carbon dioxide, and water validates the thermodynamic model, supports the stated observations, and identifies their delimiting pressures and temperatures for the anomalous states. It also demonstrates the applicability of the law of corresponding states. Notably, the critical point is a state where d3g = 0, the anomaly in the fluid's properties/behavior is maximal, and the governing parameters approach infinity. Also the following are presented: (a) the trajectory of the liquid–vapor line toward the melt-solid boundary and (b) a modified phase diagram (for water) exhibiting the anomalous region.