Identification of the phase of a substance from the derivatives of pressure, volume and temperature, without prior knowledge of saturation properties: Extension to solid phase

Venkatarathnam and Oellrich [1] proposed a phase identification parameter (ΠΠ) a few years ago to identify the phase of a fluid (vapour or liquid) through the use of the derivatives of pressure, volume and temperature. Currently, this parameter has been found to be the most sensitive parameter for fitting complex equations of state based on the Helmholtz free energy formulation [2,3]. In this paper, it is shown that the phase identification parameter can also be used to identify a solid from a vapour phase, and the mixed (second) derivative of pressure with respect to temperature and volume (∂2p/∂v∂T), which is already a part of the definition of ΠΠ, can be used to distinguish between the solid phase and the liquid/vapour phases. The proposed procedure has applications in fitting equations of state as well as process calculations involving solid phases.