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arXiv · 2101.10618

Local shape of the vapor-liquid critical point on the thermodynamic surface and the van der Waals equation of state

J. S. Yu·X. Zhou·J. F. Chen·W. K. Du·X. Wang·Q. H. Liu
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Abstract

Differential geometry is powerful tool to analyze the vapor-liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point $\left( \partial p/\partial V\right) _{T}=0$ requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume $\left( \partial p/\partial T\right) _{V}=0$. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting two parameters $a$ and $b$ in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

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J. S. Yu, X. Zhou, J. F. Chen, W. K. Du, X. Wang, Q. H. Liu. 2021-05-29. Local shape of the vapor-liquid critical point on the thermodynamic surface and the van der Waals equation of state. https://doi.org/10.3389/fphy.2021.679083

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