AUTHOR=Yu J. S. , Du W. K. , Liu Q. H. TITLE=Geometrical Aspect of Compressibility Critical Exponent JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.850296 DOI=10.3389/fphy.2022.850296 ISSN=2296-424X ABSTRACT=

Critical exponent γ ⪰ 1.1 characterizes the behavior of the mechanical compressibility of a real fluid when the temperature approaches the critical one. It results in zero Gaussian curvature of the local shape of the critical point on the thermodynamic equation of state surface, which imposes a new constraint upon the construction of the potential equation of state of the real fluid from the empirical data. All known empirical equations of the state suffer from a weakness that the Gaussian curvature of the critical point is negative definite instead of zero.