首页|Mathematical analysis of the van der Waals equation
Mathematical analysis of the van der Waals equation
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NSTL
Elsevier
The parametric cubic van der Waals polynomial pV(3)-(RT+bp)V-2+aV-ab is analysed mathematically and some new generic features (theoretically, for any substance) are revealed: the temperature range for applicability of the van der Waals equation, T > a/(4Rb), and the isolation intervals, at any given temperature between a/(4Rb) and the critical temperature 8a/(27Rb), of the three volumes on the isobar-isotherm: 3b/2 < V-A <= 3b, 2b < V-B <(3+root 5)b, and 3b < V-C < b+RT/p. The unstable states of the van der Waals model have also been generically localized: they lie in an interval within the isolation interval of V-B. In the case of unique intersection point of an isotherm with an isobar, the isolation interval of this unique volume is also determined. A discussion on finding the volumes V-A,V-B,V-C, on the premise of Maxwell's hypothesis, is also presented.
van der Waals equationMaxwell?s hypothesisCubic equationRoot isolation intervalsSTATE
NSTL
Elsevier
