Mathematical Analysis of the van der Waals Equation

Emil Prodanov

doi:10.21427/hze3-yd97

Mathematical Analysis of the van der Waals Equation

Emil Prodanov

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The parametric cubic van der Waals polynomial $p V^3 - (R T + b p) V^2 + a V - a b$ 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

Original language	English
Journal	Physica B: Condensed Matter
DOIs	https://doi.org/10.21427/hze3-yd97 https://doi.org/10.1016/j.physb.2022.414077
Publication status	Published - 1 Jan 2022

Keywords

van der Waals equation
temperature range
isolation intervals
unstable states
Maxwell's hypothesis

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10.21427/hze3-yd97Licence: CC BY-NC-ND
10.1016/j.physb.2022.414077Licence: CC BY

Cite this

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title = "Mathematical Analysis of the van der Waals Equation",

abstract = "The parametric cubic van der Waals polynomial $p V^3 - (R T + b p) V^2 + a V - a b$ 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",

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AB - The parametric cubic van der Waals polynomial $p V^3 - (R T + b p) V^2 + a V - a b$ 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

KW - van der Waals equation

KW - temperature range

KW - isolation intervals

KW - unstable states

KW - Maxwell's hypothesis

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M3 - Article

SN - 0921-4526

JO - Physica B: Condensed Matter

JF - Physica B: Condensed Matter

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Mathematical Analysis of the van der Waals Equation

Abstract

Keywords

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