Volume calculation in van der Waals equation by the cardano method

Química Nova

Braga, João P.¹  Universidade Federal de Alfenas, Alfenas, Brasil¹  Lemes, Nelson H. T.¹  Oliveira, Jessé M.¹  Universidade Federal de Minas Gerais, Belo Horizonte, Brasil¹ 

关键词: van der Waals;    Cardano;    thermodynamic.;   

DOI  :  10.1590/S0100-40422010000600020

学科分类：化学（综合）

来源: Sociedade Brasileira de Quimica

【 摘 要 】

Analytical solutions of a cubic equation with real coefficients are established using the Cardano method. The method is first applied to simple third order equation. Calculation of volume in the van der Waals equation of state is afterwards established. These results are exemplified to calculate the volumes below and above critical temperatures. Analytical and numerical values for the compressibility factor are presented as a function of the pressure. As a final example, coexistence volumes in the liquid-vapor equilibrium are calculated. The Cardano approach is very simple to apply, requiring only elementary operations, indicating an attractive method to be used in teaching elementary thermodynamics.

【 授权许可】

Unknown