Print version ISSN 0100-4042
LEMES, Nelson H. T.; OLIVEIRA, Jessé M. and BRAGA, João P.. Volume calculation in van der Waals equation by the cardano method. Quím. Nova [online]. 2010, vol.33, n.6, pp. 1325-1329. ISSN 0100-4042. http://dx.doi.org/10.1590/S0100-40422010000600020.
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.
Keywords : van der Waals; Cardano; thermodynamic.