基于改进二分法的立方型状态方程的求解

Solution for Cubic Equation of State Based on Modified Dichotomy

立方型状态方程是关于摩尔体积的三次方形式的方程,是化工热力学中流体p-V-T关系的数学模型。准确地求取体积是状态方程应用的关键。本文在传统二分法的基础上进行了改进,提出了饱和汽相体积和饱和液相体积有解区间的确定策略,用以求解立方型状态方程。采用PR状态方程实例验证证明,该方法简单易行,可以推广应用于立方形状态方程的求解,促进p-V-T状态方程在教学和工程实践中的应用。

The cubic equation of state is an equation in cubic form about molar volume,which is a mathematical model for the p-V-T relationship of fluids in chemical thermodynamics.The key to the application of equation of state is to calculate the volume accurately.Based on the traditional dichotomy method,a strategy of solution intervals is proposed to solve the cubic equation of state for the molar volume of saturated gas phase or saturated liquid phase.It is proved that the modified dichotomy is simple and feasible to apply to the solution of cubic equation of state through an example of PR equation of state.The modified dichotomy can promote the application of p-V-T equation of state in teaching and engineering practice.