The calculation of volume roots from cubic equation of state, for given temperature and pressure, is still an important operation both in industry and academic field. It is proposed the use of Ferrari's formula to calculate the pressure range containing three real positive roots (for pressure and temperature below the critical). In addition, a modification in the Cardano-Tartáglia's formula is proposed to provide the roots in the ascending order. For low values of reduced temperatures, it is proposed a simple and efficient approximation method to avoid the round-off errors presented by Cardano-Tartáglia's formula. It is also proposed a method for calculating the saturation pressure from cubic equations of state. Examples of the methods proposed are presented for the Van der Waals, Soave-Redlich-Kwong e Peng-Robinson equations of state in order to show the quality and reliability of the methods proposed.

中文翻译：

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三次状态方程的体积根解析计算分析

对于给定的温度和压力，从三次状态方程计算体积根仍然是工业和学术领域的重要操作。建议使用法拉利公式计算包含三个实数正根的压力范围（对于低于临界值的压力和温度）。此外，提议修改 Cardano-Tartáglia 公式以提供升序的根。对于降低温度的低值，提出了一种简单有效的近似方法，以避免卡尔达诺-塔塔格利亚公式提出的舍入误差。还提出了一种从三次状态方程计算饱和压力的方法。提出的方法的例子是为范德瓦尔斯提出的，