两组分理想液体混合物的温度组成曲线单调性的证明

Proof of Monotonicity of Boiling Point–Composition Curve for Ideal Liquid Mixture with Two Components

蒸馏是分离液体混合物的典型单元操作,气液平衡相图的温度组成曲线对蒸馏操作具有重要指导意义。本文以两组分理想液体混合物为研究对象,证明了无论液体饱和蒸气压是符合克劳修斯-克拉珀龙方程,还是符合安托因方程,两组分理想液体混合物的温度组成曲线(T–x或者T–y)都是严格的单调曲线。

Distillation is a typical unit operation for separating liquid mixtures.The temperature–composition curve in the gas–liquid equilibrium phase diagram is important for guiding distillation operations.An ideal liquid mixture with two components was utilized as the study system in this work.We proved that the temperature–composition curve(T–x or T–y)of ideal liquid mixtures with two components is strictly monotonic,regardless of whether the saturated vapor pressure of liquid conforms to the Clausius-Clapeyron equation or Antoine equation.This means that the bubble point temperature and dew point temperature increase monotonously with the increase of lowly volatile substance content.