大学化学

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相平衡中热力学量之间关系的数形理解

马静雯, 刘兴满, 梁斌, 杨锐, 彭娟, 宋伟明   

  1. 宁夏大学化学化工学院, 宁夏 银川, 750021
  • 收稿日期:2026-01-10 录用日期:2026-02-26
  • 通讯作者: 刘兴满, 宋伟明 E-mail:liuxm2020@nxu.edu.cn;songwm@nxu.edu.cn Xingman Liu, Weiming Song
  • 基金资助:
    宁夏大学2025年校级教学改革项目；宁夏回族自治区级本科教育教学改革与实践项目“化学基础拔尖人才培养探索与实践”

Integrating algebraic and geometric views of thermodynamic relationships in phase equilibrium

Jingwen Ma, Xingman Liu, Bin Liang, Rui Yang, Juan Peng, Weiming Song   

  1. School of Chemistry and Chemical Engineering, Ningxia University, Yinchuan 750021, Ningxia Hui Autonomous Region, China
  • Received:2026-01-10 Accepted:2026-02-26
  • Contact: Xingman Liu, Weiming Song E-mail:liuxm2020@nxu.edu.cn;songwm@nxu.edu.cn

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摘要： 在物理化学相平衡教学中，Gibbs相律的讲授常倚重相图的直观分析，缺乏与热力学基本原理及先修Raoult定律等经验定律的融合，从而影响学生对多组分相平衡动态性与系统性的深入把握。本文以相律中自由度f/f * = 1作为教学切入点，采用过程导向的教学思路，系统整合单组分与二组分体系相图中两相平衡区的特征分析、Clapeyron方程与Raoult定律的理论表达。通过构建约束方程并融合相图解析，揭示“独立变量”的物理意义，深化对两相平衡体系中热力学变量间内在约束关系的理解。该教学策略以直观经验规律为先导，借助数形结合的方式理解相图形态与热力学约束，不仅增强了知识体系的内在连贯性与逻辑衔接，更有助于学生深入理解相律的科学内涵，提升其知识迁移与综合应用能力。

关键词: 热力学, 相律, 自由度, 相平衡, 数形结合

Abstract: In the teaching of phase equilibrium in physical chemistry, the presentation of Gibbs’ phase rule often emphasizes intuitive phase diagram analysis while neglecting integration with fundamental thermodynamic principles and prerequisite empirical laws like Raoult’s law. This oversight limits students’ comprehensive understanding of the dynamic and systematic aspects of multicomponent phase equilibria. Using the condition of freedom f (or f *) = 1 in the phase rule as a pedagogical starting point, this study employs a process-oriented teaching approach to systematically integrate characteristic analyses of two-phase regions in single-component and binary system phase diagrams with theoretical formulations including the Clapeyron equation and Raoult’s law. By developing constraint equations and incorporating phase diagram interpretation, we elucidate the physical significance of “independent variables”, thereby deepening the understanding of intrinsic thermodynamic relationships in two-phase equilibrium systems. This teaching strategy, guided by intuitive empirical rules and combining numerical and graphical methods to analyze phase diagram configurations and thermodynamic constraints, not only enhances the internal coherence and logical progression of the knowledge system but also improves students’ ability to comprehend the scientific essence of the phase rule and apply this knowledge through transfer learning.

Key words: Thermodynamics, Phase ruleDegree of freedom, Phase equilibrium, Numerical-graphical integration