Lever Rule in Binary Phase Diagrams: Calculating Phase Fractions with Tie Lines

Lever Rule in Binary Phase Diagrams

MIT OpenCourseWare introduces the lever rule in a binary phase diagram with two phases, alpha and beta, separated by a two-phase region. The video shows how the overall composition and temperature determine the phase fractions, and how conservation of mass and component mass balance lead to the lever-rule expressions for the phase fractions along the tie line.

• Phase fractions are derived from mass conservation and tie-line geometry
• F_alpha and F_beta are expressed in terms of x2_alpha, x2_beta, and the overall composition x2
• The tie line length (x2_beta minus x2_alpha) is the denominator in both fractions
• The lever analogy explains why the fulcrum position governs the required amounts of each phase

Introduction

In this MIT OpenCourseWare segment, the lever rule is presented as a tool for analyzing a binary phase diagram with two phases, alpha and beta, separated by a two-phase region. The screen illustrates an overall composition X2 and temperature along an isotherm, with the two phases taking their respective X2 values, X2_alpha and X2_beta.

The lever rule connects the composition of the overall system to the compositions of the coexisting phases by relating phase fractions to distances along a tie line. This turns a mass-balance problem into a simple geometric ratio along the tie line.

"The lever rule uses a tie-line segment to relate overall composition to phase compositions, turning a balance problem into a simple length ratio" - MIT OpenCourseWare