Master the Lever Rule: Tips and Tricks for Understanding this Important Concept

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The discussion focuses on the application of the lever rule in phase diagrams, specifically regarding a eutectic composition of 50% To and 50% Lb. When cooling this homogeneous liquid to room temperature, it separates into two distinct phases: alpha and beta. The lever rule is used to determine the relative concentrations of these phases. For the beta phase, the concentration is calculated using the formula: (Lb(eutectic) - Lb(alpha)) / (Lb(beta) - Lb(alpha)). Conversely, the alpha phase concentration is determined by: (Lb(beta) - Lb(eutectic)) / (Lb(beta) - Lb(alpha)). This method illustrates that the relative concentration of each phase can be understood through the length ratios of specific lines on the phase diagram, highlighting the relationship between the phases at the eutectic point.
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Could someone please help me on this question. I do not really understand
how to use the lever rule.
Attactched is an example..
Thanks very much
 

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Consider the homogeneous liquid at the eutectic composition (50% To an 50% Lb). When you cool it to room temperature, you get two distinct phases, alpha and beta.

By the lever rule, the relative concentration f alpha and beta phases is calculated as follows:

1. beta phase: ([Lb](eutectic)-[Lb](alpha))/([Lb](beta)-[Lb](alpha))
2. alpha phase: ([Lb](beta)-[Lb](eutectic))/([Lb](beta)-[Lb](alpha))

In other words the relative concentration of alpha phase is the length ratio of the eutectic-beta and alpha-beta lines; for beta phase, that is the length ratio of alpha-eutectic/alpha-beta lines.
 

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