The tie-line rule is a graphical method used in the field of thermodynamics to determine the compositions of two phases that are in equilibrium with each other. This rule is often used in the context of phase diagrams, which are diagrams that show the phases that are present in a material as a function of temperature, pressure, and composition.
In a two-phase region of a phase diagram, such as the liquid-vapor region of a water phase diagram, a tie-line is a horizontal line that connects the compositions of the two phases in equilibrium. The tie-line rule states that the ratio of the amounts of the two phases in equilibrium at any point along the tie-line is constant.
This ratio is given by the lever rule, which states that the length of the tie-line that is intercepted by the composition line of one of the phases is proportional to the fraction of that phase in the mixture. The tie-line rule is useful in determining the compositions of the two phases in equilibrium at a given temperature and pressure, which can be important in understanding the behavior of materials in various applications.
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