In lever rule, as the overall composition C0 moves toward Cα within a two-phase region, wα decreases toward which of the following?

• A. wα increases toward 1.
• B. wα decreases toward 0.
• C. wα remains constant.
• D. wα becomes negative.

Answer: (C)

In a binary alloy with a two-phase region, the lever rule tells us how the phase fractions relate to the overall composition. The weight fraction of α is wα = (Cβ − C0) / (Cβ − Cα). As the overall composition C0 moves toward Cα, the numerator (Cβ − C0) increases because you’re subtracting a smaller C0 from Cβ, while the denominator (Cβ − Cα) stays fixed. Therefore, wα rises, approaching 1. This makes sense physically: when the overall composition is close to α, a larger portion of the material must be in the α phase to maintain the same temperature tie-line. The other possibilities don’t fit: moving toward β would push wα toward 0, keeping it constant would require C0 not to change, and a negative wα isn’t possible within the two-phase region.