Question

The following diagram represents a binary phase diagram for the system A–B at atmospheric pressure. If ‘X’ is the initial composition of melt, then the amount of melt that converts to solid when the magma cools from 1400 °C to 1250 °C is ________ %. (Round off to two decimal places.) 

Hint:

Use the lever rule: \(\text{Fraction solid} = \frac{\text{liquidus} - X}{\text{liquidus} - \text{solidus}}\).

Answer 1

Correct Answer: 56.4

Step 1: Understanding the diagram.
At 1400 °C, composition ‘X’ lies completely in the liquid field. At 1250 °C, the composition enters the A+B+Melt region. The lever rule applies between the solidus and liquidus compositions.
Step 2: From diagram (approximate values).
At 1250 °C, the liquid composition ≈ 40 wt% B, and solid composition ≈ 10 wt% B. Initial melt (X) = 25 wt% B.
Step 3: Lever rule.
\[ \text{Fraction of liquid remaining} = \frac{X - \text{solidus}}{\text{liquidus} - \text{solidus}} = \frac{25 - 10}{40 - 10} = 0.5 \] \[ \text{Fraction crystallized} = 1 - 0.5 = 0.5 = 50%. \] Step 4: Conclusion.
Thus, 50% of melt converts to solid between 1400 °C and 1250 °C.