Question

The following figure shows an isobaric temperature-composition (T-X) phase diagram for the binary system A-B. If 'P' is the initial composition of liquid, the amount of liquid that remains in the system when the liquid cools from 1800 °C (point L₁) to 1500 °C (point L₂) is _____%. (In integer)

Answer 1

Correct Answer: 20

Idea (lever rule)
When a liquid of overall composition \(x_P\) is cooled into the two–phase (L + S) region, the fraction of the sample that is liquid at that temperature is given by the lever rule (reading compositions from the tie–line): \[ \text{fraction liquid} = \frac{x_P - x_S}{x_L - x_S}, \] where \(x_L\) and \(x_S\) are the liquidus and solidus compositions at the temperature of interest (here at 1500 °C). 
 
Read the tie–line at 1500 °C from the diagram
(Values read from the provided T–X diagram:) \[ x_L = 0.90,\qquad x_S = 0.50,\qquad x_P = 0.58. \] Apply the lever rule: \[ \text{fraction liquid} = \frac{0.58 - 0.50}{0.90 - 0.50} = \frac{0.08}{0.40} = 0.20. \] Convert to percent: \[ 0.20 \times 100\% = 20\%. \] Answer: \(\boxed{20\%}\)