The binary phase diagram of metals P and Q is shown in the figure. An alloy X containing60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid andliquid (in weight percent) at 1250 °C, respectively, will be

The correct answer is 22.2% and 77.8%.

Step-by-Step Explanation:

1. Extracting data from the phase diagram:
By analyzing the provided binary phase diagram of metals P and Q:

• The horizontal axis represents the Concentration of Q (in weight %).
• The vertical axis represents the Temperature (°C).
• The alloy line X indicates an overall composition containing 60% P and 40% Q (by weight). Therefore, the overall concentration of Q is:
  $C_0=40\%$
• At the temperature of 1250 °C, we draw a horizontal tie line to find the compositions of the coexisting liquid and solid phases:
  • The intersection of the tie line with the Liquidus curve gives the concentration of Q in the liquid phase:
    $C_L=32\%$
  • The intersection of the tie line with the Solidus curve gives the concentration of Q in the solid phase:
    $C_S=68\%$

2. Applying the Lever Rule:
To determine the relative weight fractions of the solid and liquid phases, we use the lever rule.

Fraction of Solid:
The fraction of the solid phase is given by the ratio of the segment opposite the solid side to the total length of the tie line:

$f_{\text{solid}}=\frac{C_0-C_L}{C_S-C_L}$

$f_{\text{solid}}=\frac{40-32}{68-32}=\frac{8}{36}=\frac{2}{9}\approx 0.2222\text{or}22.2\%$

Fraction of Liquid:
Similarly, the fraction of the liquid phase is given by:

$f_{\text{liquid}}=\frac{C_S-C_0}{C_S-C_L}$

$f_{\text{liquid}}=\frac{68-40}{68-32}=\frac{28}{36}=\frac{7}{9}\approx 0.7778\text{or}77.8\%$

Thus, the weight percentages of solid and liquid at 1250 °C are 22.2% and 77.8%, respectively.