Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components A and B is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800 ºC, then the solidification range is

The correct option is 150 ºC.

Analysis of the Phase Diagram:
Based on the provided phase diagram, we can observe the following critical features and data points:

• The vertical y-axis represents Temperature (ºC), and the horizontal x-axis represents the Composition (weight % of B in A).
• The text legend indicates that:
  • L is the liquid phase.
  • α is the A-rich solid phase.
  • β is the B-rich solid phase.
• For pure component A (composition = 0 wt% of B), the melting point (liquidus/solidus limit) is 700 ºC.
• The Eutectic point is clearly labeled with an arrow, located at a composition of 30 wt% of B and a eutectic temperature of 400 ºC.
• The maximum solid solubility limit of B in A (the boundary of the α phase region at the eutectic temperature) is at 10 wt% of B.
• All phase boundary lines, including the liquidus and solidus lines, are straight lines.

Step-by-step Calculation:
For the binary alloy with 15 wt% of B, we need to find the solidification range, which is the temperature interval between the start of solidification (liquidus temperature, $T_{\text{liquidus}}$) and the end of solidification (solidus temperature, $T_{\text{solidus}}$).

1. Finding the Liquidus Temperature ($T_{\text{liquidus}}$):
The liquidus line for compositions between 0 wt% of B and 30 wt% of B is a straight line connecting the melting point of pure A (0 wt% B, 700 ºC) and the eutectic point (30 wt% B, 400 ºC).
Using linear interpolation, the equation for the liquidus line is:

$$T_{\text{liquidus}}=700-\left(\frac{700-400}{30-0}\right)\times \text{Composition}$$

Substituting the alloy composition of 15 wt% of B:

$$T_{\text{liquidus}}=700-\left(\frac{300}{30}\right)\times 15$$

$$T_{\text{liquidus}}=700-10\times 15=550\text{ ℃}$$

2. Finding the Solidus Temperature ($T_{\text{solidus}}$):
For a composition of 15 wt% of B (which lies between the maximum solid solubility limit of 10 wt% and the eutectic composition of 30 wt%), the alloy enters a two-phase region during cooling where primary α solidifies first. Solidification is completed when the remaining liquid reaches the eutectic composition and solidifies completely at the eutectic isotherm. Therefore, the solidus temperature is equal to the eutectic temperature:

$$T_{\text{solidus}}=400\text{ ℃}$$

3. Calculating the Solidification Range:
The solidification range is the difference between the liquidus and solidus temperatures:

$$\text{Solidification Range}=T_{\text{liquidus}}-T_{\text{solidus}}$$

$$\text{Solidification Range}=550\text{ ℃}-400\text{ ℃}=150\text{ ℃}$$

Thus, the solidification range of this binary alloy is 150 ºC.