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 answer is 150 ºC.

Analysis of the Phase Diagram:
By inspecting the provided phase diagram, we can observe the following critical labels and data points:
1. The y-axis represents the Temperature (ºC), with marked values at 0, 400, 700, and 800 ºC.
2. The x-axis represents the Composition (weight % of B in A), showing key values at 0, 10, 15, and 30 wt% of B.
3. The phases are labeled as:
- L: liquid phase
- α: A-rich solid phase
- β: B-rich solid phase
4. The Eutectic point is located at a composition of 30 wt% B and a eutectic temperature of 400 ºC.
5. The solid solubility limit of B in A at the eutectic temperature is 10 wt% B.

Step 1: Finding the Liquidus Temperature (T_L) for 15 wt% B
Since all lines in the phase diagram are straight lines, the liquidus line connecting pure component A at (0 wt% B, 700 ºC) to the Eutectic point at (30 wt% B, 400 ºC) is linear.
We can write the equation for this straight line using the two coordinate points (0, 700) and (30, 400):

$$T_L=700-\left(\frac{700-400}{30-0}\right)\times w$$

where w is the weight % of B. Substituting w = 15 wt%:

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

$$T_L=700-10\times 15=550°C$$

Thus, the solidification process begins when the alloy is cooled to the liquidus temperature, T_L = 550 ºC.

Step 2: Finding the Solidus/End of Solidification Temperature (T_S)
For an alloy with 15 wt% B (which lies in the composition range of 10 wt% to 30 wt% B), cooling past the liquidus line leads to the precipitation of primary α phase. As cooling continues, the remaining liquid is enriched in B until it reaches the eutectic composition of 30 wt% B at the eutectic temperature of 400 ºC.
At 400 ºC, the remaining liquid undergoes the eutectic reaction and solidifies completely at a constant temperature.
Therefore, the solidification is completed at the eutectic temperature:

$$T_S=400°C$$

Step 3: Calculating the Solidification Range
The solidification range is the difference between the temperature at which solidification starts (T_L) and the temperature at which it ends (T_S):

$$\text{Solidification Range}=T_L-T_S$$

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

Hence, the solidification range is 150 ºC.