Let's analyze the question: **Question:** For an iron-carbon alloy, the fraction of alpha ferrite phase is 0.85. Calculate the composition of the alloy. ### Solution #### Step 1: Use Lever Rule For the iron-carbon phase diagram at eutectoid temperature (~727°C), the two phases are: - Alpha ferrite (α): max solubility at ~0.022 wt% C - Cementite (Fe₃C): composition is 6.7 wt% C - Eutectoid composition: 0.76 wt% C Let \( x \) be the composition (wt% C) of the alloy. Fraction of alpha ferrite (\( W_\alpha \)): \[ W_\alpha = \frac{C_{Fe_3C} - C_0}{C_{Fe_3C} - C_\alpha} \] Given: - \( W_\alpha = 0.85 \) - \( C_{Fe_3C} = 6.7 \) - \( C_\alpha = 0.022 \) - \( C_0 = ? \) (Alloy composition) Plug in the values: \[ 0.85 = \frac{6.7 - C_0}{6.7 - 0.022} \] \[ 0.85 \times (6.7 - 0.022) = 6.7 - C_0 \] \[ 0.85 \times 6.678 = 6.7 - C_0 \] \[ 5.6763 = 6.7 - C_0 \] \[ C_0 = 6.7 - 5.6763 = 1.0237 \approx 1.023 \text{ wt% C} \] ### Final Answer **The composition of the alloy is:** **1.023 wt% C** (Option 1) --- **Correct answer: 1.023 wt% C**