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." ### Step-by-step Solution: #### **1. Lever Rule Application** The lever rule is used to determine the phase fractions in a two-phase region of a phase diagram (like the α + Fe₃C region in the iron-carbon system). The fraction of alpha ferrite (W_α) is: \[ W_\alpha = \frac{C_{\text{Fe}_3\text{C}} - C_0}{C_{\text{Fe}_3\text{C}} - C_\alpha} \] Where: - \(C_0\) = Composition of the alloy (wt% C, unknown) - \(C_{\text{Fe}_3\text{C}}\) = Composition of cementite = 6.7 wt% C - \(C_\alpha\) = Composition of ferrite = 0.022 wt% C (at room temperature, but can use 0.025 wt% C at just below the eutectoid temperature) - \(W_\alpha = 0.85\) #### **2. Substitute Values** \[ 0.85 = \frac{6.7 - C_0}{6.7 - 0.022} \] #### **3. Solve for \(C_0\):** \[ 0.85 \times (6.7 - 0.022) = 6.7 - C_0 \] \[ 0.85 \times 6.678 = 6.7 - C_0 \] \[ 5.6763 = 6.7 - C_0 \] \[ C_0 = 6.7 - 5.6763 \] \[ C_0 = 1.0237 \approx 1.023 \text{ wt% C} \] --- ### **Final Answer** The composition of the alloy is **1.023 wt% C**. So, the correct option is: > **1.023 wt% C**