Question textConsider 5[math]{5} kg of austenite containing 0.45[math]{0.45} wt% C, cooled to below 727[math]{727} °C How many kilograms of total ferrite form? [input] Your last answer was interpreted as follows: 4.68[math] 4.68

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BlackTom AI · Accepted Answer

The problem provides: start with 5.0 kg of austenite containing 0.45 wt% C, cooled below 727°C. At 727°C, austenite (γ) transforms into a mixture of ferrite (α) and cementite (Fe3C) in the two-phase region α + Fe3C (pearlite-forming reaction). To find the amount of ferrite formed, use the lever rule for the γ → α + Fe3C region at the eutectoid temperature where the overall carbon content must equal the average of the two end phases.

Known composition endpoints at 727°C for the α + Fe3C region:
- Carbon content in ferrite, Cα ≈ 0.02 wt% C (almost pure iron with trace C)
- Carbon content in cementite, CFe3C ≈ 6.67 wt% C

Overall carbon content of the original austenite, C0 = 0.45 wt% C.

Apply the lever rule for the fraction of ferrite (fα) in the α + Fe3C mixture:
- fα = (CFe3C − C0) / (CFe3C − Cα)
- fFe3C (fraction of cementite) = (C0 − Cα) / (CFe3C − Cα)

Plugging in numbers (Cα ≈ 0.02, CFe3C ≈ 6.67, C0 = 0.45):
- Denominator: CFe3C − Cα ≈ 6.67 − 0.02 = 6.65
- Numerator for ferrite: CFe3C − C0 ≈ 6.67 − 0.45 = 6.22
- ferrite fraction fα ≈ 6.22 / 6.65 ≈ 0.935 (93.5%)
- cementite fraction fFe3C ≈ 1 − fα ≈ 0.065 (6.5%)

Now calculate masses for the 5.0 kg of steel:
- Mass of ferrite formed = fα × total mass = 0.935 × 5.0 kg ≈ 4.68 kg
- Mass of cementite formed = fFe3C × total mass ≈ 0.065 × 5.0 kg ≈ 0.32 kg

Thus, the total ferrite formed from the 5.0 kg of austenite is about 4.68 kg.

Note: If alternative answer options were provided, you would compare the calculated ferrite fraction to each option, using the same lever-rule logic and the same end-point compositions (Cα and CFe3C) at 727°C. Any deviation in Cα or CFe3C values would slightly change the fractions, but with typical Fe–C values near 0.02 wt% and 6.67 wt% respectively, the ferrite fraction remains in the ≈0.93 range and the ferrite mass near 4.7 kg for 5 kg of steel.

Question textConsider 5[math]{5} kg of austenite containing 0.45[math]{0.45} wt% C, cooled to below 727[math]{727} °C How many kilograms of total ferrite form? [input] Your last answer was interpreted as follows: 4.68[math] 4.68单项选择题

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