Critical temperatures in the iron–carbon system (eutectoid steel) For a plain carbon steel containing exactly 0.8% carbon (eutectoid composition), how many distinct critical temperatures exist during slow heating or cooling under equilibrium conditions?

Introduction / Context:
Critical points (or critical temperatures) in the iron–carbon diagram mark transformations between phases such as ferrite, austenite, and cementite. Knowing how many critical temperatures a steel has at a given composition helps predict microstructures and heat-treatment behavior. The special case is eutectoid steel at about 0.8% carbon.

Given Data / Assumptions:

• Plain carbon steel with 0.8% C (eutectoid composition).
• Slow, near-equilibrium heating or cooling.
• Standard critical temperatures: lower critical (A1), upper critical for hypoeutectoid (A3), and for hypereutectoid (Acm).

Concept / Approach:
At the eutectoid composition, the upper and lower boundaries of the austenite field meet at a single temperature (approximately 727°C). Thus A3 and Acm coincide with A1. Eutectoid steel transforms between austenite and pearlite entirely at this single temperature under equilibrium cooling or heating, unlike hypo- or hypereutectoid steels which cross two different critical lines (A1 plus A3 or A1 plus Acm).

Step-by-Step Solution:

Verification / Alternative check:
Metallographic observation shows fully pearlitic structure below A1 and fully austenitic above A1 for eutectoid steel; no additional proeutectoid ferrite or cementite forms at another temperature, confirming a single critical point.

Why Other Options Are Wrong:

• No critical point: incorrect; austenite↔pearlite transformation still occurs.
• Two or three points: true for non-eutectoid compositions, not for eutectoid.
• Any number: physically meaningless in this context.

Common Pitfalls:
Confusing eutectoid (solid-state reaction at ~727°C) with eutectic; assuming hypo/hypereutectoid behavior applies at 0.8% C.

Final Answer: