Steelmaking route identification: The process in which pig iron is first decarbonised (oxidised) and then recarburised by adding a measured quantity of carbon (for example via spiegeleisen) to obtain steel of desired composition is called:

Introduction / Context:
Classical steelmaking routes include Bessemer, open hearth, crucible, and cementation. The Bessemer converter famously uses a blowing step to oxidise carbon and impurities, followed by controlled recarburisation to achieve the target carbon content in steel.

Given Data / Assumptions:

• Pig iron is the starting material.
• Process includes decarbonisation then measured addition of carbon.

Concept / Approach:
In the Bessemer process, air is blown through molten pig iron. Carbon, silicon, and manganese are oxidised; the heat of oxidation keeps the bath molten. After the blow, a recarburiser such as spiegeleisen or ferromanganese is added to adjust composition, providing the desired carbon and manganese levels for the final steel.

Step-by-Step Solution:

Verification / Alternative check:
Historic practice documents the decarburisation–recarburisation sequence as central to Bessemer steelmaking prior to basic oxygen and open-hearth dominance.

Why Other Options Are Wrong:

• Cementation: solid-state carburising of wrought iron to produce blister steel, not decarbonising.
• Crucible: batch melting; not defined by blowing and recarburisation from pig iron.
• Open hearth: refinery furnace with longer heat and different control steps.

Common Pitfalls:

• Assuming all historical routes recarburise in the same way; the air-blown decarburisation is Bessemer’s hallmark.

Final Answer:
Bessemer process