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# aluminum ingot which contains 15% Si and is in the process of being cast. ?

Consider an aluminum ingot which contains 15% Si and is in the process of being cast. When the ingot is 28% frozen, the remaining liquid contains 20% Si. What is the average composition of the solid at this point?

Answer is 2.1

How was answer found?

### 1 Answer

- Anonymous2 months ago
The composition of the liquid and solid is a simple mass balance.

Assume you have 100 kg of the original alloy. 15 kg is Si and the rest (assumption) is 85 kg Al.

When 28% of the material is solid, you have 28 kg of solid and 72 kg of liquid.

The liquid is given as 20% Si so you have 72 kg * 0.2 = 14.4 kg Si. The balance is Al (72 kg - 14.4 kg = 57.6 kg Al)

Al in the solid = 85 kg - 57.6 kg = 27.4 kg

Si in the solid = 15 kg - 14.4 kg = 0.6 kg

The solid is 27.4 kg / (27.4 kg + 0.6 kg) * 100 = 97.9 wt% Al. The balance is Si or 100% - 97.9% = 2.1%.

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