can be reduced by carbon at a temperature of:

50C
500C
1500C
> 2500C
An Ellingham diagram is a graph showing the temperature dependence of the stability for compounds. This analysis is used to evaluate the ease of reduction of metal oxides.
At not very high temperatures (below 1500 oC), Carbon cannot be used in the reduction of in metallurgy. Aluminum oxide is a very stable oxide and lies below the oxidation line of carbon in Ellingham Diagram.
However, at very high temperatures (say > 2500oC), the reduction of Alumina by carbon is favoured.
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