The Gibbs energy for the decomposition of ${\mathrm{Al}}_2{\mathrm{O}}_3$ at ${500}^{\mathrm{o}}\mathrm{C}$ is as follows 

$\frac{2}{3}{\mathrm{Al}}_2{\mathrm{O}}_3\to \frac{4}{3}\mathrm{Al}+{\mathrm{O}}_2 \hspace{0.17em}{\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}=+966 \mathrm{kJ} {\mathrm{mol}}^{-1}$

The potential difference needed for electrolytic reduction of ${\mathrm{Al}}_2{\mathrm{O}}_3$ at ${500}^{\mathrm{o}}\mathrm{C}$ is at least