The enthalpy of sublimation of aluminium is $330 \,kJ/mol$. Its $I^{st}, II^{nd}$ and $III^{rd}$ ionization enthalpies are $580, 1820$ and $2740 \,kJ$ respectively. How much heat has too be supplied (in $kJ$) to convert $13.5\, g$ of aluminium into $Al^{3+}$ ions and electrons at $298 \,k$