For complete combustion of ethene.

$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$

the amount of heat produced as measured in bomb calorimeter is $1406 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $300 \mathrm{~K}$. The minimum value of $\mathrm{T} \Delta \mathrm{S}$ needed to reach equilibrium is ($-$) _________ $\mathrm{kJ}$. (Nearest integer)

Given : $\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$