$4.$ You are designing a process to pre$-$heat $5$ kg$/$hr of ethylene from its underground storage container at $15$oC to $850$oC to be fed to a combustor.

a$.$ How much energy $($in kW$)$ is needed to pre$-$heat the gas?

b$.$ In industry, these types of processes $($pre$-$heating of gases$)$ are typically done by burning readily available combustibles in a scheme not too dissimilar to that shown to below. Assume that you will do the same and burn additional ethylene to pre$-$heat the gas. What percentage of the total ethylene fed to the process would be combusted to do the preheating? You can assume that the heat of combustion of ethylene is independent of temperature and equal to the value $$hrxn@$25$oC$.$