The exhaust from furnace contains the following gases: $100molC{O}_2,200mol{H}_{2}O,50$mol $O_2,$ and $1000mol{N}_2.$ The exhaust is cooled from $900C$ to $400C$ in a heat exchanger that transfers the energy to water.

a$.$ How much energy $($in kJ$)$ is transferred to the water?

b$.$ Water is fed to the heat exchanger at $25C$ and converted to $50$ bar saturated steam. How much water, in $kg,$ must be fed?