$(20)$ Prob. $5$: An iron blast furnace is assumed to be reducing pure $F{e}_2{O}_3$ to Fe and all the reduction is assumed to be performed by CO$.$ For each $960$ kg of Fe produced there is charged $300$ kg of $CaC{O}_3$ and $300$ kg of pure carbon is burned. The temperature of the blast is $800C$ and that of the escaping blast furnace gas $200C.$ The slag is $45\%$CaO. The temperature of the slag and the iron leaving the furnace is $1600C.$ The melting point of the slag and of the iron is $1500C.$

Required: $(1)$ the volume and percentage composition of the blast furnace gas per metric ton of Fe produced.

$(2)$ the volume of blast required per ton of Fe :

$(3)$ the percentage of the total calorific power of the fuel which is developed in the furnace

$(4)$ A heat balance of the furnace per $1000$ kg of iron reduced.