$1.$ For the reaction Fe$(/)+[0]$ FeO$(1),$ the equilibrium constant is expressed as a function of temperature as: log K $(6150/7)-2\mathrm{.}604.$ Given that the slag contains. CaO, SiO, and FeO and their respective mole percentages are $45\%,30\%$ and $20\%,$ use the ternary phase diagram provided in Sec. $5\mathrm{.}3\mathrm{.}7$ to calculate the equilibrium dissolved oxygen content in the bath at $1823.$

Case $1$: ignore activity coefficients.

Case $2$: consider the following activity composition relationships: log $0\mathrm{.}008[$wt$\%$ C$]-0\mathrm{.}2[$wt$\%$ O$]$ and log f $=0\mathrm{.}14[$wt$\%$ C$]-0\mathrm{.}34[$wt$\%$ O$].$

$12.$ Given that standard free energy change for the reaction $0($g$)[0]\%$ as a function of temperature is: $-117150-2\mathrm{.}897,$ on the basis of the results obtained from Problem $1,$ Calculate the oxygen potential of the slag at $1823$ K$.$

$3.$ A $200$ tonne converter is charged with hot metal containing $4\%$ C$,1\mathrm{.}2$ wt$\%$ Si and $1$ wt$\%$ Mn$.$ Calculate the volume of oxygen required to oxidize all impurities including FeO in slag as per Problem $1.$ Calculate the amount of SiO, thus generated and the amount of lime required to maintain a basicity $($V ratio$)$ of $3\mathrm{.}5.$ If density of slag is $3240$ and that of steel is $7200$ kg$/$m$,$ determine the relative mass ratio of metal to slag as accurately as possible.

$4.$ Complete oxidation of silicon to silica produces heat energy equivalent to $901,000$ kJ$/$ kg$-$mol of Si$.$ Similarly, complete oxidation of carbon to carbon monoxide liberates $150,000$ kJ$/$kg$-$mol of carbon. On the basis of the data in Problem $3(200$ tonne vessel, L$/$D$=0\mathrm{.}35),$ calculate the amount of heat evolved due to complete oxidation of silicon and carbon and the corresponding rise in bath temperature $($ignore lime heating, slag

formation, heat of mixing and heat losses$).$ Estimate the 'scrap equivalence' of heat

thus generated, given that the latent heat of melting of steel is $0\mathrm{.}12$ MJ$/$kg and specific

heat of steel is $680$ J$/$kgC$.$ For a small $60$ tonne BOF, the following data are available: $5.$

Hot metal composition: $1\%$ Si$,0\mathrm{.}15\%$ P$,4\%$ C and $0\mathrm{.}25\%$ Mn Weight of scrap $=10\%$ of hot metal

Steel at tap contains $0\mathrm{.}1\%$ C with practically no other impurity elements

Slag by weight has $18\%$ FeO and CaO$/$SiO$,=3\mathrm{.}2$ Calculate $($a$)$ amount of hot metal $($b$)$ weight of slag and $($c$)$ quantity of lime required to produce $60$ tonne liquid steel.

For the reaction $Fe(l)+[O{]}_{wt\%}$FeO$(l),$ the equilibrium constant is expressed as a function of temperature as: $logK=(\frac{6150}{T})-2\mathrm{.}604.$ Given that the slag contains CaO,$Si{O}_2$ and FeO and their respective mole percentages are $45\%,30\%$ and $20\%,$ use the ternary phase diagram provided in Sec. $5\mathrm{.}3\mathrm{.}7$ to calculate the equilibrium dissolved oxygen content in the bath at $1823K.$

Case $1$: ignore activity coefficients.

Case $2$: consider the following activity composition relationships: $log{f}_0=0\mathrm{.}008[wt\%C]-0\mathrm{.}2[wt\%O]$ and $log{f}_C=0\mathrm{.}14[wt\%C]-0\mathrm{.}34[wt\%O].$

Given that standard free energy change for the reaction $\frac{1}{2}{O}_2(g)[O{]}_{wt\%}$ as a function of temperature is: $-117150-2\mathrm{.}89T,$ on the basis of the results obtained from Problem $1,$ Calculate the oxygen potential of the slag at $1823K.$

A $200$ tonne converter is charged with hot metal containing $4\%C,1\mathrm{.}2wt\%Si$ and $1wt\%Mn.$ Calculate the volume of oxygen required to oxidize all impurities including FeO in slag as per Problem $1.$ Calculate the amount of $Si{O}_2$ thus generated and the amount of lime required to maintain a basicity $(V$ ratio$)$ of $3\mathrm{.}5.$ If density of slag is $3240$ and that of steel is $7200k\frac{g}{m^3},$ determine the relative mass ratio of metal to slag as accurately as possible.

Complete oxidation of silicon to silica produces heat energy equivalent to $901,000k\frac{J}{?}kg-$mol of Si$.$ Similarly, complete oxidation of carbon to carbon monoxide liberates $150,000k\frac{J}{k}g-$mol of carbon. On the basis of the data in Problem $3(200$ tonne vessel, $\frac{L}{D}=0\mathrm{.}35),$ calculate the amount of heat evolved due to complete oxidation of silicon and carbon and the corresponding rise in bath temperature $($ignore lime heating, slag formation, heat of mixing and heat losses$).$ Estimate the 'scrap equivalence' of heat thus generated, given that the latent heat of melting of steel is $0\mathrm{.}12M\frac{J}{k}g$ and specific heat of steel is $680\frac{J}{k}gC.$

For a small $60$ tonne BOF, the following data are available:

Hot metal composition: