Coal containing $79$ wt$\%$ carbon and $6$ wt$\%$ ash is burnt in a furnace. The clinker from the

furnace refuse pit contains $90$ wt$\%$ ash and $10$ wt$\%$ unburnt carbon. On the basis of $1$ tonne

of coal charged,

a$)$ Draw a block diagram $[1$ mark$]$ and do the DOF analysis $[1$ mark$].$

b$)$ Calculate the mass of clinker produced.