A sample of coal was found to contain $1\%N,10\%$ ash, and $5\mathrm{.}8\%S.$ Analysis of the residue showed uncoked coal with $20\mathrm{.}71\%VCM$ lost in the residue. Orsat analysis of the stack gas shows $8\mathrm{.}93\%C{O}_2,1\mathrm{.}56\%CO,0\mathrm{.}34\%S{O}_2,9\mathrm{.}87\%O_2,$ and $79\mathrm{.}3\%N_2.$ Assume that $N$ in the coal is gasified to $N_2.$ Calculate:

a$)$ ultimate analysis of coal

$(67\mathrm{.}11\%$ C$,3\mathrm{.}95\%H,12\mathrm{.}14\%$ O$)$

b$)$ complete analysis of the residue if it contains $37\mathrm{.}93\%$ ash

$(54\mathrm{.}16\%$ FC$,7\mathrm{.}91\%$ VCM$)$

c$)\%$excess $O_2$

$(39\mathrm{.}5\%)$

d$)$ thermal efficiency