A coal contains 73.0 wt% C, 4.7% H (not including the hydrogen in the coal moisture) 3.7% S 6.8% H₂O, and 11.8% ash. The coal is burned at a rate of 50,000lb_m/h in a power plant boiler with air 50% in excess of that needed to oxidize all the carbon in the coal to CO₂. The air and coal are both fed at 77°F and 1 atm. The solid residue from the furnace is analyzed and is found to contain 28.7 wt% C. 1.6% S. and the balance ash. The coal sulfur oxidized in the furnace is converted to SO₂ (g) Of the ash in the coal 30% emerges in the solid residue and the balance is emitted with the stack gases as fly ash. The stack gas and solid residue emerge from the furnace at 600°F. The higher heating value of the coal is 18,000 Btu/lb_m.

(a) Calculate the mass flow rates of all components in the stack gas and the volumetric flow rate of this gas. (Ignore the contribution of the fly ash in the latter calculation, and assume that the stack gas contains a negligible amount of CO.)

(b) Assume that the heat capacity of the solid furnace residue is 0.22 Btu/(lb∙°F), that of the stack gas is the heat capacity per unit mass of nitrogen, and 35% of the heat generated in the furnace is used to produce electricity. At what rate in MW is electricity produced?

(c) Calculate the ratio (heat transferred from the furnace)/(heating value of the fuel). Why is this ratio less than one?

(d) Suppose the air fed to the furnace were preheated rather than being fed at ambient temperature but that everything else (feed rates, outlet temperatures, and fractional coal conversion) were the same. What effect would this change have on the ratio calculated in part (c)? Explain. Suggest an economical way in which this preheating might be accomplished.