An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen nitrogen, oxygen and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Delong formula: HHV (kJ/kg) = 33,801 (C) + 144,158 [(H) – 0.125 (0)1 + 9413 (S) where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125 (O) term accounts for the hydrogen bound in the water contained in the coal.

(a) Derive an expression for the higher heating value (HKV) of a coal in terms of C, H, O, and S. and compare your result with the Delong formula. Suggest a reason for the difference.

(b) A coal with an ultimate analysis of 75.8 wt% C, 5.1% H, 8.2% 0. 1.5% N, 1.6% S. and 7.8% ash (noncombustible) is burned in a power plant boiler furnace. All of the sulfur in the coal forms SO₂. The gas leaving the furnace is fed through a (all stack and discharged to the atmosphere. The ratio Φ (kg SO₂ in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate 4, using the Delong formula for the heating value of the coal,

(c) An earlier version of the EPA regulation specified that the mole fraction of SO₂ in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing Unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.