Fuels and Combustion Questions and Answers

Answer: A

Correct answer: 1 kg

The reaction is \( \mathrm{S} + \mathrm{O_2} \rightarrow \mathrm{SO_2} \), so 32 kg of sulphur takes 32 kg of oxygen and the ratio is \[ \frac{32}{32} = 1\ \text{kg of oxygen per kg of sulphur.} \] Sulphur is usually a small fraction of the fuel, so its contribution to the air requirement is minor - it matters far more for corrosion and for the sulphur dioxide in the flue gas.

Answer: B

Correct answer: 2.48 kg

Use the three ratios, subtracting the oxygen the fuel already contains: \[ \mathrm{O_2} = 2.67\,C + 8\left(H - \frac{O}{8}\right) + S \] \[ = 2.67(0.80) + 8\left(0.05 - \frac{0.08}{8}\right) + 0.02 \] \[ = 2.136 + 8(0.04) + 0.02 = 2.48\ \text{kg.} \] The bracket is the key step: only the hydrogen not already combined with the fuel’s own oxygen needs air, and 0.08 kg of oxygen accounts for 0.01 kg of hydrogen.

Answer: C

Correct answer: 10.8 kg

Air is 23 per cent oxygen by mass, so the theoretical air is the theoretical oxygen divided by 0.23: \[ \frac{2.48}{0.23} = 10.8\ \text{kg of air per kg of coal.} \] Working by volume instead the fraction is 21 per cent, so the two must not be mixed. A good bituminous coal typically needs 10 to 11 kg of air per kg, which is a useful check on any such calculation.

Answer: D

Correct answer: 20 per cent

Excess air is the surplus expressed as a fraction of the theoretical requirement: \[ \frac{13 - 10.8}{10.8} = \frac{2.2}{10.8} = 0.204 \approx 20\ \text{per cent.} \] The denominator is the theoretical air, not the air actually supplied - dividing by 13 would give 17 per cent and is the usual error. Twenty per cent is a reasonable figure for a well-run coal fired boiler.

Answer: A

Correct answer: 7889 kcal/kg

Dulong’s formula weights each combustible element by its own calorific value, with the same correction for combined oxygen: \[ \mathrm{GCV} = 8080\,C + 34500\left(H - \frac{O}{8}\right) + 2240\,S \] \[ = 8080(0.80) + 34500(0.04) + 2240(0.02) \] \[ = 6464 + 1380 + 44.8 = 7889\ \text{kcal/kg.} \] The distractor 6464 is the carbon term alone, and 8080 is the constant itself.

Answer: B

Correct answer: 7625 kcal/kg

Every kilogram of hydrogen makes nine kilograms of water, so this coal forms \( 9 \times 0.05 = 0.45 \) kg of water per kg. The latent heat carried away with it is \[ 0.45 \times 587 = 264\ \text{kcal/kg,} \] and therefore \[ \mathrm{NCV} = 7889 - 264 = 7625\ \text{kcal/kg.} \] The net value is what a boiler can actually recover unless the flue gas is condensed, which conventional plant does not do.

Answer: C

Correct answer: 60 per cent

A proximate analysis has four parts that sum to 100, and fixed carbon is the one obtained by difference rather than by direct measurement: \[ 100 - 4 - 28 - 8 = 60\ \text{per cent.} \] It is the combustible residue left on the crucible after the volatile matter has been driven off and before the ash is determined by burning it away.

Answer: D

Correct answer: 8125 kcal/kg

The heat released equals the water equivalent times the temperature rise, and the calorific value is that heat per unit mass of fuel: \[ \frac{2500 \times 2.6}{0.8} = \frac{6500}{0.8} = 8125\ \text{kcal/kg.} \] Note the units - the water equivalent is in grams and the fuel in grams, so the quotient is kcal per gram only if the 2500 is read as cal/°C; taken as given the answer comes out directly in kcal/kg. The distractor 6500 omits the division by the fuel mass.

Answer: A

Correct answer: 90 000 kcal/h

Rate of heat release is the calorific value times the volumetric rate: \[ 4500\ \frac{\text{kcal}}{\text{m}^3} \times 20\ \frac{\text{m}^3}{\text{h}} = 90\,000\ \text{kcal/h.} \] The check is dimensional - the cubic metres cancel and kcal per hour remains, which is the only one of the four options with that magnitude.

Answer: B

Correct answer: 1-Q, 2-P, 3-R

Three gases of quite different origin. Water gas is made by passing steam over hot coke and is essentially carbon monoxide and hydrogen. Coal gas is the gas evolved when coal is carbonised, and is chiefly hydrogen and methane. Biogas is the product of anaerobic digestion, roughly two parts methane to one of carbon dioxide - and it is that inert carbon dioxide that keeps its calorific value below natural gas.