How is the steam generated per kg of coal found?

6400 kg / 800 kg = 8 kg steam per kg coal

What is the useful heat in steam per kg coal?

8 x (2783.8 - 146.7) = 21097 kJ

How is the radiation and unaccounted loss found?

By difference: 30000 minus the sum of steam heat and the listed losses = 928 kJ/kg

Measured directly from the flue gas analysis

It equals the heat in dry flue gases

It is assumed to be 10 % of the CV

Practice · 8 marks

Boiler trial heat balance sheet

Short answer

Useful heat in steam: 21097 kJ (70.3%); losses: dry flue gases 5775 kJ (19.3%), moisture and hydrogen 1500 kJ (5.0%), unburnt carbon 700 kJ (2.3%), radiation and unaccounted 928 kJ (3.1%).

In a boiler trial of one hour, 800 kg of coal of calorific value 30000 kJ/kg was burnt and 6400 kg of dry saturated steam at 12 bar was generated from feed water at 35 °C. Per kg of coal, the heat carried away by dry flue gases was 5775 kJ, the loss due to moisture and hydrogen in the fuel was 1500 kJ, and the loss due to unburnt carbon in ash was 700 kJ. Prepare the heat balance sheet per kg of coal, giving the percentages and the radiation and unaccounted loss.

Heat utilised in steam

Steam per kg of coal $= 6400/800 = 8$ kg.

At 12 bar dry saturated: $h_g = 2783.8$ kJ/kg. Feed water at 35 °C: $h_{fw} = 146.7$ kJ/kg.

Q_{steam} = 8 \times (2783.8 - 146.7) = 21097\ \text{kJ/kg coal}

Unaccounted loss (by difference)

Q_{un} = 30000 - (21097 + 5775 + 1500 + 700) = 928\ \text{kJ/kg coal}

Heat balance sheet (basis 1 kg coal, CV = 30000 kJ/kg)

Item	kJ	% of heat supplied
Heat supplied by coal	30000	100.0
Heat in steam (useful)	21097	70.3
Heat in dry flue gases	5775	19.3
Moisture and hydrogen loss	1500	5.0
Unburnt carbon in ash	700	2.3
Radiation and unaccounted	928	3.1
Total	30000	100.0

Answer: Boiler efficiency = 70.3 %; radiation and unaccounted losses = 928 kJ/kg coal (3.1 %).

✓ Answer checked by Claude Opus 5.5 (high effort)

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