---
title: "Boiler trial heat balance sheet"
subject: "Applied Thermodynamics"
chapter: 1
key: "semester_3/applied_thermodynamics:boiler-heat-balance-sheet"
source: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/boiler-heat-balance-sheet
site: BCT Engineering
---

# Boiler trial heat balance sheet

Applied Thermodynamics · Chapter 1: Boilers

- Asked in: year not given, 8 marks
- Video: [How to draw heat balance sheet in case of boiler - SPPU paper solutions](https://www.youtube.com/watch?v=wnEytppzVCI) — CHINMAY ACADEMY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/boiler-heat-balance-sheet
- Whole chapter: https://www.bctengineer.com/md/semester_3/applied_thermodynamics/chapter-1

## Question

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.

## 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%).

## Answer

#### 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 %).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is the steam generated per kg of coal found?
   A. 6400 x 800 = 5.12 x 10^6
   B. 800/6400 = 0.125 kg
   C. 6400/30000 = 0.213 kg
   D. 6400 kg / 800 kg = 8 kg steam per kg coal
   Answer: D. Divide steam produced per hour by coal burnt per hour. (Key point: Steam per kg coal)

2. What is the useful heat in steam per kg coal?
   A. 8 x (2783.8 - 146.7) = 21097 kJ
   B. 8 x 2783.8 = 22270 kJ
   C. 8 x 146.7 = 1174 kJ
   D. 6400 x 2637.1 = 1.69 x 10^7 kJ
   Answer: A. Heat in steam is steam per kg coal times (hg - hfw). (Key point: Useful heat)

3. How is the radiation and unaccounted loss found?
   A. Measured directly from the flue gas analysis
   B. By difference: 30000 minus the sum of steam heat and the listed losses = 928 kJ/kg
   C. It equals the heat in dry flue gases
   D. It is assumed to be 10 % of the CV
   Answer: B. The unaccounted loss is the balancing figure: 30000 - (21097 + 5775 + 1500 + 700) = 928 kJ. (Key point: Unaccounted loss)

4. What is the boiler efficiency from the balance sheet?
   A. 19.3 %
   B. 96.9 %
   C. 70.3 %
   D. 79.8 %
   Answer: C. Efficiency is the percentage of heat supplied that is utilised in steam: 21097/30000 = 70.3 %. (Key point: Boiler efficiency)

## Related in Applied Thermodynamics

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- [Equivalent evaporation and boiler efficiency](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aboiler-equivalent-evaporation) — Applied Thermodynamics, chapter 1
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