How is the calorific value of a solid fuel determined using a bomb calorimeter?

In one line

A known mass of fuel is burnt in excess oxygen inside a sealed steel "bomb" placed in a known mass of water, and the rise in water temperature gives the higher calorific value.

Explained simply

Imagine burning a small pellet of coal inside a strong closed steel box dipped in a bucket of water. All the heat goes into the water and the bucket. If you know how much water there is and how much it warmed up, you know how much heat the coal gave. Because the products are cooled back to near room temperature, the steam condenses, so the bomb calorimeter gives the HCV.

How it works

1. Weigh about 0.5–1 g of the fuel (x g) into a crucible (silica/nickel) placed inside the stainless-steel bomb.
2. A fine fuse wire (magnesium or platinum) touches the fuel and is connected to two electrodes.
3. Close the bomb and fill it with oxygen at about 25 atm.
4. Place the bomb in a copper calorimeter containing a known mass of water (W g), fitted with a stirrer and a Beckmann thermometer (reads to 0.01 °C). An outer air jacket/water jacket reduces heat loss.
5. Stir and note the initial temperature t₁.
6. Pass current to ignite the fuel. The fuel burns completely; heat flows to the water.
7. Note the maximum temperature t₂.

Key formula

Heat given by fuel = heat taken by water and calorimeter:

\( \text{HCV} = \dfrac{(W + w)(t_2 - t_1)}{x} \) cal/g

• \( W \) = mass of water in calorimeter (g)
• \( w \) = water equivalent of calorimeter, bomb, stirrer, thermometer (g)
• \( t_2 - t_1 \) = temperature rise (°C)
• \( x \) = mass of fuel (g)

For accurate work, corrections are applied: cooling correction (t_c) is added to the rise, and heat from the fuse wire (t_f), from acid formation (t_a, for H₂SO₄ and HNO₃) and from the cotton thread (t_t) are subtracted:

\( \text{HCV} = \dfrac{(W + w)(t_2 - t_1 + t_c) - (t_a + t_f + t_t)}{x} \)

Then \( \text{LCV} = \text{HCV} - 0.09H \times 587 \).

Quick example

0.8 g coal, W = 2000 g, w = 500 g, rise = 2.6 °C. HCV = (2500 × 2.6)/0.8 = 8125 cal/g. If H = 6%, LCV = 8125 − 0.09 × 6 × 587 = 8125 − 316.98 = 7808 cal/g (approx.).

Common mistakes

• Forgetting the water equivalent w in the numerator.
• Saying the bomb calorimeter gives LCV directly. It gives HCV.
• Adding the fuse-wire and acid corrections instead of subtracting them (they are heat not from the fuel).

How MU asks it

"Describe the determination of calorific value of a solid fuel by bomb calorimeter with a neat labelled diagram." (5–6 marks) and numericals (3–5 marks). For full marks: labelled diagram (bomb, crucible, electrodes, O₂ valve, fuse wire, calorimeter, stirrer, Beckmann thermometer, jacket), the procedure in steps, the derivation with symbols, and the corrections.