How do you calculate the calorific value of coal using Dulong's formula?

In one line

Dulong's formula estimates the higher calorific value of a fuel from its percentages of carbon, hydrogen, oxygen and sulphur (from ultimate analysis).

Explained simply

If you know what a fuel is made of, you can add up the heat from each burning element, like adding the price of items in a shopping cart. Carbon, hydrogen and sulphur give heat. But some hydrogen is already "tied up" with the fuel's own oxygen as water, so that hydrogen gives no heat. Dulong's formula subtracts this part.

How it works

1. Heat of combustion values used: C → CO₂: 8080 kcal/kg; H → H₂O: 34500 kcal/kg; S → SO₂: 2240 kcal/kg.
2. All oxygen in the fuel is assumed to be combined with hydrogen as water (H₂O, 2 g H per 16 g O). So 1 part of O locks up 1/8 part of H.
3. Available (free) hydrogen = \( H - \frac{O}{8} \).
4. Multiply each percentage by its heat value, add, divide by 100.

Key formula

\( \text{HCV} = \dfrac{1}{100}\left[\,8080\,C + 34500\left(H - \dfrac{O}{8}\right) + 2240\,S\,\right] \) kcal/kg

\( \text{LCV} = \text{HCV} - 0.09\,H \times 587 \) kcal/kg

• C, H, O, S = percentages by mass of carbon, hydrogen, oxygen, sulphur.
• Nitrogen and ash are not included because they give no heat.
• In LCV use the total H%, not the free hydrogen.

Quick example

Coal: C = 80%, H = 5%, O = 6%, S = 1%, N = 2%, ash = 6%.

• Free H = 5 − 6/8 = 4.25
• 8080 × 80 = 646400; 34500 × 4.25 = 146625; 2240 × 1 = 2240
• Sum = 795265; HCV = 7952.65 kcal/kg
• LCV = 7952.65 − 0.09 × 5 × 587 = 7952.65 − 264.15 = 7688.50 kcal/kg

Common mistakes

• Writing (H − 8/O) or (H − 8O) instead of (H − O/8).
• Using free hydrogen (4.25) in the LCV step; the LCV correction uses total hydrogen (5) because all of it forms water.
• Including N or ash, or forgetting to divide by 100.

How MU asks it

Almost always a numerical (3–5 marks): "A coal sample has the following composition... Calculate HCV and LCV using Dulong's formula." For full marks, write the formula first, show the free hydrogen step, each product, the sum, then the LCV step with units. Sometimes asked with ultimate-analysis data, where you first find C, H, S percentages and then apply Dulong's formula.