Dulong’s formula is an empirical equation widely used to estimate the Higher Calorific Value (HCV) and Lower Calorific Value (LCV) of a fuel based on its elemental composition. It provides a quick method to approximate the energy content of solid and liquid fuels when laboratory calorimetric data is unavailable.
The formula establishes a relationship between the calorific value and the percentages of carbon (C), hydrogen (H), oxygen (O), and sulfur (S) present in the fuel.
Dulong’s Formula for Calculation of Calorific Values
(All values are expressed in MJ/kg.)
Where:
- HCV (Higher Calorific Value): The total amount of heat released when 1 kg of fuel undergoes complete combustion, including the latent heat of vaporization of water.
- LCV (Lower Calorific Value): The usable heat excluding the energy used to vaporize the water formed during combustion.
- C: Percentage of carbon in the fuel.
- H: Percentage of hydrogen in the fuel.
- O: Percentage of oxygen in the fuel.
- S: Percentage of sulfur in the fuel.
Dulong’s Formula Explanation and Significance
Dulong’s formula assumes complete combustion and that all hydrogen converts into water vapor. However, during actual combustion, some of the heat is lost due to moisture in the fuel and incomplete burning. Therefore, the formula provides an approximate value rather than an exact measurement.
Despite this limitation, Dulong’s formula is still highly useful for preliminary energy analysis—especially in fields like fuel characterization, power plant design, and biomass energy assessment—where laboratory testing may be time-consuming or impractical.
Example Calculation
Example 1: f a fuel sample has:
C = 80%
H = 10%
O = 5%
S = 1%
Calculate HCV and LCV,
Then,
HCV = 33.3(0.8) + 144.4(0.1 − 0.05/8) + 93.5(0.01)
HCV = 26.64 + 13.53 + 0.94 = 41.11 MJ/kg
LCV = HCV − 9H × 2.44
LCV = 41.11 − 9(0.1) × 2.44 = 38.91 MJ/kg
Example2: Calculate the gross and net calorific values of coal having the following compositions, carbon = 85%, hydrogen = 8%, sulphur = 1%, nitrogen = 2%, ash = 4%, latent heat of steam = 587 cal/gm
Given:
C = 85%
H = 8%
S = 1%
N = 2%
Ash = 4%
Oxygen (by difference) = 100 − (85+8+1+2+4) = 0%
Latent heat of steam = 587 cal/g = 587 kcal/kg
Formula used (Dulong, in kcal/kg; percentages entered as %):
GCV (kcal/kg) = 80.8·C + 345·(H − O/8) + 22.4·S
Water formed (kg per kg fuel) = 0.09·H
Latent heat loss (kcal/kg) = (0.09·H) · L
NCV (kcal/kg) = GCV − latent heat loss
Step 1 — Compute GCV
Step 2 — Compute water formed and latent heat loss
Step 3 — Compute NCV (net calorific value)
NCV = GCV − latent heat loss = 9,650.4 − 422.64
NCV = 9,227.76 kcal/kg
Step 4 — Convert to MJ/kg (1 kcal = 0.0041868 MJ)
GCV = 9,650.4 × 0.0041868 = 40.404 MJ/kg (rounded)
NCV = 9,227.76 × 0.0041868 = 38.635 MJ/kg (rounded)
Final answers:
GCV (Gross / Higher Calorific Value) = 9,650.4 kcal/kg ≡ 40.404 MJ/kg
NCV (Net / Lower Calorific Value) = 9,227.76 kcal/kg ≡ 38.635 MJ/kg
Conclusion
Dulong’s formula remains a reliable estimation method for determining the calorific value of fuels based on chemical composition. While it cannot replace precise experimental testing, it serves as a valuable engineering tool for preliminary fuel evaluation, design calculations, and energy resource assessments.
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