--- title: "Calorific value of fuel by Dulong's formula" subject: "Internal Combustion Engines" chapter: 3 key: "semester_6/internal_combustion_engines:calorific-value-dulong-formula-numerical" source: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/calorific-value-dulong-formula-numerical site: BCT Engineering --- # Calorific value of fuel by Dulong's formula Internal Combustion Engines · Chapter 3: Engine fuels - Asked in: year not given, 5 marks - Video: [Chapter-3 Dulong's Formula & Numericals](https://www.youtube.com/watch?v=GbBHah16MxU) — Poonam Thakur - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/internal_combustion_engines/calorific-value-dulong-formula-numerical - Whole chapter: https://www.bctengineer.com/md/semester_6/internal_combustion_engines/chapter-3 ## Question Explain the difference between higher and lower heating value. A liquid fuel has the following composition by mass: carbon 84%, hydrogen 12.5%, oxygen 1.5%, sulphur 1% and ash/others 1%. Using Dulong's formula, calculate the higher and lower heating values. Take the latent heat of steam at 25 degrees C as 2442 kJ/kg. ## Short answer HCV = 46.2 MJ/kg, LCV = 43.5 MJ/kg. HCV includes latent heat of water vapor; LCV excludes it. Dulong’s formula applied with given composition. ## Answer #### HCV and LCV - **Higher (gross) calorific value, HCV:** heat released when 1 kg of fuel is burned completely and the products are cooled to the original temperature, so that the water vapour is condensed and its latent heat is recovered. - **Lower (net) calorific value, LCV:** the same, but the water leaves as vapour, so its latent heat is not available. Engines exhaust hot gas, so LCV is used for efficiency calculations. $$ \text{LCV} = \text{HCV} - m_w h_{fg} $$ where $m_w = 9\,\text{H}$ kg of water is formed per kg of fuel (H is the mass fraction of hydrogen). #### Dulong's formula $$ \text{HCV} = 33\,800\,\text{C} + 144\,200\left(\text{H} - \frac{\text{O}}{8}\right) + 9400\,\text{S}\ \ \text{kJ/kg} $$ Here the oxygen in the fuel is assumed to be already combined with part of the hydrogen (O/8). #### Calculation $$ \begin{aligned} 33\,800 \times 0.84 &= 28\,392 \\ 144\,200 \times (0.125 - 0.015/8) &= 144\,200 \times 0.123125 = 17\,754.6 \\ 9400 \times 0.01 &= 94 \\ \text{HCV} &= 28\,392 + 17\,754.6 + 94 = 46\,240.6\ \text{kJ/kg} \end{aligned} $$ $$ \begin{aligned} m_w &= 9 \times 0.125 = 1.125\ \text{kg water/kg fuel} \\ \text{LCV} &= 46\,240.6 - 1.125 \times 2442 = 43\,493.4\ \text{kJ/kg} \end{aligned} $$ **Answer:** HCV $\approx 46.2$ MJ/kg and LCV $\approx 43.5$ MJ/kg. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the difference between HCV and LCV? A. HCV includes the latent heat of the condensed water vapour; LCV does not B. LCV includes it, HCV does not C. HCV is for gas and LCV for liquid D. No difference Answer: A. LCV = HCV - m_w h_fg, because engine exhaust leaves as vapour. (Key point: HCV vs LCV) 2. Which value is used for engine efficiency calculations, and why? A. HCV, as water condenses in the engine B. LCV, as exhaust gas leaves hot and water remains vapour C. HCV, as it is larger D. LCV, as it has no hydrogen Answer: B. The latent heat of the water vapour is not recovered in an engine. (Key point: Which value for engines) 3. Why is H - O/8 used in Dulong's formula? A. Oxygen increases heat release B. Oxygen forms sulphur dioxide C. Oxygen in fuel is assumed already combined with part of the hydrogen D. To account for ash Answer: C. One kg of O combines with 1/8 kg of H, which is therefore not available to burn. (Key point: Oxygen term in Dulong) 4. How much water forms per kg of fuel with hydrogen mass fraction H? A. H/9 kg B. 8H kg C. 18H kg D. 9H kg Answer: D. 2 kg of H gives 18 kg of water, so 9 kg water per kg H; here 9 x 0.125 = 1.125 kg. (Key point: Water formed) ## Related in Internal Combustion Engines - [Efficiency ratio and specific fuel consumption](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Arelative-efficiency-sfc-numerical) — Internal Combustion Engines, chapter 8 - [Cooling water and radiator air flow calculation](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aengine-coolant-flow-radiator-numerical) — Internal Combustion Engines, chapter 7 - [Heat balance sheet of a diesel engine](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Adiesel-engine-heat-balance-numerical) — Internal Combustion Engines, chapter 8 - [Combustion of octane with excess air](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aoctane-combustion-air-fuel-numerical) — Internal Combustion Engines, chapter 3 - [IP, BP and efficiencies of a petrol engine](https://www.bctengineer.com/question.md?key=semester_6%2Finternal_combustion_engines%3Aindicated-brake-power-efficiency-numerical) — Internal Combustion Engines, chapter 8 ## Related in other subjects - [Calorific value and air from ultimate analysis](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Adulong-calorific-value-fuel-oil) — Energy Resources, chapter 1 - [Fuel cell voltage, efficiency and hydrogen use](https://www.bctengineer.com/question.md?key=semester_6%2Fenergy_resources%3Afuel-cell-stack-numerical) — Energy Resources, chapter 6 - [Consequences of higher or lower SCR](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Ascr-higher-lower-consequences) — Power Plant Design, chapter 4, asked 3× - [Hydrogen fuel advantages and disadvantages](https://www.bctengineer.com/question.md?key=semester_7%2Fenergy_environment_and_society%3Ahydrogen-fuel-adv-disadv) — Energy Environment and Society, chapter 3, asked 3×