Calorific value of fuel by Dulong's formula

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.