Question

The higher heating value of a hydrocarbon fuel \(\mathrm{C}_{n} \mathrm{H}_{m}\) with \(m=8\) is given to be \(1560 \mathrm{MJ} / \mathrm{kmol}\) of fuel. Then its lower heating value is \((a) 1384 \mathrm{MJ} / \mathrm{kmol}\) (b) \(1208 \mathrm{MJ} / \mathrm{kmol}\) \((c) 1402 \mathrm{MJ} / \mathrm{kmol}\) \((d) 1514 \mathrm{MJ} / \mathrm{kmol}\) \((e) 1551 \mathrm{MJ} / \mathrm{kmol}\)

Short answer

Answer: The lower heating value of the hydrocarbon fuel is 1208 MJ/kmol.

Step-by-step solution

Understand the difference between HHV and LHV

Higher heating value (HHV) represents the total energy released when a given fuel is completely combusted, while lower heating value (LHV) represents the energy released when the combustion process results in water vapor instead of liquid water. The main difference between HHV and LHV lies in the heat of vaporization involved in the combustion process.

Calculate the difference between HHV and LHV

In hydrocarbon fuel combustion, the hydrogen atoms present in the fuel combine with oxygen to form water molecules. We can calculate the heat of vaporization needed to convert liquid water to water vapor using the following formula: Difference = (Heat of vaporization of water) * (number of moles of hydrogen atoms in a hydrocarbon fuel molecule) Given that \(m=8\), and there is one mole of hydrogen for each mole of hydrocarbon molecule, the number of moles of hydrogen atoms in a hydrocarbon fuel molecule is equal to 8. The heat of vaporization of water is \(44 \mathrm{MJ} / \mathrm{kmol}\) Difference = \(44 * 8 = 352 \mathrm{MJ} / \mathrm{kmol}\)

Calculate the lower heating value

To find the lower heating value (LHV) of the hydrocarbon fuel, we simply subtract the calculated difference from the given higher heating value (HHV). LHV = HHV - Difference LHV = \(1560 - 352 = 1208 \mathrm{MJ} / \mathrm{kmol}\) Therefore, the lower heating value of the hydrocarbon fuel is \(\boxed{1208 \mathrm{MJ} / \mathrm{kmol}}\), which corresponds to option (b).