Choosing a Fuel for a Remote Field Station
A field station must choose between two fuels for heating and cooking. Fuel A is methanol (CH₃OH, M = 32.0 g/mol, ΔHc = −726 kJ/mol). Fuel B is propane (C₃H₈, M = 44.0 g/mol, ΔHc = −2220 kJ/mol). Storage space is limited to 20.0 kg of fuel, and the station needs about 4.0 × 10⁵ kJ of useful heat over a season. A student notes that methanol is a liquid at room temperature while propane must be stored under pressure. A previous trial with a spirit burner gave only about 55% of the theoretical heat to the water being heated, because of heat loss and incomplete combustion. The station manager wants a recommendation backed by calculation, not just 'propane has more energy per mole'.
1. Calculate the energy density (kJ per gram) of each fuel and determine which delivers more total heat from the 20.0 kg limit.
Read the worked answer
Methanol: energy per mole = 726 kJ. Per gram = 726 / 32.0 = 22.7 kJ/g. For 20.0 kg: 22.7 × 20 000 = 4.54 × 10⁵ kJ.
Propane: energy per mole = 2220 kJ. Per gram = 2220 / 44.0 = 50.5 kJ/g. For 20.0 kg: 50.5 × 20 000 = 1.01 × 10⁶ kJ.
Propane delivers about 2.2 times more total heat within the same mass limit. Comparing per mole is misleading because the molar masses differ; energy density per gram (or per litre) is the relevant comparison for a storage constraint. On mass alone, propane is clearly superior.
2. Apply the 55% efficiency to both fuels and judge whether either meets the 4.0 × 10⁵ kJ seasonal demand within the mass limit.
Read the worked answer
Useful heat = theoretical heat × 0.55.
Methanol: 4.54 × 10⁵ × 0.55 = 2.50 × 10⁵ kJ. This is below the 4.0 × 10⁵ kJ requirement - methanol fails by a wide margin.
Propane: 1.01 × 10⁶ × 0.55 = 5.56 × 10⁵ kJ. This exceeds 4.0 × 10⁵ kJ, with about 39% headroom.
Judgement: only propane meets the demand within the 20.0 kg limit. The efficiency factor is essential; without it, methanol's theoretical 4.54 × 10⁵ kJ looks marginally adequate, but the realistic value falls well short. This is the kind of trap the exam sets: theoretical energy content is not usable energy.
3. Propane must be stored under pressure, which adds cost and a safety constraint. Weigh this against the energy result and give a justified recommendation.
Read the worked answer
The calculation strongly favours propane: it provides 5.56 × 10⁵ kJ of useful heat versus 2.50 × 10⁵ kJ for methanol, and only propane meets the 4.0 × 10⁵ kJ demand. Methanol would require roughly 4.0 × 10⁵ / (22.7 × 0.55) ≈ 32 kg, exceeding the 20.0 kg limit, so it cannot work without extra storage.
The pressure-storage drawback is real: propane needs rated cylinders, leak detection and ventilation, adding capital and safety-management cost. However, these are one-off infrastructure costs, whereas the mass limit is a hard physical constraint that methanol cannot satisfy at any reasonable cost. The judgement is that the safety and cost penalty of pressure storage is outweighed by the decisive energy advantage, provided cylinders are certified and stored outdoors with appropriate controls. Recommendation: choose propane, budget for compliant storage, and keep a small methanol reserve only for low-demand backup, not as the primary fuel.