Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S4 / 1 / 3 / Solution

Use equal combustion energy as the displacement criterion. The petrol mass and energy areThis needs ethanol mass $M_e=Q_p/(30.5\times 10^6)=1.04115\times 10^{10}\mathrm{kg}$. The ethanol fermentation stoichiometry converts $180$ mass units of glucose to $92$ of ethanol, so the ethanol yield per square kilometre is $(1500)(92/180)=766.667$ tonnes. ThereforeThe carbon mass fraction in octane is $8(12)/(8(12)+18)=96/114$. The displaced fossil carbon is thusThis is the ideal net reduction if the crop regrows and its carbon dioxide uptake balances the biogenic carbon released in fermentation and combustion, with negligible additional life-cycle emissions. Ethanol combustion is not carbon-free: it releases about $5.43$ million tonnes of carbon here, and fermentation releases further biogenic carbon. Those are balanced by crop uptake in the stated ideal accounting, rather than being ignored. Farming, fertilizer manufacture, processing heat, transport and land-use carbon losses reduce the actual benefit and may even reverse it. The equal-heat calculation also assumes equal useful-energy conversion efficiencies in the displaced application; it does not establish equal engine mileage automatically.