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

Annual conversion is reduced by several multiplicative losses. Only roughly $40$–$50\%$ of incident sunlight lies in the photosynthetically useful visible band. Reflection and transmission prevent complete absorption; the photon budget and unavoidable relaxation losses limit conversion of absorbed radiation into chemical energy. Photosynthesis also has to support respiration and maintenance, while seasonal growth, incomplete canopy cover, water and nutrient limitations reduce the annual harvested yield.

An illustrative loss budget, not a universal biological constant, is $0.45\times 0.8\times 0.25\times 0.5\times 0.11\simeq 0.005$. The factors represent useful spectrum, absorption, photochemical conversion, retained net production, and combined annual interception and growing-condition limitations, respectively. Thus $\boxed{{\eta }_{\mathrm{annual}}\sim 0.5\%}$ is plausible for a land-averaged crop yield even though a leaf under favourable illumination can be more efficient. The result depends on crop, climate, harvested fraction and the definition of dry biomass energy. When the input is already annual mean insolation, night-time must not be counted as a second independent loss.

Take an explicitly illustrative European annual mean ground-level irradiance of $100\mathrm{W}{\mathrm{m}}^{-2}$, the stated conversion fraction $0.005$, and dry carbohydrate heating value $16\mathrm{MJ}\mathrm{k}{\mathrm{g}}^{-1}$. One square kilometre then producesHence $\boxed{M\sim 10^3\mathrm{tonnes}\mathrm{k}{\mathrm{m}}^{-2}\mathrm{yea}{\mathrm{r}}^{-1}}$, or about $10\mathrm{tonnes}\mathrm{h}{\mathrm{a}}^{-1}\mathrm{yea}{\mathrm{r}}^{-1}$, as a dry-mass order-of-magnitude estimate. The assumed irradiance is not a site-specific value supplied by the paper. The result scales linearly with irradiance and conversion efficiency and inversely with heating value; wet harvested mass would additionally depend on water content.

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.

Three advantages of biomass energy are:

Three disadvantages are: