The definition of exergy efficiency f is somewhat arbitrary. We could draw the line (between f and g) in several ways. However, the most convenient division, partly for reasons of data availability, is the following. Finished exergy, the numerator of f consists of three components, namely physiological work by humans and farm animals, mechanical work by prime movers (internal combustion engines of all kinds and electric power produced by any means) and chemical exergy (heat) produced for any purpose other than driving an engine, including driving chemical reactions. The chemical exergy embodied in finished materials (contained in structures and durable goods) is almost entirely derived from fuels or electric power. The exergy contribution from metal ores is small and mostly attributable to sulfur in sulfide ores, which can be lumped with fuels.
The above definition omits end-use efficiency, the efficiency with which heat or electric power delivered to a user is converted, within the service sector or within the household, into the ultimate service (climate control, cooking, washing, information processing or communication). This omission is unfortunate, since most of the technological progress in recent years, and most of the efficiency gains, have been in this area. Nevertheless, it is conceptually useful to distinguish the efficiency with which 'raw' exergy is converted into 'finished' exergy, consisting of work or heat delivered to a user and chemical exergy embodied in finished materials.
On the input side, exergy consists of the following: products of photosynthesis (phyto-mass), fossil fuels, nuclear heat, hydroelectric power, and metal ores and other minerals. Photosynthetic exergy utilization in the USA in 1998 consisted of primary agricultural phytomass generated for the food system (including grazing animals) - 24.5 exaJoules (EJ) - plus a small contribution by non-food crops (mainly cotton) plus wood. This analysis was made with the aid of an extremely comprehensive agricultural model (Wirsenius 2000) using FAO data for the years 1992-1994. The model works back from final food intake to primary production requirements, adjusting for trade. Food eaten in the USA itself amounted to just about 1 EJ, and exports increased this to 1.37 EJ (equivalent). The calculated efficiency of the US production system was 5.6 per cent, implying gross primary production of 24.5 EJ. Of this 15.6 EJ was actually utilized (harvested and processed or fed to animals), the remainder being unharvested, lost or used for other purposes such as seed, mulch or fuel. Roundwood harvested (for lumber and paper) accounted for an additional 4.85 EJ. Fuelwood is lumped with fossil fuels, which amounted to 80.9 EJ in 1998. Nuclear reactor heat added 7.3 EJ and hydroelectric power added 1.1 EJ. So-called 'energy' inputs altogether accounted for 89.3 EJ. Finally, the exergy value of metal ores added 0.41 EJ. The grand total of all inputs was slightly more than 114.8 EJ. This is the denominator of the efficiency ratio, f as of 1998.
The 'finished exergy' output components are mechanical work (done by humans, animals and machines), useful heat and materials. These can be evaluated numerically with modest effort and some reasonable assumptions. Animal and human work can be calculated from the caloric value of metabolizable food consumption, adjusted for metabolic efficiency and fractional working time. In the USA for the year 1998, farm animals did too little work to be counted. Humans in the USA consumed 1.0 EJ of food (caloric value) in 1998. Food consumption by 270 million people, at 3300 Cal/day, amounts to just over 1 EJ. However, men in the USA (and Europe) spend less than 20 per cent of lifetime 'disposable' hours doing work for pay (that is within the economic system). As regards women - because they live longer and spend somewhat less time doing paid work - the figure is probably around 15 per cent. Assuming very little exergy is needed during 'non-disposable' hours (sleeping, eating, personal hygiene and so on), the overall average fraction of exergy consumption devoted to economically productive work is still not above 15 per cent, at present. (It was probably twice that in 1900, however, when people worked many more hours and died younger.) The muscular efficiency of the human body is about 20 per cent. The product of the two efficiencies is less than 0.03; that is to say, human labor amounted to less than 0.03 EJ which is negligible. The details do not matter, since the absolute number is so small.
Prime movers (mostly car, truck, bus and aircraft engines) not used for electricity generation consumed 26.6 EJ, but the mechanical work done amounted to about 6.4 EJ (assuming 25 per cent net efficiency, after allowing for internal losses in vehicle drive trains and other parasitic loads). Net electric power output delivered was 13.3 EJ in 1998.
Finally, chemical exergy supplied for other purposes (mostly heat) consumed 33.6 EJ in fuel terms. The 'conversion' efficiency in this heterogeneous commercial-household-industry sector is difficult to estimate, since it includes space heat, domestic cooking and washing, and all kinds of chemical and metallurgical reduction and transformation processes driven by chemical (and, to some extent, electrical) exergy. The space heating, water heating and cooking component is especially difficult to evaluate, since end-use efficiencies in this area are extremely low in the 'second law' sense (that is, in comparison with the minimum amount of exergy required in principle by the most efficient possible way of delivering the same services. A 10 per cent figure for fuel is probably optimistic. The efficiency of most metallurgical and chemical processes (measured as exergy embodied in final products to exergy of fuel consumed) is somewhat higher, probably on average closer to 30 per cent. Combining the two, very roughly indeed, one might assume an average 15 per cent conversion efficiency. More precision is impossible without a detailed process-by-process analysis. On this basis, the 'output' in 1998 amounted to something like 5 EJ. It is important to remember that most of the net exergy 'content' of asphalt, plastics and metals (around 4 EJ) is mostly derived from fossil fuels (or electric power), so it is already included. Adding wood and paper products, the exergy efficiency of the US economy for 1998 was of the order of 27/115 (23 per cent) plus or minus 2 or so.
A similar calculation for 1900 can be carried out, albeit a little less accurately. In that year the primary agricultural biomass was probably about 20 per cent less than that for 1993. The argument is that the total amount of land devoted to agriculture in the USA has changed very little since 1900; land made more productive by irrigation (mainly in California and the southwest) is roughly balanced by land lost to agriculture in the southeast and northeast as a result of extensive erosion and urbanization. Elsewhere, as in the great plains, irrigation is mainly compensation for falling water tables. Similarly, the net impact of fertilizers is largely to replace nutrients lost to harvesting and topsoil erosion. Increases in net food production can be attributed mainly to reduced need for animal feed (for horses and mules), improved seeds (yielding more grain or other useful product per unit of phytomass), animal breeding (more milk or eggs per unit of feed) and reduced losses to insects, rodents and other pests.
Other inputs were from fossil fuels and fuelwood (8.92 EJ), and timber (2.04 EJ), for a total of about 31 EJ. The exergy outputs included mechanical work on farms done by horses and mules, which was about 0.22 EJ in 1920, and 20 per cent lower than that in 1900. In the 1920s, land needed to provide feed for horses and mules amounted to 28 per cent of total agricultural land in the USA (US Census 1975). Assuming this figure applied in 1918, the peak year (when the horse and mule population was 26 723 000), it would appear that gross primary production of the order of 7 EJ was required to feed horses and mules. It has been estimated that these animals required 33 units of food energy to produce one unit of work. On this basis, the net work output of farm animals would have been about 0.22 EJ, with an uncertainty of at least 20 per cent. For comparison, Hayami and Ruttan (1971) estimated that 6 EJ was used by the food system around 1920 for both animal feed and fuelwood. This would imply a somewhat lower share for animals. For comparison, by 1960, when tractors had essentially replaced farm animals, machines and chemicals consumed about 5 EJ of fuel (Steinhart and Steinhart 1974). Assuming 15 per cent net efficiency (high), this would have been equivalent to 0.75 EJ of net work. However, it is probable that farmers did more physical work in 1960, thanks to the availability of mechanization, than they would have done with animals in 1920, simply because machines are faster and require much less human labor.
There was a similar contribution by railroads and stationary engines in 1900, around 0.18 EJ (assuming 10 per cent thermal efficiency of the steam engines in use at the time). Other fuel use, consisting of domestic heat, process heat and exergy embodied in wood for construction and paper, might have been as large as 3 or 3.5 EJ. Adding them up, the overall exergy conversion efficiency in 1900 was probably less than 3.9/34.4 = 11.3 per cent, also plus or minus 2 per cent or around half of present levels. In short, f has been increasing, albeit at a modest rate, as indicated in Figure 16.2.
The exergy embodied in raw materials but not embodied in finished materials is, of course, lost as waste heat or waste materials (pollution), denoted W. All exergy converted to
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