Free Energy Lunch

In honor of oil tapping $100/bbl these last couple days, I thought I’d trouble the readers of this blog with some napkin math, of the sort that renewable energy engineering types find themselves doing at odd hours. To begin with, we note that the US uses approximately 20 million barrels of oil per day, approximately 25% of the worldwide total (the US has about 4.5% of the global population). A barrel of the type that is used to denominate oil sales is 42 gallons – approximately a bathtubful. A rough number for the energy content of a barrel of oil is 6.1 GJ – to get some intuitive idea of how much energy that is, imagine filling a bathtub with gasoline and touching it off. Now imagine filling 20 million bathtubs…

We next note that the population of the US is very nearly 300 million. By simple calculation we arrive at:

2o Mb/day * 6100 MJ / 300 Mpeople = 400 MJ/person/day – average, for every man, woman, child, and invalid in the land

Most people don’t have an intuitive feel for megajoules, nor do many people actually burn gasoline in bathtubs, so we might put it in more familiar terms, as follows:

400 MJ/person/day * 1 day/24 hours * 1 hour/3600 seconds = 4.6 kW/person

To get a sense for what 4.6 kW is, imagine surrounding yourself with 46 big, bright old-fashioned incandescent lightbulbs – that’s a lot of light, and a LOT of heat. But my intention is to put our per-capita oil consumption in very human terms. Let’s estimate that a healthy person exerting him/herself can deliver 100 watts of useful power over an 8 hour day via an efficient mechanism (bicycling; see human output graph, a useful tidbit on howstuffworks.) The energy content of a day’s labor, then, is:

100 J/s * 3600 seconds/hour * 8 hours/workday = 2.9 MJ/person/day

400 MJ/day (oil) / 2.9 MJ/person/day = 140 persons

Dividing, we find that the energy content of the oil consumed by the average American is equivalent to the power output of approximately 140 people at continuous hard labor 8 hours per day. You could think of this as a crowd of 140 full-time “virtual energy servants”, following you around and doing your bidding. In fact it’s much better than that, because they don’t get in your way, you don’t have to provide living quarters for them, and you don’t have to feed them – they were “fed” by the sun eons ago, as the source beds for the oil deposits were gradually laid down over the course of millions of years. Of course, creating an industrial society is not as simple as pouring oil in – the energy endowment of petroleum has been engaged most cleverly by engineers in myriad ways – not only directly as heat and motive power for transportation, but also to process into useful materials and drive efficient manufacturing processes. But, viewed broadly, this simple analysis goes a long way towards explaining why even the today’s working classes can enjoy a material quality of life (ability to travel, physical comforts, foods from across the globe) that compares favorably to that of the nobility of preindustrial times. And, as the thin leading edge of petroleum scarcity begins to wedge itself into the cracks of our global systems, it lends added urgency to the quest for clean energy. Not every person will be able to afford to employ 140 persons as servants as the “virtual energy servants” grow tired.

As with any napkin calculation, there are caveats. Chiefly, much of that petroleum is burned in internal combustion engines, which deliver perhaps just a third of that energy as useful work (large diesel engines approach 50%, while smaller gas engines may be closer to 25%) – though some is used to provide heat, where the efficiencies are probably closer to 80%. On the other hand, bicycling is a uniquely efficient way of delivering human power compared to, say, shoveling dirt, or smashing rocks with a large hammer. Further, petroleum is merely a largish chunk of our total energy consumption, which includes sizeable contributions from gas (also depleting rapidly), coal (polar bear Buchenwald), nuclear, hydro, and a modest contribution from other renewables. If we want to maintain our current standard of living, we had best get to work developing clean, renewable, carbon-neutral energy sources to replace our petroleum energy servants.


One Response to “Free Energy Lunch”

  1. pingswept » Blog Archive » From teaching high school to renewable energy engineering in less than 10 years Says:

    […] drive cars with an average fuel economy of less than 30 miles per gallon, and I hope that some of our 140 servants will have been replaced with renewable sources of […]

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