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Sunday, May 4, 2008

Even in Arcadia: Energy, Entropy, and Efficiency
How Physics Tells Us to Go Green

On the emptying fairgrounds the carousel drifts slowly, slowly, an echo of motion, creaking to a gradual halt. The fields beyond are darkening to indistinctness, punctuated only by the occasional flare sent up by a firefly. Though the carnival has defied the close of day for hour after giddy hour, late spring twilight finally and definitively creeps in to collect its due.

In the vats of lemonade, the ice-cubes have melted and left no trace of themselves but an absence, a thinning of flavor. It is the inevitable way of things, that all heat differences tend to smooth out, that everything dense must rarefy, that the motion of a spinning carousel will be muffled and stilled into friction.

Time's arrow strains unbendingly forward. In the hiss of the bowstring echo the distant pounding shores of chaos, and destruction. Left to itself, everything orderly must move toward disorder. Though W.H. Auden's lover may sing on that summer evening under the archway,

"I'll love you, dear, I'll love you
Till China and Africa meet,
And the river jumps over the mountain,
And the salmon sing in the street,"

still comes the reply even from our petty everyday tragedies:

"The glacier knocks in the cupboard,
The desert sighs in the bed,
And the crack in the teacup opens
A lane to the land of the dead."[1]

All the sorrowing for lost loves and empires, for ballads forgotten and palaces crumbled, is due to the laws of thermodynamics. Undergirding all of physics, there are four thermodynamical laws, but two are most important:

I. Energy can neither be created nor destroyed;
II. Over the course of any natural process in an isolated system, entropy must increase, barring external interference.

Entropy is a name for the disorderliness of a system, and hence the extent to which its energy cannot be mustered to do work. This increase of entropy described by the second law of thermodynamics sums up all our earthly trials. Even the beloved children's book character, Arnold Lobel's eponymous Owl At Home, makes his tear-water tea by thinking of "mashed potatoes left on a plate because no one wanted to eat them, and pencils that are too short to use."[2] Everything hot grows cold; everything useful outlives its productivity.

Not surprisingly, the laws of thermodynamics and their implications for efficiency were discovered in the decades following the invention of the steam engine, in the mid-nineteenth century. A steam engine converts heat into work: burning coal heats and vaporizes water into steam, whose expansion forces the piston outwards and begins the engine's cycle, turning the crankshaft.

However, the piston will not retreat and complete the cycle unless it is cooled by a water source. In this process, along with the work of turning the crankshaft, heat is transferred from the burning coal to the cool water supply. At the end of one cycle, the engine has returned to its initial state and the piston is ready to advance and retreat again. However, the heat source and water supply which power the engine have not returned to their initial state; they have degraded. The steam engine's conversion of heat into work is incomplete, because some of the heat necessarily dissipates into the water rather than powering the turning crankshaft.

As the engine completes cycle after cycle, the cool water grows still more heated and hence less effective. In accordance with the second law of thermodynamics, the steam engine left to itself becomes disorderly and less capable of doing work.

The second law of thermodynamics can be stated entirely in terms of the conversion of heat into work, with no mention of entropy. As worded by P.W. Atkins in his excellent book The Second Law,

No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.[3]

This is the form of the second law discovered by the scientist and engineer William Thomson, 1st Baron Kelvin (1824-1907). Although famous for many achievements ranging from work in electricity and telegraphy to the proposal of an early model analogizing the atom as an English plum pudding, Kelvin's greatest contributions laid the cornerstone for the field of thermodynamics.

By Kelvin's statement of the second law, some degree of wastage is inevitable in principle, no matter to what heights of refinement our engine technology soars. This being the case, the search for an economical source of energy to heat and power the engines took on still greater importance, and from coal the industrial world moved on to oil. In 1859 oil was discovered and drilled for in Titusville, Pennsylvania, beginning an industry boom which rapidly spread to other oil-rich areas of the world.[4]

In 1930, 100 barrels of oil could be extracted using the energy equivalent of a single barrel of oil.[5] Oil is a highly concentrated source of energy: one barrel (42 US gallons) yields 1,700 kWh of energy,[6] enough to run a 100 Watt light bulb for nearly two years, 24 hours a day, 7 days a week.

Considering how the earth's oil was formed, its energy-richness is hardly surprising. Petroleum, or crude oil, is the result of an extremely special confluence of geologic circumstances whereby fossilized marine microorganisms are heated and compacted deep in the earth, smelted from rock into oil. Formation of an oil field also requires the bedrock to mold a cavity protecting petroleum from leaking to the surface and decaying due to the action of modern-day microorganisms. Stores of oil represent the intense geothermal compression of solar energy assimilated by the original prehistoric zooplankton.[7]

Clearly, the total global oil supply is finite, and if not static, then subject only to infinitesimally slow increase by petroleum formation. Using geological sampling estimates of total drillable oil in the 48 contiguous US states and in the world as a whole, geophysicist M.K. Hubbert wrote two papers (1949 and 1956) constructing a mathematical model of projected future oil production. Hubbert's production curves accurately predicted that oil production in the US would reach a peak around 1970, thereafter entering a period of decline more or less sharp according to the height of peak production.

Hubbert's model predicted global peak oil production around the year 2000, an estimate which proved to be slightly early in part due to the conversion of many heating systems from oil to natural gas. However analyses by the international think tank Energy Watch Group of data from the US Energy Information Administration point toward a 2006 peak having occurred in conventional oil production. This view has been corroborated by Sadad Al Husseini of Saudi Arabia's national oil company Saudi Aramco, and by the Texas oilman T. Boone Pickens.[8]

Because the most easily accessible oil has already been harvested, it is no longer remotely possible to recover 100 barrels at the mere expenditure of one barrel's worth of energy. The energy return on investment of US domestic oil production has fallen from 100:1 in 1930 to 30:1 in 1970 and to 11-18:1 in 2000.[9] The same principles apply to global oil production.

While the value of energy sources is commonly assessed using standard economic analyses, the alternate measure of energy return on investment (EROI) can in some cases offer information which is not captured in, or is distorted by, monetary values. For example high prices during the 1973 oil crisis were caused not by shortages but by oil embargoes the Organization of Arab Petroleum Exporting Countries (OAPEC) imposed as political leverage against Western countries for their support of Israel in the Arab-Israeli conflict. Ensuing economic recession in the affected countries in turn caused the oil glut and lowered prices of the 1980's. Quoting not a currency price per barrel but the price in energy to extract one barrel yields a cost immune to the influence of political forces. The global buying power of energy for energy, of one barrel of oil to win us more barrels of oil, has been falling more or less steadily, independent of economic vicissitudes.

Just as coal once fueled the steam engines of locomotives, oil fuels most of industrialized society, from the electricity that plays Mozart on the stereo, to the ships bringing mangoes to our groceries. As oil supplies dwindle, must the world as we know it run out, like a neglected engine whose fires die down, like a carousel grinding to a halt at the end of a day?

Oil fuels the cycling pistons of a cargo ship's engines, and by extension the cycling routes the vessels themselves shuttle. But the Earth supports many engines besides these: the cycling of wind currents around the globe, and of water evaporated from oceans and rained onto mountains to fuel the rivers.

Jet streams and river deltas do not run down because their wasted and dissipated energy is continually replaced by the Sun's radiation bathing the Earth. The Earth is not a closed system, drearily marching toward heat death in isolation. For as long as the Sun lives, the Earth enjoys a reprieve from the one-way arrow of entropy.

However, this renewal of cycles granted by the Sun's largesse does not extend to fossil fuels, because the timescale of their formation is too slow and the circumstances required too special. From the standpoint of oil, the Earth is a closed system, and no external source replenishes the bounty.

M.K. Hubbert's 1949 paper "Energy from Fossil Fuels" goes on to construct a production curve not only for oil but for water power. As Hubbert notes, "water power represents a fraction of current solar energy which changes but slowly with time, and is being continuously degraded into waste heat irrespective of whether it is utilized or not."[10] Using 1947 figures for the water power utilization and potential of major sources in each continent, Hubbert extrapolates a global production curve which, like that for oil, will reach a maximum, but rather than falling due to finitude of resources, levels out at a maximum plateau. As technology improves, the energy return on investment for water power should asymptotically approach the maximal value representing an ideal state of affairs. This maximal return, Hubbert asserts, could theoretically supply us with as much energy as we currently enjoy from fossil fuels.

Energy return on investment has been researched for a large range of alternative energy sources by energy researcher Charles Hall at SUNY Syracuse's College of Environmental Science & Forestry. Hall depicts his findings in what he calls "the balloon graph." The vertical axis of this graph represents energy return on investment, while the horizontal axis shows the amount of energy being consumed from each source (or having been consumed, for past sources). Every energy source appears as a balloon, color coded for year of consumption (red is present-day). The size of a balloon indicates the uncertainty in the data used to plot that energy source's position on the graph.

To illustrate the graph's meaning, arrows connecting the balloons for US domestic oil use in 1930, 1970, and the present day trace a rough version of Hubbert's oil peak curve. The fact that energy return on investment was all the while decreasing for domestic oil can be seen in the lowering heights of the three balloons for 1930, 1970, and today.

Also visible from the graph is the fact that energy return on investment is higher for both hydroelectric and wind power than for imported oil today. In an excellent series of five articles at TheOilDrum.com, Charles Hall examines the potential of all alternative energy sources shown on the balloon graph, as well as the drawbacks of each. None is problem-free: hydroelectric power, for instance, implies serious environmental and social threats due to the land use demands of water engineering, and almost every source poses difficulty related to energy storage and transportation.

Despite the various problems still present with each energy source, however, renewable sources such as water or wind give us effectively infinite time to improve and perfect our technology, approaching a maximum return on expenditure. The carnival of easy oil is finally running down, and an increasing trend shows that former Texas oil moguls, including T. Boone Pickens, are moving their operations to capitalize instead on Texas wind.

We may not be able to control the motions of wind and water as we could once control the flow of oil from the rigs, but we can learn to adapt our technology to capture and store this bounty which flows from the sun. Or, as the W.H. Auden poem concludes,

"Life remains a blessing
Although you cannot bless."

Note: The title of this post comes from the Latin quotation "Et in Arcadia ego" ("Even in Arcadia, there am I"), a memento mori spoken by personified Death. Even in the most ideal of engines, there is entropy. The title is a reference to Tom Stoppard's imaginative play "Arcadia," also titled from the Latin memento mori, and centering around the invention of the steam engine and the discovery of entropy. The fictional plot of this play vividly brings to life the era of the development of thermodynamics.

How will life change after peak oil? Which alternative energy source do you see as most promising? What is the most important action we as ordinary people can take to conserve energy? What did you think of Arcadia? Please share your comments!


[1] ^ W.H. Auden, As I Walked Out One Evening, http://www.poets.org, retrieved 5.4.2008.

[2] ^ Arnold Lobel, Owl at Home.

[3] ^ P.W. Atkins, The Second Law.

[7] ^ http://en.wikipedia.org/wiki/Petroleum, and references therein, retrieved 5.4.2008.

[8] ^ http://en.wikipedia.org/wiki/Predicting_the_timing_of_peak_oil, and references therein, retrieved 5.4.2008.

[10] ^ M. King Hubbert, Energy from Fossil Fuels, retrieved 5.4.2008.