Useful energy can only be used once

It's understandable that with all the concern about climate change and talk of "peak oil" that the central issue in both cases, our use of energy, has received a lot of attention. It is also understandable that with that attention have come many instances of what may charitably be called "optimistic business plans", acclaimed for some time, even quite lengthy periods of time, as "the" solution, or a "core" solution to our energy problems. There are some real solutions out there; there is also a lot of hype and hucksterism. With this and one or two follow-on articles I hope to help people not so familiar with the underlying science get a better grasp of the distinction. Don't be worried if this all seems very hard to understand - even such prominent energy and climate pontificators as Amory Lovins, Joe Romm and Al Gore have messed up on this at times. 

The following discussion derives from the fundamental physical science of thermodynamics, accepted and reasonably well understood since the mid 1800's. A particularly good introduction to the issues for the layperson is given in physicist David Goodstein's short 2004 book Out of Gas: The End of the Age of Oil, and I will excerpt some of his writing on relevant points. The main point I want readers to understand is the claim of my title: useful energy can only be used once. I will try to explain carefully what "useful" and "used" means in that statement, so it can become a reliable heuristic for you in evaluating any claimed energy solution.

In particular, I hope by the end of my discussion you will see exactly what is wrong with Gore's statement in "Our Choice" (p. 244) that "Overall U.S. electrical generation converts only 33 percent of fuel to electricity, but combined heat and power (CHP) plants extract more than twice as much useful energy by using energy twice." Using energy twice, in the sense Gore seems to imply, and that also implied by the URL for is physically impossible. And unfortunately statements of this sort are exceedingly widespread - almost every energy commentator seems to want to talk about the low efficiency of electrical generation, but they get their conclusions on how to fix that problem completely backwards. To the extent the statements on using energy twice or "recycling" energy are at all meaningful, they are deeply confusing - perhaps also to those who make the claims themselves. Let's try to get to the bottom of why this sort of claim is just wrong.

First, what does it mean to "use" energy? The first law of thermodynamics states that energy is conserved - it can be neither created nor destroyed. So how can we "use it up"? Let's start with Goodstein's entertaining historical account of how the first law came about (Chapter 2, p. 48ff):

A Brief History of Energy

In the eighteenth century, heat was thought to be a fluid called caloric. Just as water runs downhill, caloric could flow down in temperature from a hotter body into a cooler one. And like water, caloric was neither created nor destroyed while it flowed. To use the jargon of modern physics, caloric was thought to be a conserved quantity. The caloric theory was rigorous and quantitative. A chunk of copper at a certain high temperature contained a known amount of caloric. If you put it into a container of a known amount of cool water, you could calculate how much caloric would flow out of the copper into the water, and thereby predict with precision the temperature at which the two substances would come to equilibrium. Nevertheless, a former American colonist named Count von Rumford found the caloric theory wanting.

Benjamin Thompson [von Rumford] ... is best remembered today for pointing out in a scientific paper that boring out cannon barrels seemed to create quite a lot of caloric out of nothing. According to the caloric theory, that should not have been possible.

Count von Rumford's cannon barrels and many other observations would eventually blow the caloric theory out of the water. Caloric, or heat, would not turn out by itself to be a conserved quantity. Instead, it turned out to be just one of the possible forms of what we now call energy. Rumford and others during the first half of the nineteenth century tried to measure how much friction or other mechanical action would produce a given amount of heat. In a sense, what we now call the law of conservation of energy was discovered at least nine different times. When such a thing happens, credit for the discovery goes not to the first person who discovered it but to the one who discovered it last - the one who discovered it so well that it never had to be discovered again. This person's name was James Prescott Joule.

... In his most famous experiment, [Joule] arranged for a horizontal brass paddle wheel in a water tank to be turned by means of weights and pulleys ... after which the rise in temperature of the water was measured by means of a sensitive thermometer. Joule repeated the whole experiment nine different times and performed control experiments to determine the heating or cooling of the water by the atmosphere, without the churning paddle wheel. From the results of those experiments, he concluded that the amount of heat needed to warm a pound of water by 1F - an amount now known as the British thermal unit, or Btu - was equivalent to the amount of mechanical work required to lift a weight of 890 pounds through a distance of 1 foot. He achieved similar results in three more experiments: a magneto-electric experiment, another that involved the cooling of air by expansion, and another that measured the heating of water by constricting its flow in narrow tubes. Averaging the results of all these measurements, he arrived at a value of 817 pounds lifted through 1 foot as the equivalent of 1 Btu. The accepted value today is 775 pounds.

Joule's experiment utilizes two forms of energy transfer - work (the various mechanisms he used to turn the paddle wheel) and heat (the old "caloric" in the water that heated the thermometer a measurable amount). Work can be used to turn one form of energy into another: gravitational energy (the motion of a weight up and down in Earth's gravity), other forms of potential energy, electrical energy, energy of motion of large objects (kinetic energy), etc. The various forms of potential and kinetic energy are interchangeable with no physical limit: a battery or fuel cell can convert arbitrarily close to 100% of chemical potential energy into electrical energy, and a battery can also operate in reverse when charging. An electric motor can convert electrical energy into motion with arbitrarily close to 100% efficiency, or it can similarly operate in reverse, converting motion back into electricity with essentially no loss. These forms of potential and kinetic energy are all "useful" - this is all "useful energy" in the sense that I mean by my title, and it can be exchanged back and forth in principle arbitrarily many times. Getting more done with a given quantity of useful energy is the subject of efficiency - and there is still considerable room for efficiency improvement in our use of energy now.

For example, let's take my hybrid Prius for a short drive. Disable the extremely inefficient gasoline engine so we're just operating off the battery. Closing a circuit causes the chemical potential energy stored in the battery to start to generate electricity; that electricity generates magnetic fields in the electric motor that starts that motor turning, that turning motor then starts turning the wheels of the car, and the car starts moving. We have converted chemical potential energy into electrical and magnetic energy, and then into kinetic energy of the moving car. Now take the car up a hill. If we just coast up, not using the engine at all, the car slows down as its kinetic energy is turned into the gravitational potential energy associated with altitude. Coasting down the other side of the hill, the car accelerates again as that gravitational potential energy is converted back into its own kinetic energy of motion. Slowing down the car with the regenerative brakes turns that kinetic energy back into reverse motion of the electric motor, creating electrical energy which then recharges the battery, turning everything back into chemical potential energy once again. If I end at the same altitude I started, in principle the battery can be just as full after that drive as if I had never left the parking lot.

That is, transportation does not necessarily "use up" any useful energy at all. There are no fundamental physical limits to energy efficiency in transportation. Moving objects from one place to another requires conversion of useful energy between several different forms, but it does not necessarily deplete the overall supply of useful energy.

Now you may have several objections to my example here. First, isn't this example in contradiction with my title, that "Useful energy can only be used once"? I've just stated that the chemical energy in a car battery could do at least three different things (create electricity, kinetic energy, gravitational potential energy), and then do the same in reverse - isn't that using the same energy 3 or 5 times at least?

But that is a poor interpretation of the word "use". Because we could do the same thing repeatedly, over and over, in principle. So by this definition the same energy could be "used" 100 times, a million times, infinitely. Energy is conserved, and in an ideal system, useful energy can be exchanged between its different forms, doing work, indefinitely. Goodstein gives the example of a bowling-ball pendulum that continually exchanges energy between its potential and kinetic forms. Each swing back and forth exchanges that energy twice. Would you call that "use" of the energy? Exchanging energy between its different useful forms is not what I mean by "use". Exchange, which can be carried on indefinitely, does not "use up" or deplete the store of useful energy.

What does destroy useful energy is inefficiency: friction, electrical resistance, irreversible expansion of gases, noise or electromagnetic emissions that dissipate heat into the thermal background of our environment. In Joule's experiment, the resistance of the water to the paddle-wheel converted his work into heat in the water. That was an irreversible change turning useful energy into a useless form. It is impossible to extract the work back again out of the slightly hotter water (more on this change below). It is in this sort of conversion that the initial quantity of useful energy becomes "used up".

This gets to the second objection you may have to my idealized transportation example: there's waste heat released in every energy exchange; none of them are 100% efficient in conversion of useful energy from one form to another. Moving at any speed also brings rolling and air resistance and mechanical friction of moving parts in the car, so that kinetic energy is gradually dissipated into the surrounding air, ground, and the vehicle itself. And electrical resistance in the wiring similarly ensures that there is some loss to heating in the electric systems of the vehicle. Batteries gradually lose their charge thanks to nonzero internal conductivity, and so forth.

But all of those are things that could, with technical means, be done away with. Electrical wiring could be replaced by superconductors which lose no electricity. Wheels could be replaced by magnetic levitation, with no rolling resistance and no internal moving parts either. The transportation system could be placed underground in an evacuated tunnel, with no air, leaving no losses to resistance at all. The only net energy "use" in such a transportation system would be running the lights and radio - conveniences for their human occupants, not necessities for transportation itself.

So "use" or consumption of energy, destruction of useful energy, is not comprised of the useful things that are done with it, but rather comes from the losses caused by inefficiencies while doing those things. And in that sense of dissipating it into the environment, you can "use" useful energy only once, and then it is irretrievably gone. No recycling of used, dissipated, energy is possible.

This distinction between "energy" and "useful energy" is nothing new. People talk about "energy quality", or have introduced new terms like "exergy" to explain the distinction. The (misleadingly named) term "free energy" used by scientists is essentially the same thing - though there is an important dependency of these values on the surrounding environmental temperature that makes quantification slightly tricky. The most precise definition involves entropy, itself a notoriously difficult thing to understand (for example, Jeremy Rifkin's popular book "Entropy" was grossly wrong on a number of levels).

Goodstein gives a pretty thorough account of where the concept of entropy came from and what it means in relation to these issues of heat energy dispersing into the surrounding environment (starting on p. 83 of "Out of Gas"):

The steam engine is only one of a class of machines called heat engines. All heat engines start with heat at high temperature, turn part of that energy into work, and must ... dump part of the heat at low temperature in order to return to their starting points and keep on going. Heat engine types include the internal combustion engines of most cars (known to engineers as the Otto cycle), diesel engines, turbines, and the Stirling engine. ...

Electric motors are not heat engines. They don't need to dump waste heat at ambient temperature, so they can be, and often are, close to 100 percent efficient. Of the energy available in electric form, nearly all can be turned into mechanical work. ...

The Entropy Principle

Nicolas-LĂ©onard-Sadi Carnot ... tried to abstract the essence of what an engine was all about. In the course of working this out, he invented the beginnings of a powerful new science. ...

How could caloric [heat] make an engine run? Carnot reasoned by analogy to a waterwheel. Running downhill, water can do useful work by turning a waterwheel. The water doesn't get used up; it merely descends to a lower level. There's still just as much water at that level, but it can no longer be made to do useful work. Just so, thought Carnot, caloric can do work while running through an engine from high temperature to low temperature. At the end, the caloric is still there; it's just not as useful anymore, because it can no longer do work. To translate Carnot's reasoning into modern terms: Heat energy at high temperature is capable of driving an engine and doing work. The same amount of energy at low temperature is not capable of doing useful work. The same amount of energy is still there, but something about it has changed. That something is what we have come to call entropy.


Since the second law [of thermodynamics] is so important, let's look carefully in modern terms at what it says. It says you can't build a machine that will extract heat at low temperature and deposit that same amount of energy at higher temperature, without having any other effect. ...

In Carnot's world and ours, heat always runs downhill, from high temperature to low. Just as all the rainwater that falls on the land eventually finds its way to the ocean, all heat, generated by whatever means, at high temperature will eventually wind up as the same amount of heat at ambient temperature. If we devise a "proper machine," part of the heat energy can be made to do work along the way, but whatever the case, it always winds up in the air or the oceans. Of course, "high temperature" and "low temperature" are relative terms. In principle, a machine can be made to do work using heat as it runs between any two temperatures, as long as one is higher than the other. But Carnot was able to show that the higher the high temperature, and the lower the low temperature, the more efficient the engine would be. For all practical purposes, the burning fuel determines the high temperature and our surroundings - the air or the seas - become the low temperature for real engines.

... Heat is energy, and so is work. Energy is always conserved, but when it's at high temperature - and, for that matter, when it's still in the form of unburned fuel - it's capable of being turned at least partly into work. The same amount of energy, dumped into the atmosphere at ambient temperature, has become useless. The quantity of energy hasn't changed but somehow its quality has changed. How to describe the change of quality?

To do that job, Clausius coined the word entropy. Entropy measures the temperature of energy. A given amount of thermal energy - the random motions of atoms and molecules - has low entropy when it's at high temperature, and the same amount of energy has higher entropy when it's at lower temperature. Thus the principle that energy always runs downhill to lower temperature is completely equivalent to saying that entropy always increases.

... Think of heat and the temperature of two different gases. One is the gas involved in the combustion of a fossil fuel; it could be the air in the combustion chamber of a steam engine. Heat is the quantity of energy that comes from the burning fuel. Once the fuel is burned, it takes the form of the kinetic energy of the gas molecules bouncing rapidly around in the combustion chamber. The absolute temperature is directly proportional to the kinetic energy of the gas molecules. ... Eventually, however, the same quantity of heat will wind up at lower temperature, the temperature of ambient air. Then, too, it takes the form of kinetic energy - in this case, a very slight increase of the kinetic energy of the air molecules in the atmosphere. On the average, each molecule of the cool gas (the ambient atmosphere) has gained much less kinetic energy than each molecule of the hot gas (the air in the combustion chamber) gained from the burning fuel. But the total amount of energy is the same. That must mean that the same quantity of heat is spread out into a much larger quantity of gas. Instead of being concentrated in the intense heat of the combustion chamber, it has spread into the benign cool of the great outdoors. This spreading out of heat as the temperature decreases renders the energy useless to do work. That is the essence of increasing entropy.

... in applying these laws you mustn't consider only part of what's happening. You have to consider the whole thing. You can reduce the entropy of one thing, provided that in doing so you increase the entropy of something else by even more. Then the two processes considered together will have increased the entropy of the universe.

... [Even the Carnot engine ...] still has a limited efficiency. It obeys the iron rule of heat engines that only a fraction of the heat energy in the fuel can turn into useful work. The maximum possible efficiency of any heat engine (called the Carnot efficiency) depends on how high the temperature of the heat source (i.e., the burning fuel) is and how low the temperature at which the excess heat is deposited is.

All real engines do less well than the ideal engine envisioned by Carnot. Whether by the design of the engine cycle or by the ever-present effects of friction and other dissipative processes that are a necessary part of any real engine's operations, entropy happens. The rule of thumb commonly used by engineers is that only about a third of the energy content of a heat source, such as fossil fuel, can be turned into a useful form, such as electricity. ... That is an inescapable consequence of the entropy imperative that rules the natural world.


Summing Up

Now that we understand the basic principles of energy and entropy, let's replay the story of how it all works. The radiant energy that arrives at Earth from the Sun at a temperature of 6,000 kelvins is a very low-entropy form of heat. Some of it is reflected, making it possible to see Earth from space, and the rest is absorbed by the atmosphere and Earth itself. A tiny fraction of that energy is stored away at low entropy in the form of the high potential energy of fossil fuels. The rest drives the winds and ocean currents, causes water to evaporate and make the clouds, or simply falls as sunlight upon the land. Eventually all that energy that wasn't reflected back into space winds up as the thermal energy of the waters and the land, at the temperature of Earth's surface. The energy is absolutely conserved, but its entropy has increased irreversibly and forever. Earth warms to a temperature at which it radiates (in the form of invisible infrared radiation) just as much energy as it receives. Most of that is trapped by the atmosphere and radiated back to Earth, but a portion of it, equal almost exactly to the amount absorbed from the Sun, is radiated back into empty space, as cold, useless infrared radiation. Viewed from space, the whole drama has had no point but to do its inexorable job of increasing the entropy of the universe.

The third thing you may object to about my Prius example is the origin of the useful energy in the first place. How did it get into the battery? If it can only be used once, then eventually whatever the battery starts with will be drained through those inevitable frictions and inefficiencies, and then we'll be completely out of useful energy to run our transportation system. This is also the essential thing so often forgotten in those discussions of the wonders of the "hydrogen economy". Hydrogen, like batteries, is not a naturally available source of useful energy here on Earth.

The way hybrid cars work right now, that proximate source of useful energy is still the chemical energy in a fossil fuel. The gasoline engine in a hybrid car runs when it needs to charge the battery (or to help providing motive power when needed directly). In doing so it uses one of those "heat engine" processes - the slightly more efficient "Atkinson cycle" in the case of the Prius - so that the high temperature of the burning fuel-air mixture can be converted into mechanical work that then, as with the regenerative brakes, runs the electric motor in reverse and charges the battery. Since that conversion from chemical energy in the fossil fuel to chemical energy in the battery goes through an irreversible heat engine process on the way, a portion (at least 60%) of the initial useful energy in the fuel is "used up" immediately, and cannot be recovered by any technical means after that point. The only way to improve that efficiency and prevent some of the destruction of useful energy, if you are going through a heat engine process at all, is to run the engine at higher temperatures and compression ratios, but then you start to hit the limits of practically useable materials.

The promise of fuel cells is that they can avoid the "heat engine" step, and convert chemical energy more directly to electrical forms, although in practice the efficiency for high power output tends to be considerably less than for most other types of useful energy conversions anyway. Given that the typical useful energy input to a fuel cell (hydrogen) is itself not naturally available, you then have to step back and ask where that useful energy came from. Battery-electric vehicles can also side-step "heat engine" losses by being directly charged from the electric supply - the "plug-in" hybrid solution. And then where does the useful energy on the electric grid come from?

Our supply of useful energy on the Earth comes largely from three sources: incoming radiant energy from the Sun (solar, wind, hydro, wave, and biofuel all obtain useful energy directly or indirectly from incoming sunlight - though unfortunately biofuels at least seem to require some fossil input as well), solar energy accumulated as biological materials beneath the Earth's surface over millions of years (the fossil fuels), and the energy associated with the mix of elements and their isotopes that our planet was formed with (nuclear, geothermal, and fusion energy). In the case of the latter two, it is sobering to remember the main point of this post: we can only use that useful energy once. Our planet has received a particular endowment of stored energy in these forms, and once we've used that up, it's gone. This is the ultimate in limited supply; useful energy cannot be manufactured from the ambient environment, it must be provided to us from some outside source. Once used, it is gone forever. In the context of discussion of "sustainability" in recent years, no use of fossil or nuclear fuels is sustainable by definition. A very small quantity of geothermal energy can be used in a sustainable manner, only because nuclear isotopes in Earth's interior do decay at a steady rate, sending heat out to us at a rate we cannot reduce. But otherwise, anybody claiming their technology is sustainable while relying on fossil or nuclear fuels is very confused.

Of course we do have an outside source, the Sun, providing our planet with a profligate amount of useful energy that is presently being almost entirely "wasted" as far as humans are concerned, just dissipating into the environment at will. In turn the Sun's endowment of nuclear isotopes - protons in particular - is the ultimate source of its useful energy. The Sun is burning up that endowment at a steady rate that would likely be even harder to alter than the decay rate of the isotopes in Earth's interior; we do have a few billion years to try to resolve that problem though. But even with the Sun, that store of useful energy it was born with can be used only once.

And to reiterate what I mean here by "used" - a given quantity of energy starts in a useful form, with low (high temperature) or even zero (electric, mechanical, potential) entropy. Using up that useful energy means running it through a process that dissipates that same quantity of energy into the environment at low temperature, increasing its entropy to the maximum possible here on Earth. As soon as you have converted chemical energy into a form of heat (burning fuels, for example) you have raised the entropy of that energy, and destroyed a portion of its original endowment of useful energy. Each step in an engine, turbine, or other process to use that heat involves spreading that heat around and lowering its temperature, raising its entropy still further. But the very start of the process, burning fuel in a combustion chamber (or extracting heat from a fission reaction chamber), already causes the loss of a high percentage of the original useful energy. That initial fraction lost can be estimated by dividing 300 K ambient temperature by the combustion chamber temperature - at 500 K you lose 60% just in burning, at 1000 K just 30%.

So when Al Gore (and far too many others) complain about how "Overall U.S. electrical generation converts only 33 percent of fuel to electricity" the vast majority of the problem there is energy lost at the very first stages of the process, burning chemical fuels to make heat. We can not solve that problem downstream, by "using energy twice" or "recycling" it. The only way to solve that inefficiency is to completely change the way we turn chemical or nuclear energy into electricity, specifically by abandoning steam turbine generators. That we certainly will do as we eliminate our nation's use of fossil fuels in coming years; in the mean time there are probably more important things to worry about that the low efficiency of some old coal power plants.

Part 2: Efficiency in heating
Part 3: Cogeneration: only a small part of the solution

Created: 2009-12-24 08:26:16 by Arthur Smith
Modified: 2010-03-03 08:52:45 by Arthur Smith