Carnot, and Limits

There’s a type of question I get a lot in my line of business. “What’s the latest development in solar panels?” “Is the price going to drop a lot more?” “Are the solar panels out now going to be obsolete in a few years?” “Is there some big development in panel efficiency right around the corner?”

There are a lot of questions like this in the energy business in general. People watch computer technology advance in step with Moore’s law, with everything getting smaller, faster, and more whiz-bang by the month. I see an expectation out there that energy technology could, and should, do the same. It’s a large and complex question, and I’ll take a whack at it from various angles in no particular order.

I’ll start with a general thesis, as efficiently expressed by a friend of mine who has long experience with electric vehicles. He and another soccer dad were on the sidelines discussing the problems of transportation, energy, pollution, and the like. The other dad summed up by saying “They’ll think of something.” My friend responded, “I am they, and we won’t.”

Let’s think of energy in terms of conventional automobiles. At highway speeds, most of the energy required by a car is used to push air out of the way. The two factors in this are the frontal area of the car (the shadow cast by a light lined up directly in front of it) and the Cd, or coefficient of drag. This is the factor of how the shape of the car, with all its curves and projections, slips through the air.  A beer can travelling sideways has a Cd of about 1. Your average modern sedan has a Cd of about 0.35, a pickup about 0.45, and a Toyota Prius about 0.26. The GM EV-1 managed 0.195. Below that, you get into solar race cars that look like space ships.

If you design a car with two people sitting side by side in a reasonably upright position there is a certain bare minimum frontal area necessary.  In other words, no matter how slick you make the car, there’s some minimum amount of energy that it will take to make it go 65 mph on the highway. Add rolling resistance, acceleration, and hill climbing; beating 80 miles per gallon is a serious challenge.

With wind turbines there is a factor called the Betz Limit. No wind turbine can get 100% of the energy out of the wind. If it did, then the air coming out the back of the turbine would come to a dead stop, and no new air could come in the front. Albert Betz figured out that the theoretical maximum energy extraction would be 59%. Modern wind turbines get around 75% of that. It really isn’t going to get much better.

Standard commercial photovoltaic modules tend to have efficiencies in the teens to about 20%. This compares well with the 33.7% Shockley-Quiesser limit, the theoretical maximum for a single layer silicon cell. Every so often you might read about some laboratory reaching an efficiency of around 40%, but this is with an expensive multiple layer cell under sunlight concentrated by lenses or mirrors.

Batteries are getting better bit by bit, but are still much less energy dense than fossil fuels. Part of the problem is just the nature of the physics involved – electrochemical electron transfer versus combustion. What it really gets down to is that every molecule in a can of gasoline is potential energy, while in a battery much of the material involved is a base on which the energy transfer takes place. That base is generally a flat plate that has to be mechanically strong and conductive to electricity, meaning metal, meaning heavy.  Another problem is thermal. As we try to pass more energy through a smaller object, the inefficiency of the process will heat up that object. The battery packs in modern electric cars tend to have cooling systems.

An economic problem with battery development is the old adage that you can’t make a baby in one month, even with nine women on the job. Battery developers can’t know the lifespan of a battery until they test a battery for its entire lifespan. In fact, they don’t know until they have run it through its lifespan in a number of different ways. Investors don’t like delay and uncertainty, and battery development is full of that.

And then there is Carnot. In the early 19^th century Nicolas Carnot figured out that the maximum efficiency of an engine that turns heat into motion was defined by the operating temperature of the engine compared to its environment. That is, the hotter the fuel burns and the colder the surrounding temperature, the more efficient the engine. We can’t do much about the environmental temperature except by moving to Antarctica, but we can burn the fuel hotter. Except that then we have to create exotic materials that won’t melt. There’s a limit to that, both physical and economic, and to the ultimate combustion temperature of readily available fuels.

Huge diesel engines can approach 50% efficiency, but most automobile engines operate down around 15%. Your average automotive engine is really a rather efficient furnace that happens to make a driveshaft rotate in its spare time. We’re stuck with that.

The physical world is hard. I get the impression that many futurists have been seduced by the ease of the virtual world. No, programming is not easy, but it doesn’t run up against physical constraints in the manner of combustion chemistry or aerodynamics. That’s why I don’t expect some breathtaking energy breakthrough that will conveniently make our problems go away.

We do have a lot of technologies that will help us towards a sustainable energy future, but they are trumped by habit, law, and vernacular design. We’re used to apparently cheap energy and behave as if it is actually cheap and endless. We’ve structured our lives around these false assumptions. Our laws governing transportation, subsidies, zoning, building codes, and foreign policy are based on these false assumptions. The past and present design of our buildings, transportation infrastructure, and electrical infrastructure are guided by these habits, laws, and assumptions. It will be a long, difficult fight against our emotional investment in obsolete ideas.

So no, with energy there will be no great leap forward. (Where have I heard that phrase before?) We have to accept incremental technological progress and equally incremental social progress. It will take more psychological skill than technical knowledge. Much of that psychological effort will be overcoming the propaganda of those who are making immense quantities of money from the status quo. It would be nice to think that some genius will come up with the great invention that will save the world. In reality it will be each of us out there, face to face, changing opinions, one person at a time.

Comments

[Lisa]

I agree with your premise that technology will not instantly save us from ourselves. The big obstacle out there is our own lifestyle. We need to look ahead and start figuring out better, more efficient, and DIFFERENT ways to move people and to change how we build our communities. In many ways we need to look back at the "olden days" before cheap oil to see how we used to live and work. It will mean significant changes to our society and we had better start planning now.