Principles of Energy Conversion

Thermodynamics was one of my favorite subjects in school–it was elegant, compelling, and instructive about so many aspects of life. But one thing it was not was intuitive. In fact, thermodynamics can make predictions that sound downright nutty to someone who’s never heard them before. But one of the beauties of the subject is that once you learn it, you see examples all around you in daily life.

Thermodynamics is also a very important subject for those of us who want to make electricity from nuclear energy, and for the consumers of electricity out there who want to understand how their electricity is generated.

There are two basic laws of thermodynamics–the first, simply put, is that energy is always conserved. No matter what you do, the total amount of energy doesn’t change–it just changes forms. Sounds pretty good! Why are we worried about an energy crisis? If the energy never goes away, then it should all be floating around somewhere waiting for us to use it again, right?

Well, that’s where the second law of thermodynamics comes in, and it says, simply put, that energy is always degraded. So every time you change energy from one form to another, you are degrading it, and it is less useful. What does it mean to “degrade” energy? It means that you can extract less and less useful work from it, until finally you can’t extract any at all…

Work, power, energy, electricity, heat–what do they all mean? What do they have in common? Let’s quickly define them: work, heat, and electricity are all forms of energy. All work is energy, but not all energy is work. All heat is energy, but not all energy is heat (although it all gets there). Power is the rate at which energy flows–some rate of energy per unit time. So we measure the work rate of an engine in power, but you can also measure the rate at which heat energy flows in terms of power as well. Electricity is also a form of energy, which can quite easily be turned into work, and work can easily be turned into electricity. In each case, you want to turn work into electricity while turning as little into heat as possible–the inverse is true as well. It’s very easy to turn either work or electricity into heat, but rather difficult to turn heat into work or electricity.

Are you getting the idea that maybe heat isn’t the most useful form of energy? Then you’re on the right track. Heat (or thermal energy) is the energy in the random motion of molecules. It is disordered kinetic energy, the energy of motion. Work and electricity are ordered kinetic energy–all the molecules of the shaft of an engine moving the same way, or all the electrons in a wire moving the same way. It is easy to turn order into disorder (you should see my office) but more difficult to turn disorder into order.

Why worry about all this? Because with a nuclear reactor we make heat–thermal energy–and we want to turn it into work (turning a shaft) and then into electricity (the shaft turns an electrical generator). How much of the heat can be turned into electricity?

The classic engineering answer to everything–it depends. In this case, it fundamentally depends on how hot the heat source is, and how cool the “sink” the heat will be rejected to is. Whoa! What’s a heat sink? Why does it have to be cold? Well, let me cover a little ground first.

Back in the early 1800s, there was a French engineer named Sadi Carnot, who wanted to know how to make the most efficient engine he could (the one that would make the most work for a given amount of fuel). Unfortunately, Carnot didn’t have the nice convenient laws of thermodynamics to guide him. He didn’t even have a correct understanding of matter or thermal energy. Which makes his discoveries even more amazing.

Carnot used to watch waterwheels. He watched the water flow over a wheel and turn it, and the wheel would grind wheat or some other activity. Carnot imagined attaching another waterwheel to the first one, but the second wheel would lift the water back up again after it had fallen. He wondered if he could ever build a system where he could lift up more water than had fallen to drive the first wheel. Intuition says no, but he wanted to know why. Of course, we know there would be friction between the wheel bearings and so forth, but he imagined a perfect wheel with no friction, and he realized that the VERY BEST he could do would be to lift an equal amount of water as had fallen. It just couldn’t get any better than that.

Then he applied some of his reasoning to engines–how much energy could be extracted as work from heat? It turned out that even in a perfect engine, only a certain amount of energy could be extracted as directed, ordered energy from an undirected, disordered thermal energy source. He imagined a perfect engine that could do this, and unsurprisingly, that engine is still called a Carnot cycle.

It turned out that the whole answer to how much work (ordered energy) could be extracted from heat (disordered energy) depended on how how the original thermal energy source was, and how cold the sink to which the unconverted thermal energy (original thermal energy minus work energy) would be rejected. If the hot side was hot and the cold side was cold, you could extract a certain amount. The hotter the hot side, the more work could be extracted. The colder the cold side, the more work could be extracted. But between any two temperatures, there was only a certain amount of work that could be extracted, even by a perfect engine.

The equation turned out to be really simple. The fraction of work that could be extracted was one minus the sink temperature divided by the source temperature.

 begin{displaymath} eta_{text{thermal}} = 1 - frac{T_{text{low}}}{T_{text{high}}} end{displaymath}

where nth is the work fraction, T(low) is the sink temperature, and T(high) is the source temperature. Let’s say we had a perfect Carnot cycle where the high temperature side was boiling water at 100°C, and the low side was almost freezing water at 2°C. How much work could we extract? First we have to use the absolute temperature scale, measured in Kelvins. 100°C is 373 K, and 2°C is 275 K. So plugging those numbers in we get:

 begin{displaymath} eta_{text{thermal}} = 1 - frac{275}{373} = 0.262 end{displaymath}

Wow–only 26% of the heat could be turned into work? That’s not very much. So we want to get the high side hotter, and the cold side colder. But let’s say, for sake of argument, that 2°C is about as cold as we can reasonably hope for on Earth. You can get colder, but the water turns to ice, and it’s much harder to reject heat to ice than to water (little problem with the flow). So let’s leave the cold side at 2°C (275 K).

We must get the hot side hotter. And getting the hot side hotter is the principle concern of the nuclear engineer. He/she wants to convert as much of the energy generated from fission to electricity, and so must get the reactor to generate the heat at as high a temperature as can be practically achieved. By accomplishing this, the reactor will make more electricity, reject less heat to the environment, and in general have superior economic performance. I’ll talk more about how to do this in some unconventional ways in an upcoming post.

For those of you who would like to understand all of this a lot better than I have explained, check out The Mechanical Universe, an excellent scientific series that explains so many physical concepts in a visual and compelling manner. Episode 46 will explain more about Carnot and his cycle. The programs can be viewed online for free after a brief registration. You’ll love it!



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