Wed. Nov 30th, 2022
Two single-cylinder steam engines.
enlarge / None of these steam engines come close to the Carnot efficiency.

Almost all modern physics comes down to understanding steam engines. Yes, we have all kinds of fancy laws about the universe and atoms, but thermodynamics rules them all (and not in Sauron’s benevolent dictatorship style). When thermodynamics hits you, you feel it. In a new theory paper, a few physicists have risked being beaten by nature. They have proposed a heat engine that can be practical – for some value of practical – and operate very close to the limits of physical law.

Carnot rules

A famous limit of thermodynamics is that heat engines, such as steam engines and combustion engines, must be less efficient than a Carnot heat engine (a heat engine cycle designed by French engineer Carnot). While the Carnot efficiency is very easy to calculate, it is very impractical to build an engine that works with that efficiency.

It’s not just the impractical mechanics of such an engine. The nature of the motor suggests that ideal operating efficiency is only achieved at zero power output. Not very useful, in so many words. But it gets even less useful than that. By diving into the details, you will notice that as the power output approaches zero, the fluctuations in the output power become very large. In other words, even if we could build such an engine, it would run erratically and drive the operator insane.

The source of the problem lies in how all heat engines work. It works by taking heat from an energy reservoir (a heat source) and delivering it to a cold region, extracting energy along the way. The heat energy is provided by particles or waves; in both cases, the trajectory they follow through the energy landscape is random. They only follow the route described by Carnot on average.

As our power output drops (and we get closer to the Carnot efficiency), the number of particles providing energy decreases to just one or two undergoing the cycle at a time. So the energy per unit time is given by the individual path of these one or two particles, which can be very different from the average. Therefore, the power fluctuates over time. In an ideal engine, these fluctuations reach infinity when the average power output reaches zero, where the average efficiency reaches the Carnot efficiency.

The back and forth Carnot

However, these results are for a heat engine that operates continuously. What about a motor that works cyclically? As it turns out, cycling the motorcycle allows for some remarkable features. First, it seems that the motors can be practical – we’ll understand what that means in a moment – even though they use the same series of thermal operations as a Carnot motor.

Cyclic heat engines seem to deliver a non-zero amount of energy over a finite time. In fact, they do better than that: their power output can be quite high if the power fluctuations get small. In the event that the fluctuations go to zero, the motor would operate at the Carnot efficiency.

Power delivery relies on reducing fluctuations, but it turns out a cyclic heat engine will too. The researchers show that the fluctuations do not increase as the total output power decreases. Instead, they are smoothed to a finite value.

Why is this happening? I think it’s a bit of skill. In a stationary heat engine, the operating conditions require that we follow the thermodynamic trajectory only a small number of particles at a time. We are subject to large fluctuations in power because the particles follow random paths. But when we cycle, there are periods when there are absolutely no particles in the system, and to make up for that, there must be more during the cycle, meaning their collective behavior is closer to the average.

To summarize, what we have now is not a heat engine with an average output power of zero and large random fluctuations. Instead, we have a heat engine with large familiar fluctuations (the output during the cycle) separated by known periods of zero output power.

A practical cycling Carnot?

I said the engine is practical and I stand by that statement. Motorcycles have many uses and can be found in unusual places. For example, enzymes are a kind of engine that works on the basis of chemical reactions. They are still subject to the Carnot efficiency. They, and other micromachines, are also engines that are more likely to cycle and therefore approach Carnot efficiency.

The researchers also calculated that their motor could be demonstrated using something like a glass bead held by optical tweezers. The optical tweezers can be used to work on the bead with a cycle initiated externally by changing the laser power or focal conditions.

These may not be the things that come to mind when you think of engines. But they are practical. Especially as we look to a future full of micromachines and enzymes that produce everything from food to fuel.

Physical Assessment Letters2018, DOI: 10.1103/PhysRevLett.121.120601 (About DOIs)

By akfire1

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