Elusive Entropy

partial mixWe’ve all heard it. We think we understand it: entropy is a measure of disorder. Combined with the Second Law of Thermodynamics—that the total entropy of a closed system may never decrease—it seems we have a profound statement that the Universe is destined to become less ordered.

The consequences are unsettling. Sure, the application of energy can reverse entropy locally, but if our society enters an energy-scarce regime, how can we maintain order? It makes intuitive sense: an energy-neglected infrastructure will rust and crumble. And the Second Law stands as a sentinel, unsympathetic to deniers of this fact.

A narrative has developed around this theme that we take in low entropy energy and emit a high entropy wake of waste. That life displays marvelous order—permitted by continuous feeding of this low entropy energy—while death and decay represent higher entropy end states. That we extract low entropy concentrations of materials (ores) from the ground, then disperse the contents around the world in a higher entropy arrangement. The Second Law warns that there is no going back: at least not without substantial infusion of energy.

But wait just a minute! The preceding paragraph is mostly wrong! An unfortunate conflation of the concepts of entropy and disorder has resulted in widespread misunderstanding of what thermodynamic entropy actually means. And if you want to invoke the gravitas of the Second Law of Thermodynamics, you’d better make darned sure you’re talking about thermodynamic entropy—whose connection to order is not as strong as you might be led to believe. Entropy can be quantified, in Joules per Kelvin. Let’s build from there.

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The Energy-Water Nexus

The principal challenge of this century, in my view, will be adapting to a life without abundant, cheap fossil fuels. It has been the lifeblood of our society, and turns out to have some really fantastic qualities. The jury is still out as to whether we will develop suitable/affordable replacements. But additional challenges loom in parallel. Water is very likely to be one of them, which is especially pertinent in my region. For true believers in the universality of substitution, let me suggest two things. First, come to terms with the finite compactness of the periodic table. Second, try substituting delicious H2O with H2O2. It has an extra oxygen atom, and we all know that oxygen is a vital requisite for life, so our new product will be super-easy to market. Never-mind the hydrogen peroxide taste, and the death that will surely visit anyone foolish enough to adopt this substitution. Sometimes we’re just stuck without substitutes.

Substitution silliness aside, water and energy are intimately related in what has been termed the Energy-Water Nexus (see for example the article by Michael Webber from this conference compilation; sorry about the paywall). We’ll explore aspects of this connection here, touching on pumping water, use of water for the production and extraction of energy, and desalination. As glaciers and snowpack melt and drought becomes more common in the face of climate change, our water practices will need to be modified, hitting energy right in the nexus.

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Blow-by-Blow PV System Efficiency: A Case Study for Storage

A short while back, I described my standalone (off-grid) urban photovoltaic (PV) energy system. At the time, I promised a follow-up piece evaluating the realized efficiency of the system. What was I thinking? The resulting analysis is a lot of work! But it was good for me, and hopefully it will be useful to some of you lot as well. I’ll go ahead and give you the final answer: 62%. So you could peel away now and risk using this number out of context, or you could come with me into the rabbit hole…

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Solar Data Treasure Trove

I have not kept it secret that I’m a fan of solar power. Leaving storage hangups aside for now, the fact that the scale of available power is comfortably gigantic, that perfectly efficient technology exists, that it’s hard-over on the reality axis (vs. fantasy: it’s producing electricity on my roof right now), and that it works well almost everywhere—what’s not to like? Did you trip over that last part? Many do. In this post, we’ll look at just how much solar yield one may expect as a function of location within the U.S.

The ancient Mayans laboriously accumulated a substantial set of observational data on solar illumination across America well ahead of the present need. Okay, it wasn’t actually the ancient Mayans. It was the National Renewable Energy Lab (NREL), who embarked on a 30-year campaign beginning in 1961, covering 239 locations across the U.S. and associated territories. Imagine this. How many people were even cognizant of solar power in 1961? Yet the forward-thinking scientists at NREL appreciated the value of a solid baseline dataset way back then. This level of foresight seems akin to the Mayans constructing a calendar going all the way to 2012. That’s all I’m saying. It’s a gift from the past.

I have often consulted and enjoyed the product of this work over the years—called the NREL Redbook, or more formally, the Solar Radiation Data Manual for Flat Plate and Concentrating Collectors. But with a snazzy blog post as motivation, I have taken it up a notch and produced a variety of graphical representations of the dataset to explore what it can tell us. Let’s begin the guided tour.

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Do the Math Turns One: Place Your Orders

One year ago today, Do the Math was born with a post on the absurdity of continued growth—in this case illustrating a Galaxy-consuming civilization in a mere 2500 years. Within a month, the site was getting thousands of pageviews per day, as I cranked out a backlog of thoughts and analysis surrounding the energy challenges we face.

In the process, adhering to a weekly schedule forced me to perform many new calculations on topics I had not previously explored very deeply. So besides being a cathartic experience, I gained new understanding, finding the exercise of constructing the alternative energy matrix to be particularly clarifying. One of the major lessons for me has been that while the physical scale of any alternative energy resource is important—and sometimes a showstopper—more often it’s the practical limitations that form the biggest barriers.

Finding the time and (mental) energy to keep the blog rolling has been challenging, but it’s you folks who inspired me to keep trucking. Knowing that each post would be read by thousands, and knowing that I could look forward to some excellent and thought-provoking (although sometimes just provoking) comments made the enterprise worthwhile.

At this point, I have dropped the cadence to bi-weekly, and my list of future topic ideas is slowly being whittled down. Many comments in the past have requested that I write a post about issue or another. I invite you to submit requests (even if repeated) in the comment forum below. Note that I might not have the background, interest, or time to invest if serious analysis is required. But there is some chance I’ll take the bait—and the idea may already even be on my list! Please refer to the Guide to Posts for a refresher of what’s been covered already.

Also, I think it fitting on this first anniversary to extend a note of gratitude to Asher Miller of the Post Carbon Institute for inspiring me to start writing, and for putting me in touch with the fine folks at the Energy Bulletin. The EB editors: Bart Anderson, Kristin Sponsler, and Simone Osborn offered early guidance and good advice (plus instant readership) that was vital to getting Do the Math off the ground. So a hearty thanks to these folks! 1.5 million pageviews later, their contributions have clearly had an impact.

And thanks to you, the readers, for your role in making this a successful and rewarding endeavor.

Heat Pumps Work Miracles

Part of the argument that we cannot expect growth to continue indefinitely is that efficiency gains are capped. Many of our energy applications are within a factor of two of theoretical efficiency limits, so we can’t squeeze too much more out of this orange. After all, nothing can be more than 100% efficient, can it? Well, it turns out there is one domain in which we can gleefully break these bonds and achieve far better than 100% efficiency: heat pumps (includes refrigerators). Even though it sounds like magic, we still must operate within physical limits, naturally. In this post, I explain how this is possible, and develop the thermodynamic limit to heat engines and heat pumps. It’s a story of entropy.

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Spectral Extravaganza: The Ultimate Light

What do you get when you cross an astronomically-inclined physicist with concerns over energy efficiency in lighting? Spectra. Lots and lots of spectra. In this post, we’ll become familiar with spectral characterization of light, see example spectra of a number of household light sources, and I’ll even throw in some mind-blowing photos. In the process, we’ll evaluate just how efficient lighting could possibly be, along the way understanding something about the physiology of light perception and the definition of the increasingly ubiquitous lighting measure called the lumen. Buckle your physics seat-belt and prepare to think like a photon.

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My Neighbors Use Too Much Energy

From www.christmasvacationcollectibles.com

I have described in a series of posts the efforts my wife and I have made to reduce our energy footprint on a number of fronts. The motivation stems from our perception that the path we are on is not sustainable. Our response has been to pluck the low-hanging fruit, demonstrating to ourselves that we can live a “normal” life using far less energy than we once did. We are by no means gold medalists in this effort, but our savings have nonetheless been substantial. Now we shift the burden off of ourselves, and onto our neighbors. You don’t have to run faster than the bear—just faster than the other guy. In this post, I summarize our savings relative to the national average, add a few more tidbits not previously covered, put the savings in context, and muse about ways to extend the reach of such efforts.

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Easing Off the Gas

The Do the Math blog series has built the case that physical growth cannot continue indefinitely; that fossil fuel availability will commence a decline this century—starting with petroleum; that alternative energy schemes constitute imperfect substitutes for fossil fuels; and has concluded that a very smart strategy for us to adopt is to slow down while we sort out the biggest transition humans have ever faced. The idea is to relieve pressure on the system, avoid the Energy Trap, and give ourselves the best possible chance for a successful transformation to a stable future. Since building this case, I have described substantial adaptations in our home energy use, but have not yet addressed the one that bears most directly on the immediate problem: transportation and liquid fuels. Let’s take a look at what can be done here.

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