Archdruid. He's a smart and thoughtful guy who worries about some of the same things I worry about, though he tends to have decided they are all hopeless, whereas I tend to see society as having a lot more options than he perceives. He has read very widely and often comes up with interesting historical analogies that hadn't occurred to me, so he's well worth the spot in my reader.

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# Limits on the Thermodynamic Potential of Archdruids

I often read John Michael Greer, the Archdruid. He's a smart and thoughtful guy who worries about some of the same things I worry about, though he tends to have decided they are all hopeless, whereas I tend to see society as having a lot more options than he perceives.  He has read very widely and often comes up with interesting historical analogies that hadn't occurred to me, so he's well worth the spot in my reader.

Where he tends to go horribly wrong, and why I think his overall take on the subject is too negative, is when he tries to talk about physics. In a recent series of three posts:

He has been trying to argue that there are fundamental physical barriers to society surviving the transition away from fossil fuels, and getting horribly snarled up.

Now, I am not a working physicist, but I may well be the nearest thing that will admit to reading the Archdruid - I trained in Physics, have a PhD in the subject, and then went into Computer Science.  But the points at issue are pretty elementary here, so let me try to straighten the Archdruid out, and at least place something in the record for anyone that might be confused by his arguments.

In short, there are no fundamental physical barriers to a non-fossil-fuel based economy - the main problems are social, economic, and practical, not issues of physical law.

Here's the nub of his argument:

The second issue, though, is the one I want to stress here. It’s seen a lot less discussion, but it’s even more important than the issue of net energy, and it unfolds from the most ironclad of all the laws of physics, the second law of thermodynamics. The point that needs to be understood is that how much energy you happen to have on hand, even after subtracting the energy cost, doesn’t actually matter a bit when it comes to doing work. The amount of work you get out of a given energy source depends, not on the amount of energy, but on the difference in energy concentration between the energy source and the environment.

Please read that again: The amount of work you get out of a given energy source depends, not on the amount of energy it contains, but on the difference in energy concentration between the energy source and the environment.

Got that? Now let’s take a closer look at it.

Left to itself, energy always moves from more concentrated states to less concentrated states; this is why the coffee in your morning cuppa gets cold if you leave it on the table too long. The heat that was in the coffee still exists, because energy is neither created nor destroyed; it’s simply become useless to you, because most of it’s dispersed into the environment, raising the air temperature in your dining room by a fraction of a degree. There’s still heat in the coffee as well, since it stops losing heat when it reaches room temperature and doesn’t continue down to absolute zero, but room temperature coffee is not going to do the work of warming your insides on a cold winter morning.

And he then goes on to argue that since sunshine is dilute, not concentrated, it doesn't have very much usable energy in, and therefore cannot power civilization (eg via PVs or concentrated solar power).

The trouble here is that a) normal daily use of the term energy is different than it's technical use in physics, and b) the Archdruid is conflating two different issues - the potential for work due to the temperature difference of two things, and the spatial concentration of that potential.

Let's do a very brief review of the two main principles of thermodynamics that were worked out in the nineteenth century (basically coming about during the time when society was developing better and better steam engines, and engineers and scientists were working through the underlying physical principles that governed their operations).

The first is called "The First Law of Thermodynamics", or "Conservation of Energy".

Energy can neither be created nor destroyed. It can only change forms.

In any process in an isolated system, the total energy remains the same.

For a thermodynamic cycle the net heat supplied to the system equals the net work done by the system.

This basically says that there is some quantity in physical systems and it's conserved. Obviously, this would be less meaningful except for the fact that people had already worked out that various things were forms of energy - for example, a hot body (like the Archdruid's coffee) contains a certain amount of energy on account of it's temperature. If he throws the cup across the room, it will have some kinetic energy - one half of it's mass times the square of it's velocity, and so forth.

The big discovery, which was originally made empirically, was that the total amount of all these different forms of energy, in a closed or isolated system, is constant. The nineteenth century physicists didn't realize, and it's still not widely known outside of physics circles today, but there is actually a really deep theoretical reason for this. Noether's theorem, named after twentieth century mathematician Emmy Noether, says that any (differentiable) symmetry in a physical system must give rise to a conserved quantity. And the conserved quantity due to the time-translation invariance of physics is what gives rise to the conserved quantity of energy.  In other words, the fact that the laws of physics appear to work the same regardless of time - if you do your experiments carefully, you'll get the same answer regardless of which day, week, or year, you do them in, is what gives rise to the conservation of energy.

However, again, I warn that "energy" as used by physicists and other physical scientists - the conserved quantity arising out of physical law - and "energy" as used by non-specialists in daily life (and by economists in their literature) are subtly different - though they are measured in the same units.  Let's proceed to explore that.

The second law of thermodynamics can be defined in various ways:

There are many ways of stating the second law of thermodynamics, but all are equivalent in the sense that each form of the second law logically implies every other form. Thus, the theorems of thermodynamics can be proved using any form of the second law and third law.

The formulation of the second law that refers to entropy directly is as follows:

In a system, a process that occurs will tend to increase the total entropy of the universe.

Thus, while a system can go through some physical process that decreases its own entropy, the entropy of the universe (which includes the system and its surroundings) must increase overall. (An exception to this rule is a reversible or "isentropic" process, such as frictionless adiabatic compression.) Processes that decrease the total entropy of the universe are impossible. If a system is at equilibrium, by definition no spontaneous processes occur, and therefore the system is at maximum entropy.

A second formulation, due to Rudolf Clausius, is the simplest formulation of the second law, the heat formulation or Clausius statement:

Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature.

Informally, "Heat doesn't flow from cold to hot (without work input)", which is true obviously from ordinary experience. For example in a refrigerator, heat flows from cold to hot, but only when aided by an external agent (i.e. the compressor). Note that from the mathematical definition of entropy, a process in which heat flows from cold to hot has decreasing entropy. This can happen in a non-isolated system if entropy is created elsewhere, such that the total entropy is constant or increasing, as required by the second law. For example, the electrical energy going into a refrigerator is converted to heat and goes out the back, representing a net increase in entropy.

The exception to this is for statistically unlikely events where hot particles will "steal" the energy of cold particles enough that the cold side gets colder and the hot side gets hotter, for an instant. Such events have been observed at a small enough scale where the likelihood of such a thing happening is significant.[2] The mathematics involved in such an event are described by fluctuation theorem.

A third formulation of the second law, by Lord Kelvin, is the heat engine formulation, or Kelvin statement:

It is impossible to convert heat completely into work in a cyclic process.

That is, it is impossible to extract energy by heat from a high-temperature energy source and then convert all of the energy into work. At least some of the energy must be passed on to heat a low-temperature energy sink. Thus, a heat engine with 100% efficiency is thermodynamically impossible.

A fourth version of the second law was deduced by the Greek mathematician Constantin Carathéodory. The Carathéodory statement:

In the neighbourhood of any equilibrium state of a thermodynamic system, there are equilibrium states that are adiabatically inaccessible.

A final version of the second law was put to rhyme by Flanders and Swann[3], based on the Clausius statement:

Heat won't pass from a cooler to a hotter

You can try it if you like but you far better notter

'cos the cold in the cooler will get hotter as a ruler

'cos the hotter body's heat will pass to the cooler!

Cute.

Entropy was initially defined by physicists without knowing the fundamental basis for it, but later work discovered that entropy is basically the degree of disorder of the microscopic description of the system. It turns out that the universe apparently began in a fairly unlikely state (high order, low entropy), and now always evolves in the direction of more likely conditions (lower order, more entropy).

Now, the second law gives us some idea that not all energy (in the physicist sense) is equally useful. Since heat (a form of energy) won't flow, for example between two bodies at the same temperature, a room-temperature cup of coffee cannot be used to generate energy. In contrast, a body at a high temperature (relative to the environment) can be put to use. (By "put to use" here, we mean "made to do work"). So when the gasoline inside your car engine burns, it's at a much higher temperature than the environment, which is why a car engine can do lots of useful work. In particular, and what I think the Archdruid is trying to grope towards, the second law of thermodynamics can be used to prove a fundamental theorem on the thermodynamic limits of the efficiency of any process for turning heat into work:

The second law of thermodynamics puts a fundamental limit on the thermal efficiency of all heat engines. Surprisingly, even an ideal, frictionless engine can't convert anywhere near 100% of its input heat into work. The limiting factors are the temperature at which the heat enters the engine, $T_H\,$, and the temperature of the environment into which the engine exhausts its waste heat, $T_C\,$, measured in an absolute scale, such as the Kelvin or Rankine scale. From Carnot's theorem, for any engine working between these two temperatures:[4]

$\eta_{th} \le 1 - \frac{T_C}{T_H}\,$

This limiting value is called the Carnot cycle efficiency because it is the efficiency of an unattainable, ideal, reversible engine cycle called the Carnot cycle. No device converting heat into mechanical energy, regardless of its construction, can exceed this efficiency.

Examples of $T_H\,$ are the temperature of hot steam entering the turbine of a steam power plant, or the temperature at which the fuel burns in an internal combustion engine$T_C\,$ is usually the ambient temperature where the engine is located, or the temperature of a lake or river that waste heat is discharged into. For example, if an automobile engine burns gasoline at a temperature of $T_H = 1500^\circ F = 1089 K\,$ and the ambient temperature is $T_C = 70^\circ F = 294 K\,$, then its maximum possible efficiency is:

$\eta_{th} \le 1 - \frac{294 K}{1089 K} = 73.0%\,$

This is the fundamental problem with the luke warm coffee - it's temperature is very similar to the environment, so it doesn't have much potential to do work.  Not only is there not that much energy in the heat difference to begin with, but even what there is is doing to have a very small efficiency in the usage - say the room is at 70F = 294K and the coffee is at 80F = 304K, then the thermodynamic efficiency of a heat engine using the coffee is at most 1 - 294/304 = 3.3%.

And it's this amount of useful work that you can get out of something (the exergy in a fairly modern christening) that we really care about.  My observation is that ordinary daily use of the term "energy" means something like "The amount of useful work we could get out of this if we could do it at 100% efficiency".  That's roughly what we mean by the energy content of gasoline, for example.  So the luke warm coffee has much less useful energy than it appears, because the thermodynamic efficiency of using it is inevitably going to be so low.  In the modern coinage of "exergy = useful work obtainable from the system", the exergy content is much less than the energy content.

However, it's not the fundamental problem with sunlight.  By trying to use "concentration" to cover both thermodynamic potential to do work, and concentration in space, the Archdruid is getting confused. Sunlight is (pretty close to) black-body radiation at an effective temperature of the surface of the sun - around 5500K.  So the thermodynamic constraints on using sunlight to do work in an environment at the temperature of the surface of the earth are not an issue 1 - 294/5500 = 94%.  Practical efficiencies are far lower (for example PV panels generally achieve 10-20% efficiency, which is still an order of magnitude better than plants).

It is true that sunlight is dilute, but that's a different issue, and a practical engineering and economic one.  Basically, it comes down to the net energy of whatever collecting environment you have - it better take less energy to build and deploy it than you get out of it.  But look, really, the high positive net energy of solar panels was settled long ago.  Do a quick literature search on, say, net energy photovoltaic, and you'll come up with boatloads of relevant papers. For example, here's a 2004 paper by Richardson and Watt in Renewable and Sustainable Energy Reviews:

EYR values for three different PV products (a single multicrystalline silicon module, 2 kW rooftop grid-connected system, and a solar home system) are determined to be 4.8–13.9, many times the energy inputs required to fabricate the system.

Or, here's a table from Application of Life-Cycle Energy Analysis to PhotoVoltaic Module Design, a 1997 paper by Keoleian and Lewis, using very conservative PV solar efficiencies by modern standards:

The last column indicates that, at least in sunny places, you get many times the energy out that you put in, and even in Detroit, you get several times more.

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