## Sunday, November 04, 2007

### Le Chatelier's principle and nature's adaptation

The discussion about the ocean carbon sink and Henry's law inevitably evolved into chemistry, especially the question how various concentrations in the equilibrium respond to external changes. I would like to say a few words about an important principle that is respected by all these processes, namely Le Chatelier's principle.

The principle says that
reactions that determine the equilibrium values of many quantities - such as concentrations, temperature, pressure, or volume - respond to an external change so that they partially undo the initial external perturbation.
An example. Let us add CO2 into the ocean. There exist various reversible chemical reactions in the ocean such as
CO2 + OH- <=> HCO3-.
This reaction, much like others, can transform the compounds on the left hand side to those on the right hand side, or vice versa. Under fixed conditions, detailed science decides how many ions of HCO3- there are vs. how many pairs of CO2 and OH- there are. The reaction will go in one of the directions in order to reach the prescribed equilibrium.

But let us try something more complicated. Let us add CO2 into the ocean. The question is how various concentrations will change. The principle will tell us which way the reactions will go. Well, we added CO2 so its concentration surely increased. But according to the principle, all other players will try to make the right reactions so that the original increase of CO2 will look smaller (although still positive).

So it is obvious that the reaction will run in the forward direction: some CO2 that we added will react with the OH- ions and create the HCO3- ion. This is the right answer, according to the principle, because this reaction reduces the CO2 concentration. On the other hand, you can easily see that it increases the concentration of HCO3- because it is produced while it decreases the concentration of OH- because it is consumed by the reaction, together with CO2.

There are other reactions such as
H3O+ + OH- <=> 2 H2O.
Obviously, if OH- decreases, then this reaction will run in reverse i.e. backwards, in order to produce some OH- that was consumed elsewhere. That means that the concentration of H3O+ will increase. The more H3O+ ions we have, the more acidic the solution is (the smaller pH it has because this is how pH is defined). So you can see that one of the effects of adding CO2 into the upper ocean is to reduce its pH. It was 8.17 around the year 1800, now it is around 8.10. It will stay above 7.8 at least until 2100. It will still be significantly alkaline (above 7), if you care.

La Chatelier's principle therefore implies that if we add XY, the compounds, ions, heat, pressure or other things that occur on the opposite side of reactions than XY will increase while the compounds, ions, heat, or other things that occur on the same side of reactions as XY will decrease.

Some people can't live without a video lecture about the principle.

Generalization of the principle and the climate

We may say that Nature always tries to adapt. It always adjusts various quantities so that the effects of the external changes are distributed among all players and reduced. If you insert or increase wakalixes, whatever it is, the reactions will run in such a way that the increase in wakalaxies is partially consumed by all players.

Because even chemists can use it not only for concentrations but also for energy or pressure, you might think that the principle is probably much more general. And you would be right. It applies to all stable systems. Below, we will even explain that it is important in economics.

One possible way to describe Le Chatelier's principle is to say that feedback mechanisms in stable systems are negative. When you add CO2, various processes that consume it (such as photosynthesis) become more frequent. So the ultimate increase in CO2 will be lower than if those processes didn't exist. For the concentration of CO2, it is essentially a standard example of the principle in action. No one doubts it.

However, the principle also applies to other quantities including heat. On the Wikipedia page about the principle, it is the second example. If you increase the temperature, the principle guarantees that reactions that consume heat and cool the system down (endogenic reactions) will be encouraged while the heat-producing reactions (exogenic reactions) will be suppressed. The result is that the external increase in temperature is reduced by the internal reactions.

This principle surely applies to ordinary chemical reactions. But there are probably not too many relevant reactions like that that occur in the atmosphere and change its temperature. What about the clouds and other water-related physical effects that are probably more crucial? If we increase the temperature as an external parameter by the greenhouse effect, will they try to magnify the temperature change or will they, on the contrary, reduce it? If the principle could be applied to clouds, one of the answers would be that the bare greenhouse warming would be reduced by the effects of clouds. But is it true?

The answer depends on the question whether the whole system is thermodynamically stable. If it is stable, La Chatelier's principle still works. On the other hand, unstable systems may be described in a different, equivalent way: they are able to exponentially inflate a certain quantity: they are able to run out of control.

What about the clouds? Well, I think that the observations make it rather likely that the clouds are a stable system. For example, the temperature during the glaciation cycles never started to run out of control. It had the tendency to stay in a certain interval. If it is true that the responses of clouds on the external temperature and CO2 concentration were a good description of the effective laws of physics governing these processes, it follows that we deal with a stable system. Le Chatelier's principle must apply and feedbacks must be negative.

It means that something like Lindzen's adaptive iris effect must take place. Now, Lindzen's iris effect is just one possible mechanism how it can occur and I can't promise you that this is exactly what happens. But I think that much more general principles of physics make it extremely likely that the main result - namely that clouds and other things provide us with a negative feedback - is true.

By the way, Roy Spencer recently submitted a new article showing that some hypothetical positive feedbacks were probably misdiagnosed because the cause and its effect were confused. It is based on previously published peer-reviewed work of his team.

If you care about a related question, the iris effect as described by Richard Lindzen works like this. Higher temperatures increase precipitation at places where the air goes up. That leads to a reduced number of water molecules that are ready to form cirrus clouds. The number of cirrus clouds decreases. Because these high cirrus clouds are generally warming the Earth, you see that the effect of clouds and rains is to reduce the warming we started with: they are a negative feedback.

While the environmentalists are obsessed with positive feedbacks, we see that most feedbacks in Nature, especially those that decide about the evolution in extreme situations and in the long run, are negative feedbacks. Of course that there exist positive feedbacks in certain situations. But the idea that positive feedbacks dominate or that they are the ones who win at the end simply contradicts basic laws of thermodynamics.

The principle in economics

In the case of chemistry and thermodynamics, we saw how various quantities respond to external perturbations. A moment ago, we suggested that La Chatelier's principle may be much more general. Are there "established" examples outside chemistry where it is important? Of course there are. Analogous mathematics describes many other systems, including systems in economics.

In 1947, Paul Samuelson - an uncle of Lawrence Summers - introduced Le Chatelier's principle to economics. As a graduate student at Harvard, Samuelson was taught many things by Edwin Bidwell Wilson, a polymath. Thermodynamics was among them. Samuelson's PhD thesis was thus largely based on Willard Gibbs' 300-page-long 1876 paper on the equilibrium of heterogeneous substances.

For his building of quantitative pillars of statics (as well as dynamics) of economic science, Samuelson received the second economics Nobel prize in 1970.

Samuelson is a fair guy so he, of course, used the term "Le Chatelier's principle" even in economics. What does the principle explain in economics? For example, it explains why the elasticity of short-term demand is lower than the elasticity of long-term demand.

Well, I must explain a few words. Something is elastic if its relative change is higher than the relative change of things that are not so elastic. ;-) Here we talk about the elasticity of demands. As you can see, demands are elastic if people are ready to buy much more or much less of something if the conditions change.

For example, food demand is not elastic in rich countries. Everyone needs to eat almost every day so the demand is pretty much fixed. In very poor countries, people are used to starve so that the food demand is more elastic there. ;-) Nevertheless, food demand is not too elastic. Analogously, energy and oil demand is not too elastic either because energy is comparably essential. This is why these products are volatile: their price may wildly fluctuate.

On the other hand, there are things that people buy in the long run rather than every day. Their price is more stable while the demand is more elastic. Why is it so? Why is the long timescale associated with a high elasticity of the demand and rather constant prices? Well, it is because in the long run, there are many more possible processes that may consume (or stop to consume or produce or stop to produce) these products. It follows that the elasticity of the demand for these long-term things is higher.

Equivalently, the price of these things is much more stable because the market knows that small price variations may easily change the demand dramatically - because there are many channels or reactions available in the long run - and restore equilibrium of supply and demand.

Typos, parrots, and consensus

Le Chatelier's principle is an important observation about reality. Finally, I want to use it to show the nature of the "scientific consensus" and the ways how the information propagates in certain corners. Note how the principle is spelled. It is not too surprising that certain people can misspell it. Well, some people surely write
Le Chatlier's principal.
Note that there are two typos in it. Click the link above. You will see four links pointing to websites with this double mutation (plus one Reference Frame that you shouldn't count for obvious reasons). The first one are fascists at "DailyKos" while the last one are their equally communist comrades at "Socialism or Your Money Back". It turns out that Google didn't show you the original source, namely this 2005 article by David Archer at RealClimate.ORG: search for "principal" to see that his double typo was no one-time event but a way how he really wants to spell it.

Just to compare: search for the correctly spelled principle to see that none of the top 100 hits links to pages written by communist activists even though they have written 3/5 of the doubly-mutated pages.

The message is that a misleading text written by one activist that has many errors, misconceptions, and typos is routinely copied and parroted by all other activists in his political wing. This is how consensus science works: a lousy text by one scientist below the average is simply copied among thousands of his political allies who are completely unable to think independently. It's not surprising that most conclusions of similar processes are absurd. A rational observer knows that there is no non-trivial consensus of 2,500 people in certain questions but rather a consensus of 1 or 2 average scientists followed by 2,499 or 2,498 parrots.

And that's the memo.

#### 2 comments:

1. can you discuss more about how typhoons or hurricanes are formed in relative to Le Chatelier's Principle? thank you.

2. I don't think that the principle is relevant for them; indeed, the growth of tropical cyclones is an example of positive feedbacks that allow the configuration of winds to strengthen. Well, it's only a temporary process and the cyclones ultimately decay, too.