science history – Bean Thinking

Americano, Maxwell's demon — So innocent looking. But could an imaginary demon lurking within help us to understand more fully a major theory in physics?

Is there a way of preparing an Americano that can reveal a particularly knotty problem in physics with implications for information theory?

The question arises out of a field of physics, developed through the nineteenth century, that deals with energy and temperature: thermodynamics. It is the theory that describes how a hot coffee, left in a cold room, will eventually cool to the temperature of the (ever so slightly warmer) room. And though this may seem a trivial example, the theory is immensely powerful with applications from steam engines to superconductors. But it is back with the cooling coffee that we may find a demon, and it is worth finding out a bit more about him.

There are four laws of thermodynamics (the original three and then what is known as the ‘zeroth’ law). But it is the second that concerns us here. It can be phrased in a number of different ways but essentially says that there is no process for which the only result is the transfer of heat from a cold object to a hot one. To think about our coffee, the coffee will cool down to the same temperature as the room, but as the law describes, the room cannot get colder by giving its heat to the coffee cup (so the coffee gets hotter)!

It is in fact, one of the few places in physics where there is a ‘direction’ to time. For most of the laws of physics, time could run in the opposite direction without changing the effect, but not so for this one. The second law of thermodynamics is a definite provider for an arrow of time.

coffee clock, Rosslyn coffee — The clock at Rosslyn Coffee in the City of London. But the image alludes to a fundamental truth: the way that coffee cools is one of the few areas of physics for which it matters which way time ‘flows’.

But that is a digression. We ought to return to the demon in the coffee. The second law of thermodynamics seems to be based on our common sense (though perhaps that is because our common sense is formed within the laws of physics that determine the second law of thermodynamics). But with confidence in our common sense to understand the second law of thermodynamics, let’s do a thought experiment in which we make a strange type of Americano. Imagine a cup of coffee with an impermeable partition cutting through it. Into one half of the cup we pull a lovely, single origin, espresso. The crema rising onto the surface with some brilliant tiger striping on show. Into the other half of the cup we pour some water, initially at the same temperature as the coffee. We drill a small hole in the partition and watch what happens. Of course we know what happens. Ever so slowly, the coffee starts to get into the water and the water into the coffee until we are left with a balanced Americano on both sides with both sides at the same temperature.

Great, but now let us introduce the demon. Actually, he’s called “Maxwell’s Demon” because it was Maxwell who first proposed him (in ~1871), but we can call him anything we like. Perhaps he’s not a he at all. Our demon sits next to the small hole we have made in the partition and watches as the molecules travel towards the hole from the water’s side and the side holding the coffee. This demon is a bit of a trouble maker and so any fast moving molecules (hot) from the water he allows to get into the coffee and any slow moving molecules (cold) from the coffee he allows to get into the water. He does not allow slow molecules from the water into the coffee or fast molecules from the coffee into the water. Just to add to the mix, any coffee solubles he returns to the coffee allowing only water molecules through the hole in the partition.

If our demon exists, we would end up with a lot of very fast molecules on the coffee side (which will therefore be hotter) while the water would hold slower molecules (and be colder). We’d have a very hot espresso on one side of the partition and some luke warm water on the other. It’s not only a terrible Americano but a violation of the second law of thermodynamics! Which is worse?

Although he was proposed as a thought experiment, it is a problem with serious implications for the second law of thermodynamics (which otherwise seems to be a very good model of how things work). Because while we may not seriously consider an actual demon in the coffee, what stops some mechanical tool that we make from violating the second law, if the demon, in principle, could exist? Could the second law be wrong? Could there be a way of getting heat into our coffee from a cold room?

3D hot chocolate art on an iced chocolate, Mace, Mace KL, dogs in a chocolate — Art on a hot chocolate at Mace in KL. Well, what is your mental image of Maxwell’s demon?

The consensus has been that even were the demon to exist, ultimately he is powerless against the second law which does not get overturned by his presence. Because even if we could end up with a super hot espresso on one side of the barrier and cold water on the other side, this is not the whole system; the whole system includes the demon. And the second law applies to the whole system not the system minus the demon. So when we consider the energy (and entropy) of the demon in doing the work necessary to decide which molecules to let through and which to filter out, we find that work is done on the system (by the demon) and the entropy, the disorder if you like, of the whole system has increased (which is another way of phrasing the second law). Calm is restored, we get our Americano back, the laws of physics as we understand them are retained.

But Maxwell’s demon has not been completely exorcised yet, or at least, he is proving to be quite helpful. Because it turns out that there are methods for which the energy cost for the demon is minimal and the argument above no longer works. It seems we are back to square one. But even in that situation, it was realised that the demon has to record, make a note of, which molecules are fast and which are slow, which are coffee and which are water. It has led to an understanding that information has to be part of our consideration of thermodynamics. And as our ability to manipulate nanostructures and individual atoms improves, so experiments are able to explore how information ties into thermodynamics and why Maxwell’s demon still has not undone the second law yet. But it is here that we encounter another demon, the one that is found in the details, so if you are interested you can read more about it here.

Coffee as an art at Briki, Exmouth Market

exterior of Briki coffee London — Briki London on the corner of Exmouth Market

Traditionally made coffee always appeals to my sense of coffee history. Coffee made its way out of Ethiopea via Turkey and the method of brewing the finely ground coffee in a ‘cezve’ or ‘briki’ is one that goes back a long way. It’s therefore always interesting when a new cafe arrives on the scene that offers “Greek” or “Turkish” coffee on its menu. Briki, in Exmouth Market, opened in May last year and so it was only going to be a matter of time before I visited to try it out. Aesthetically Briki appealed to me as soon as I walked through the door. Spacious and with the bar along one wall, there are plenty of seats available at which to slowly enjoy your coffee. The cafe itself is almost triangular and the other two walls have windows running all along them. What better way to sit and enjoy the moment (and your coffee) than to gaze out a window? Still, given that I had gone to a cafe called ‘Briki’ and that it advertised “Briki coffee” on the menu behind the bar, it was obvious that I had to try the briki coffee. The coffee was rich, flavoursome and distinctive, well worth the time taken to savour it. There was also an impressive selection of food behind the counter and the dreaded “does it contain nuts” question was met with a friendly check of the ‘allergen’ folder. I was therefore able to also enjoy the lovely (nut free) chocolate cake. Briki definitely gets a tick in the “cafes with good nut knowledge” box on my categories list.

image from British Museum website — Folio 109b from an album of paintings showing Turkish sultans and court officials. Kahveci. A youth who serves coffee. He is holding a cup in each hand, circa 1620.
© The Trustees of the British Museum

However as I realised later, the coffee was not brewed in the traditional way but in a Beko coffee maker – a coffee maker specifically designed for optimising the brewing of Turkish coffee. The idea of the Beko is that it carefully controls and automates the entire brewing process so that you get a perfect coffee each time. But just how do you make a ‘perfect’ Turkish coffee?

A quick duckduckgo (it’s a mystery to me why has this verb failed to catch on while ‘to google’ is used so frequently) revealed two sets of instructions on how to make Turkish coffee. The first set, (including some otherwise very good coffee brewing websites) suggested ‘boiling’ the coffee repeatedly in the pot (cezve/briki). The second set, which seemed to be more specifically interested in Turkish coffee (as opposed to interested in coffee generally), were much more careful, even to the point of writing, in a very unsubtle way, “NEVER LET IT BOIL“. According to this second set of websites, the coffee in the cezve should be heated until it starts to froth, a process that begins at around 70C, far below the 100C that would be needed to boil it. Warming the cezve to 70C produces these bubbles and the lovely rich taste of the traditionally made coffee. Heating it to boiling point on the other hand destroys the aromatics* that form part of the flavour experience of coffee and therefore makes a terrible cup of coffee.

The contrasting instructions however led me to recall a discussion in Hasok Chang’s Inventing Temperature. Perhaps we all remember from school being taught how thermometers need two fixed points to calibrate the temperature scale and that these two fixed points were the boiling point and the freezing point of water. Perhaps this troubled you at the time: Just as with making coffee in a cezve, just how many bubbles do you need in order to say that the coffee (or water) is ‘boiling’? How were you supposed to define boiling? How much did it matter?

Cezve, ibrik, Turkish Coffee Creative Commons license — Cezve, image © http://www.turkishcoffee.us

It turns out that these questions were not trivial. There is a thermometer in the science museum (in London) on which two boiling points of water are marked. The thermometer, designed by the instrument maker George Adams the Elder (1709 – 1773) marked a lower boiling point (where water begins to boil) and an upper boiling point (where the water boils vigorously). The two points differed by approximately 4C. So how is it that we now all ‘know’ that water boils at 100C? And what was wrong with Adams’ thermometer? The Royal Society set up a committee to investigate the variability of the reported boiling point of water in 1776. Careful control of the heating conditions and water containers reduced the temperature difference observed between different amounts of boiling. However, as they experimented with very pure water in very clean containers they found that things just became more complicated. Water could be heated to 120C or even higher without ‘boiling’. They had, unintentionally, started investigating the phenomenon that we now know as ‘superheating‘. Superheating occurs when water is heated to a temperature far above its boiling point without actually boiling. What we recognise as boiling is the escape of gas (which is usually a mix of air and water vapour) from the body of the water to its surface. In order to escape like this, these bubbles have to form somehow. Small bubbles of dissolved air pre-existing in the water or micro-cracks in the walls of the container enable the water to evaporate and form steam. These bubbles of gas can then grow and the water ‘boils’. If you were to try to calibrate a thermometer using very pure water in very clean containers, it is highly likely that the water would superheat before it ‘boiled’, there just aren’t the ‘nucleation’ sites in the water to allow boiling to start. The Royal Society’s committee therefore came up with some recommendations on how to calibrate thermometers in conditions that avoided superheating which meant thermometers were subsequently calibrated more accurately and superheating (and improved calibration points) could be investigated more thoroughly.

Perhaps viewed in this way there are even more parallels between Turkish coffee and physics. It has been written that “making Turkish coffee is an art form“. It is a process of practising, questioning and practising again. The Beko coffee machine automates part of the process of making Turkish coffee. When it’s done well though, Turkish coffee is far more than just the temperature control and the mechanics of heating it. There is the process of assembling the ingredients, the time spent enjoying the coffee and the atmosphere created by the cafe in which you drink it. Coffee as art in Briki is something that I would willingly spend much more time contemplating.

Briki is at 67 Exmouth Market, EC1R 4QL

“Inventing Temperature”, by Hasok Chang, Oxford University Press, 2004

*Although these aromatics are part of what gives coffee such a pleasurable taste, they decay very rapidly even in coffee that is left to stand for a while, it is this loss of the aromatics that is part of the reason that microwaving your coffee is a bad idea. A second reason involves the superheating effect, but perhaps more on that another day.