The problem teapot
A few weeks ago, while having lunch with colleagues, one of them was complaining about his problems with his morning tea. So desperate he was to get his cup, he kept tipping the teapot to steeper and steeper angles in an attempt to increase the rate of pouring. Unfortunately, when he did so, the flow out of the spout became chaotic and, rather than having a nice cup of tea, he had a mess on the table. Another colleague suggested (sensibly) that it was a problem with the air-hole at the top of the teapot, not enough air was getting into the pot to enable the tea to flow smoothly out. In fact, my colleague’s tea pot problem turned out to have a different cause that will be featured in the Daily Grind in a few weeks. However, it did get me thinking about the purpose of the air hole in take-away coffee cups.
On the lid of a take-away cup are two holes. One, for drinking from while in a rush to get from A to B, the other, a very small air inlet hole that allows the coffee to flow nicely from the drinking hole. The requirement for such an air inlet has been known for millenia, however it was not understood why it was needed. Traditionally it was explained by saying that “nature abhors a vacuum”, the idea being that the coffee could not leave the cup because if it did so it would leave a vacuum which nature ‘does not allow’.
The lid of a take-away cup has two holes. One for drinking from, the other to let air in.
An immediate problem with such an argument is that it implies that coffee has a will; nature ‘does not want’ a vacuum. Indeed for Rene Descartes (of “I think therefore I am” fame) this was a key problem with the traditional explanation. Descartes died in Stockholm in 1650, although for twenty years before that he had lived in Holland. For Europeans, the Dutch were fairly fast off the mark in terms of the introduction of coffee into their society. They had managed to get hold of a coffee plant in 1616 but only started properly growing coffee for themselves (in Ceylon!) in 1658, a few years after Descartes’ death. It is therefore unlikely that Descartes ever had the opportunity to try much coffee. Instead, when Descartes thought about the importance of air holes, the example that he used was a wine cask. In ‘The World‘, written in about 1632 he states “When the wine in a cask does not flow from the bottom opening because the top is completely closed, it is improper to say, as they ordinarily do, that this takes place through ‘fear of a vacuum’. We are well aware that the wine has no mind to fear anything; and even if it did, I do not know for what reason it could be apprehensive of this vacuum…”
The space behind a swimming fish is immediately filled with water as the fish moves forward.
For Descartes, the reason that an air hole was needed in the wine cask was not because nature hated a vacuum but because, on the contrary, nature was completely ‘full’ of matter. Whether that matter was wine, air or the material that made up the barrel, the world was full of ‘stuff’, meaning that if wine came out of the cask the air that it displaced had to go somewhere. Having nowhere else in the universe to go, this displaced air would have to go into the region of the cask that the wine had just vacated. Descartes compared this movement of air into the top of the cask to the displacement of water by fish as they swam through water. We may not notice the water in front of the fish moving to the back as the fish swims through the water but we know that the water must fill the empty space left by the moving fish. In the same way we do not perceive the air to flow from the outlet of the wine cask to the top of the barrel, but we know that it must (because, Descartes thought, it had nowhere else that it could go).
This explanation had far reaching consequences for Descartes world view. He could explain gravity and the motion of the planets as a consequence of the planets moving in a giant vortex of a substance around the Sun. The image of the solar system as a giant cup of coffee being stirred is one that the Daily Grind is sure to return to at some point. For the moment though, we need to step back and think. We know that the universe is not ‘full’ in the sense meant by Descartes and so this part of his explanation must be wrong, but why is it that blocking the air inlet hole stops the flow of water out of the cup?
Whether coffee leaves the cup or not depends on a balance of forces
Think about the schematic shown here. Gravity is pulling on the mass of coffee in the cup through the drinking hole. Air pressure is acting against this pull, pushing the coffee back into the cup (if you ever wanted a demonstration of how powerful air pressure can be, try sealing an empty water bottle before coming down a mountain or at the start of the descent in a plane). There is also air pressure inside the cup acting downwards on the coffee. With the air hole open, this air pressure is fairly equal to that outside of the cup. The inside air pressure cancels the outside air pressure, gravity wins and the coffee comes out. Imagine now closing the air hole. No air can get into the cup so, after a little coffee leaves, the air pressure inside the cup drops to less than the air pressure outside of the cup. This time, the air pressure outside the cup pushes the coffee back into the cup more than gravity pulls it out and the coffee stays in the cup. Can we test this explanation? One way to test the theory would be to somehow change the pressure inside the cup. Using two identical cups (which I got from the very friendly people with good coffee at Iris and June), the video below shows two experiments. In the first, both cups are filled with the same amount of cold ‘coffee’ (no coffee is ever wasted in these videos, dregs are recycled). The second experiment shows one cup holding cold coffee, one holding steaming coffee. Why might these experiments support the theory that it is air pressure that keeps the coffee in? Perhaps you can think of better experiments, or improvements to this one, let me know in the comments section below, but most of all, enjoy your coffee while you do so.
(note that the cups had got a bit water damaged through practise runs before filming. Note also that for this experiment to be meaningful, you would need to repeat the measurements many times so that you can build up a statistical picture, but that would make the video quite boring).