The universe is in a cup of coffee but to understand rising sea levels, it’s helpful to look at tea.
The universe is in a glass of wine. So said Richard Feynman. It has been the focus of this website to concentrate instead on the universe in a cup of coffee, partly because it is much easier to contemplate a coffee over breakfast. However there are times when contemplating a cup of tea may be far more illuminating. Such was the case last week: if only a politician had paused for a cup of tea before commenting on rising sea levels.
There are many reasons to drink loose leaf tea rather than tea made with a bag. Some would argue that the taste is significantly improved. Others, that many tea bags contain plastic and so, if you are trying to reduce your reliance on single-use plastic, loose leaf tea is preferable. Until last week though, it had not occurred to me that brewing a cup of tea with a mesh ball tea infuser (or a similar strainer) was a great way to understand the magnitude of our problem with rising sea levels. If a stone were to enter a pond, the pond-level would rise; if a spherical tea strainer (full of loose leaf tea) were to be placed in a cup, the soon-to-be-tea level would rise.
Clearly, because we know our physics, we would not place a strainer of tea into an existing cup of hot water as we know the brewing process relies on diffusion and turbulence, not just diffusion alone. So what we more commonly observe in the cup is actually a tea-level fall as we remove the straining ball. Fortunately, we can calculate the tea level decrease, h:
My cylindrical tea mug has a radius (d) of 3.5cm. The radius (r) of the mesh ball is 2cm. We’ll assume that the tea leaves completely expand filling the mesh ball so that the ball becomes a non-porous sphere. Clearly this bit is not completely valid and would anyway create a poor cup of tea, but it represents a worst-case scenario and so is good as a first approximation.
Volume of water displaced = volume of mesh ball
πd²h = (4/3)πr³
A bit of re-arrangement means that the height of the tea displaced is given by
h = 4r³/(3d²)
h = 0.87 cm
This answer seems quite high but we have to remember that the mesh ball is not completely filled with tea and so the volume that it occupies is not quite that of the sphere. Moreover, when I check this answer experimentally by making a cup of tea, the value is not unreasonable. Removing the mesh-ball tea strainer does indeed lead to a significant (several mm) reduction in tea level.
The Blue Marble, Credit, NASA: Image created by Reto Stockli with the help of Alan Nelson, under the leadership of Fritz Hasler
What does this have to do with politicians? Last week a congressman from Alabama suggested that the observed rising sea levels could be connected with the deposition of silt onto the sea bed from rivers and the erosion of cliffs such as the White Cliffs of Dover. If only he had first contemplated his tea. Using a “back of the envelope” calculation similar to that above, it is possible to check whether this assertion is reasonable. As the surface area of the oceans is known and you can estimate a worst-case value for the volume of the White Cliffs falling into the sea, you can calculate the approximate effect on sea levels (as a clue, in order to have a significant effect, you have to assume that the volume of the White Cliffs is roughly equal to the entire island of Great Britain).
Mr Brooks comments however do have another, slightly more tenuous, connection with coffee. His initial suggestion was that it was the silt from rivers that was responsible for the deposition of material onto the sea bed that was in turn causing the sea level to rise. About 450 years ago, a somewhat similar question was being asked about the water cycle. Could the amount of water in the rivers and springs etc, be accounted for by the amount of rain that fell on the ground? And, a related question, could the amount of rain be explained by the amount of evaporation from the sea?
The initial idea that the answer to both of those questions was “yes” and that together they formed the concept of the “water cycle” was in part due to Bernard Palissy. Palissy is now known for his pottery rather than his science but he is the author of a quote that is very appropriate for this case:
“I have had no other book than the heavens and the earth, which are known to all men, and given to all men to be known and read.”
Attempts to quantify the problem and see if the idea of the water cycle was ‘reasonable’ were made by Pierre Perrault (1608-80) in Paris and Edmond Halley (1656-1742) in the UK. Perrault conducted a detailed experiment where he measured the rain fall over several years in order to show that the amount of rain could account for the volume of water in the Seine. Halley on the other hand, measured the amount of evaporation from a pan of heated water and used this value to estimate the evaporation rate from the Mediterranean Sea. He then estimated the volume of water flowing into that sea from a comparison to the flow of the water in the Thames at Kingston. Together (but separately) Perrault and Halley established that there was enough water that evaporated to form rain and that this rain then re-supplied the rivers. Both sets of calculations required, in the first place, back of the envelope type calculations, as we did above for the tea-levels, to establish if the hypotheses were reasonable.
If you missed the coffee connection, and it was perhaps quite easy to do so, the question that Halley studied concerned the rate of evaporation as a function of the water’s temperature. This is something that is well known to coffee drinkers. Secondly however, one of Halley’s experiments about the evaporating water was actually performed at a meeting of the Royal Society. It is known that after such meetings, the gathered scientists would frequently adjourn to a coffee house (which may have been the Grecian or, possibly more likely, Garraways). As they enjoyed their coffee would they have discussed Halley’s latest results and contemplated their brew as they did so?
What this shows is that sometimes it is productive to contemplate your coffee or think about your tea. Notice what you observe, see if you can calculate the size of the effect, consider if your ideas about the world are consistent with your observations of it. But in all of it, do pause to slow down and enjoy your tea (or coffee).