Air raising

Small waves seen from Lindisfarne

How do clouds form? How does temperature vary with altitude, and what does coffee have to do with any of it?

You put a drop of alcohol on your hand and feel your hand get cooler as the alcohol evaporates, but what has this to do with coffee, climate and physics?

Erasmus Darwin (1731-1802) was the grandfather of Charles of “Origin of the Species” fame. As a member of the Lunar Society (so-called because the members used to meet on evenings on which there was a full moon so that they could continue their discussions into the night and still see their way home) he would conduct all sorts of scientific experiments and propose various imaginative inventions. Other members of the Lunar Society included Matthew Boulton, Josiah Wedgwood and Joseph Priestley. The society was a great example of what can happen when a group of people who are interested in how things work get together and investigate things, partly just for the sake of it.

One of the things that Darwin had noticed was that when ether* evaporates from your hand, it cools it down, just as alcohol does. Darwin considered that in order to evaporate, the ether (or alcohol or even water) needed the heat that was provided by his hand, hence his hand started to feel cooler. But then he considered the corollary, if water (ether or alcohol) were to condense, would it not give off heat? He started to form an explanation of how clouds form: As moist air rises, it cools and expands until the moisture in the air starts to condense into droplets, clouds.

hole in water alcohol

There are several cool things you can notice with evaporating alcohol. Here a hole has been created in a thin layer of coffee by evaporating some gin. You can see the video of the effect here.

As with many such ideas, we can do a ‘back of the envelope’ calculation to see if Darwin could be correct, which is where we could also bring in coffee. The arabica growing regions are in the “bean belt” between 25 °N and 30 °S. In the sub-tropical region of that belt, between about 16-24°, the arabica is best grown at an altitude between 550-1100 m (1800-3600 ft). In the more equatorial regions (< 10º), the arabica is grown between 1100-1920m (3600-6300 ft). It makes sense that in the hotter, equatorial regions, the arabica needs to be grown at higher altitude so that the air is cooler, but can we calculate how much cooler it should be and then compare to how much cooler it is?

We do this by assuming that we can define a parcel of air that we will allow to rise (in our rough calculation of what is going on)¹. We assume that the parcel stays intact as it rises but that its temperature and pressure can vary as they would for an ideal gas. Assuming that the air parcel does not encounter friction as it rises (so we have a reversible process), what we are left with is that the rate of change of temperature with height (dT/dz) is given by the ratio of the gravitational acceleration (g) to the specific heat of the air at constant pressure (Cp) or, to express it mathematically:

dT/dz = -g/Cp = Γa

Γa is known as the adiabatic lapse rate and because it only depends on the gravitational acceleration and the specific heat of the gas at constant pressure (which we know/can measure), we can calculate it exactly. For dry air, the rate of change of temperature with height for an air parcel is -9.8 Kelvin/Km.

contrail, sunset

Contrails are caused by condensing water droplets behind aeroplanes.

So, a difference in mountain height of 1000 m would lead to a temperature drop of 9.8 ºC. Does this explain why coffee grows in the hills of Mexico at around 1000 m but the mountains of Columbia at around 1900 m? Not really. If you take the mountains of Columbia as an example, the average temperature at 1000 m is about 24ºC all year, but climb to 2000 m and the temperature only drops to 17-22ºC. How can we reconcile this with our calculation?

Firstly of course we have not considered microclimate and the heating effects of the sides or plateaus of the mountains together with the local weather patterns that will form in different regions of the world. But we have also missed something slightly more fundamental in our calculation, and something that will take us back to Erasmus Darwin: the air is not dry.

Specific heat is the amount of energy that is required to increase the temperature of a substance by one degree. Dry air has a different specific heat to that of air containing water vapour and so the adiabatic lapse rate (g/Cp) will be different. Additionally however we have Erasmus Darwin’s deduction from his ether: water vapour that condenses into water droplets will release heat. Condensing water vapour out of moist air will therefore affect the adiabatic lapse rate and, because there are now droplets of water in our air parcel, there will be clouds. When we calculate the temperature variation with height for water-saturated air, it is as low as 0.5 ºC/100 m (or 5 K/Km), more in keeping with the variations that we observe in the coffee growing regions†.

We have gone from having our head in the clouds and arrived back at our observations of evaporating liquids. It is fascinating what Erasmus Darwin was able to deduce about the way the world worked from what he noticed in his every-day life. Ideas that he could then either calculate, or experiment with to test. We have very varied lives and very varied approaches to coffee brewing. What will you notice? What will you deduce? How can you test it?


*ether could refer to a number of chemicals but given that Erasmus Darwin was a medical doctor, is it possible that the ether he refers to was the ether that is used as an anaesthetic?

†Though actually we still haven’t accounted for microclimate/weather patterns and so it is still very much a ‘rough’ calculation. The calculation would be far better tested by using weather balloons etc. as indeed it has been.

¹The calculation can be found in “Introduction to Atmospheric Physics”, David Andrews, Cambridge University Press



Why politicians should drink loose leaf tea

Coffee Corona

Notice the rainbow pattern around the reflected light spot?
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:

A schematic of the tea brewing process

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.

Earth from space, South America, coffee

Assuming we are truly interested in discovering more about our common home, we can gain a lot through contemplating our tea.
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.”

Reflections on a cup of tea.

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).

Strumming along on a coffee

coffee at Watch House

What links a coffee to a guitar amplifier?

What links a coffee to music by the likes of Eric Clapton and Jimi Hendrix?

As we sit back and enjoy the aroma from our coffee, we may rue the fact that our precious brew is evaporating away. We know from experience that hot coffee evaporates faster than cold coffee and we may dimly remember the physics that explains why this is. But have you ever stopped to consider that it is this bit of your coffee that forms a link between your drink and those famous guitarists?

The link concerns the mechanism behind the evaporation. To evaporate out of the coffee, a water molecule needs to overcome a certain energy barrier, let’s call it W, in order to escape. Given that W is constant, the more energy a water molecule has, the greater its likelihood of escape. So we could say that the probability of a water molecule escaping the coffee goes as exp{-W/kT} which means, the higher the temperature, T, the smaller the ratio W/kT and hence the greater the probability (because the exponential is raised to a negative power and hence is a dividing factor). The k is a constant known as the Boltzmann constant.

thermometer in a nun mug

Hot coffee evaporates more. Something that Halley had noticed in his experiments at the Royal Society

Now think about how the amplifiers used by many musicians work. It seems that many guitarists favour valve amplifiers owing to the type of sound they produce. Certainly Clapton and Hendrix were well known for their use of valve amps. A valve amp works by a process of thermionic emission in which electrons are ‘evaporated’ from a hot metal wire before being accelerated to a positively charged plate. This bit is the ‘valve’. In order to escape the metal wire, the electrons have to overcome a certain energy barrier, let’s call it Ω. Just as with W and the coffee, this barrier is a property of the metal that the electron evaporates from. The more energy an electron has (the higher its temperature), the greater the likelihood of it escaping the metal filament and fulfilling its role in the valve amplifier. Hence the mathematics describing thermionic emission is the same as the mathematics describing the evaporation in your coffee cup¹ and the probability of thermionic emission goes as exp{-Ω/kT}.

Now the size of the barrier is of course different in the two cases (Ω is much larger than W) which is why you have to plug in your amplifier to the electricity supply rather than just let it sit on the table top. But this is a difference of size rather than of kind. It is another of those connections between your coffee cup and the world that can be stranger than you may at first think.

If you think of a connection between your coffee and an interesting bit of physics, why not share it in the comments section below.

¹This discussion originally appeared in (and was adapted from) the Feynmann Lectures on Physics, Vol. 1

Theme on a V60

bloom on a v60

V60 bubbles. There is much to be gained by slowing down while brewing your coffee.

Preparing a coffee with a pour-over brewer such as a V60 is a fantastic way to slow down and appreciate the moment. Watching anti-bubbles dance across the surface as the coffee drips through, inhaling the aroma, hearing the water hit the grind and bloom; a perfect brewing method for appreciating both the coffee and the connectedness of our world. The other week, while brewing a delightful Mexican coffee from Roasting House¹, I noticed something somewhat odd in the V60. Having placed it on the kitchen scales and, following brewing advice, measured the amount of coffee, I poured the first water for the bloom and then slowly started dripping the coffee through. Nothing unusual so far and plenty of opportunity to inhale the moment. But then, as I poured the water through the grind, I noticed the scales losing mass. As 100g of water had gone through, so the scales decreased to 99g then 98g and so on. It appeared the scales were recording the water’s evaporation.

science in a V60

Bubbles of liquid dancing on the surface of a brewing coffee.

It is of course expected that, as the water evaporates, so the mass of the liquid water left behind is reduced. This was something that interested Edmond Halley (1656-1742). Halley, who regularly drank coffee at various coffee houses in London including the Grecian (now the Devereux pub), noted that it was probable that considerable weights of water evaporated from warm seas during summer. He started to investigate whether this evaporating vapour could cause not only the rains, but also feed the streams, rivers and springs. As he told a meeting of the Royal Society, these were:

“Ingredients of a real and Philosophical Meteorology; and as such, to deserve the consideration of this Honourable Society, I thought it might not be unacceptable, to attempt, by Experiment, to determine the quantity of the Evaporations of Water, as far as they arise from Heat; which, upon Tryal, succeeded as follows…”²

Was it possible that somehow Halley’s demonstration of some three hundred years ago was being replicated on my kitchen scales? Halley had measured a pan of water heated to the “heat of summer” (which is itself thought provoking because it shows just how recent our development of thermometers has been). The pan was placed on one side of a balance while weights were removed on the other side to compensate the mass lost by the evaporating water. Over the course of 2 hours, the society observed 233 grains of water evaporate, which works out to be 15g (15 ml) of water over 2 hours. How did the V60 compare?

Rather than waste coffee, I repeated this with freshly boiled water poured straight into the V60 that was placed on the scales. In keeping with it being 2017 rather than 1690, the scales I used were, not a balance, but an electronic set of kitchen scales from Salter. The first experiment combined Halley’s demonstration with my observation while brewing the Mexican coffee a couple of weeks back. The V60 was placed directly on the scales and 402g of water just off the boil was poured into it. You can see what happened in the graph below. Within 15 seconds, 2 g had evaporated. It took just a minute for the 15g of water that Halley lost over 2 hours (with water at approximately 30 C) to be lost in the V60. After six minutes the rate that the mass was being lost slowed considerably. The total amount lost over 12 minutes had been 70g (70ml).

evaporation V60 in contact with scales

A V60 filled with 400g of water just off the boil seemed to evaporate quite quickly when placed directly on the scales.

Of course, you may be asking, could it be that the scales were dodgy? 70g does seem quite a large amount and perhaps the weight indicated by the scales drifted over the course of 12 minutes. So the experiment could be repeated with room temperature water. Indeed there did appear to be a drift on the scales, but it seemed that the room temperature water got moderately heavier rather than significantly lighter. A problem with the scales perhaps but not one that explains the quantity of water that seems to have evaporated from the V60.


Hot water (red triangles) loses more mass than room temperature water (grey squares).

Could the 70g be real? Well, it was worth doing a couple more experiments before forming any definite conclusions. Could it be that the heat from the V60 was affecting the mass measured by the electronic scales? After all, the V60 had been placed directly on the measuring surface, perhaps the electronics were warming up and giving erroneous readings. The graph below shows the experiment repeated several times. In addition to the two previous experiments (V60 with hot water and V60 with room temperature water placed directly on the scales), the experiment was repeated three more times. Firstly the V60 was placed on a heat proof mat and then onto the scales and filled with 400g of water. Then the same thing but rather than on 1 heat proof mat, three were placed between the kitchen scales and the V60. This latter experiment was then repeated exactly to check reproducibility (experiment 4).

You can see that the apparent loss of water when the V60 was separated from direct contact with the scales was much reduced. But that three heat proof mats were needed to ensure that the scales did not warm up during the 12 minutes of measurement. Over 12 minutes, on three heat proof mats, 14g of water was lost in the first experiment and 17g in the repeat. This would seem a more reasonable value for the expected loss of water through evaporation out of the V60 (though to get an accurate value, we would need to account for, and quantify the reproducibility of, the drift on the scales).

V60 Halley

The full set: How much water was really lost through evaporation?

Halley went on to estimate the flow of water into the Mediterranean Sea (which he did by estimating the flow of the Thames and making a few ‘back of the envelope’ assumptions) and so calculate whether the amount of water that he observed evaporating from his pan of water at “heat of summer” was balanced by the water entering the sea from the rivers. He went on to make valuable contributions to our knowledge of the water cycle. Could you do the same thing while waiting for your coffee to brew?

Let me know your results, guesses and thoughts in the comments section below (or on Twitter or Facebook).

¹As this was written during Plastic Free July 2017, I’d just like to take the opportunity to point out that Roasting House use no plastic in their coffee packaging and are offering a 10% discount on coffees ordered during July as part of a Plastic Free July promotion, more details are here.

²E Halley, “An estimate of the quantity of vapour….” Phil. Trans. 16, p366 (1686-1692) (link opens as pdf)