Material: the question asked at the counter is the wrong one
How much heat does the cup take from the coffee?
Start the scene or choose a stage. The animation simplifies the mechanism; what follows gives the details and the available references.
An espresso of 30 grams has the specific heat of water: its thermal mass, the mass multiplied by the specific heat, is 125 joules per kelvin. A porcelain cup of 150 grams is worth about 120. Thermally, the cup weighs almost as much as the coffee it receives.
Read the stages without animation
- A 30 g espresso at 90 °CAn espresso of 30 grams has the specific heat of water: its thermal mass, the mass multiplied by the specific heat, is 125 joules per kelvin. A porcelain cup of 150 grams is worth about 120. Thermally, the cup weighs almost as much as the coffee it receives.
- Cold cup: 56 °CPoured into this cup at 20 °C, the coffee would fall to 56 °C if everything equalized; between 52 and 61 °C over the whole range of published specific heats. This is a calculation, and an upper bound: the wall does not equalize at once and the cup also loses heat to the air.
- Preheated to 60 °C: 75 °CThe same cup preheated to 60 °C takes much less heat from the coffee: it would fall to 75 °C, between 74 and 77 depending on the values used.
- Thinner, 60 g: 71 °CA thin cup of 60 grams starting at 20 °C leaves the coffee at 71 °C. Between porcelain, stoneware and glass, the difference at serving is not the material: it is the mass. A thick glass cup takes more heat from the coffee than a thin porcelain one.
- Over what thickness?Thermal diffusivity, the conductivity divided by the product of the density and the specific heat, says how far the heat enters while one pours. In ten seconds: 2.5 to 7 mm in porcelain, the whole wall; 2.3 to 2.5 mm in glass; 6.4 mm in stainless steel, which equalizes at once and then conducts the heat toward the hand.
To remember: at serving, the heat that the cup takes from the coffee depends on its mass and its specific heat; conductivity governs only the slow leak that follows.
Read the full article and its sources ↓
People always ask which material keeps the heat. The right question is a different one, and it changes the answer: how much heat does the vessel take from the coffee at the moment it is poured. These are not the same physics, and they do not point to the same cups.
Three quantities are enough. Density says how much a given volume weighs. Specific heat says how much energy it takes to warm one kilogram by one degree. Thermal conductivity says how fast heat crosses the wall. The first two govern the loss at serving, that is, what happens in the ten seconds when the coffee arrives. The third governs the loss afterward, and what the hand feels.
The calculation that clarifies everything is that of thermal mass, which is the mass multiplied by the specific heat and is counted in joules per kelvin. An espresso of 30 grams has the specific heat of water, or about 4,180 joules per kilogram per kelvin: its thermal mass is 125 joules per kelvin. A porcelain cup of 150 grams is worth about 120 joules per kelvin. The cup therefore weighs, thermally, about as much as the coffee it receives. This single ratio explains almost everything we observe.
One must draw the unsettling consequence. Between porcelain, stoneware and glass, the difference at serving is not the material: it is the mass. A thick glass cup takes more heat from the coffee than a thin porcelain one, whatever their respective conductivities.
The published values, the cooling calculation, and a correction to make to a source
A warning first. There is not, to our knowledge, a published set of measurements on tableware porcelain. The available values concern technical porcelains, those of electrical insulators classified by the IEC 60672 standard, which cover ten formulations and therefore give wide ranges. One database gives 600 to 1,000 joules per kilogram per kelvin; Spence and Carvalho cite 753 for porcelain and 782 for ceramic, from a commercial database. Neither measured a cup.
- Technical porcelain2,300 to 3,000 kg/m³, specific heat of 600 to 1,000 J/(kg·K), conductivity of 1.8 to 6.5 W/(m·K). Hard tableware porcelain is fired at about 1,400 degrees, therefore vitrified and non-porous.
- Soda-lime glass2,400 kg/m³, 720 to 800 J/(kg·K), 1.0 to 1.1 W/(m·K), expansion of 8.8 to 9.0 µm/(m·K).
- Borosilicate 3.32,230 kg/m³, conductivity 1.2 W/(m·K) at 90 degrees, expansion 3.3 µm/(m·K). This expansion, three times lower, is the whole difference: it is what lets it withstand boiling water without cracking.
- 304 stainless steel7,930 kg/m³, specific heat close to 500 J/(kg·K), conductivity 16.2 W/(m·K) at 100 degrees, ten times that of a ceramic.
- Expanded polystyrene0.030 to 0.040 W/(m·K), fifty to two hundred times less than a ceramic. It is an insulator in the strict sense.
Now the calculation. If everything equalized, an espresso at 90 degrees poured into a 150 gram porcelain cup at 20 degrees would fall to 56 degrees. With the same cup preheated to 60 degrees, it would fall to 75 degrees. With a thin 60 gram cup starting at 20 degrees, to 71 degrees. Across the whole published range of specific heat, the first number goes from 52 to 61 degrees, the second from 74 to 77, the third from 67 to 74. These are calculations and not measurements, and they are moreover upper bounds, since the wall does not equalize instantly and the cup also loses heat to the air.
Over what thickness does the heat enter while one pours? The answer lies in thermal diffusivity, that is, the conductivity divided by the product of the density and the specific heat. In ten seconds, heat penetrates porcelain to a depth of 2.5 to 7 millimeters depending on the values used, that is, at least the thickness of a cup wall. Over the time of a serving, the whole wall therefore warms up, and its whole mass counts.
Soda-lime glass gives 2.3 to 2.5 millimeters, the same order. Stainless steel gives 6.4 millimeters, more than the thickness of a metal cup: it equalizes at once, then conducts toward the hand.
The correction. Spence and Carvalho write in 2019 that Pyrex would be the most suitable cup material for keeping the drink hot, on the grounds that its conductivity is the lowest. The argument does not hold for serving. Conductivity governs the slow leak to the outside, not the heat taken from the coffee while it is poured, which depends on mass and specific heat, which the three materials compared have close to each other. A heavy glass will cool an espresso more than a light porcelain.
In this plateThe 15 sections
- 01Three things we must stop confusing
- 02The handleless cup, and the holder that takes on the status
- 03The Ethiopian sini, and a ceramic route older than coffee
- 04Europe does the opposite: it adds a handle and removes the holder
- 05The tazzina, and what the texts really say
- 06Material: the question asked at the counter is the wrong one
- 07Preheating, porosity, and two beliefs to sort out
- 08Shape: the only solid measurement in the file, and its counterexample
- 09Color, weight, rim thickness: three very unequal beliefs
- 10The cupping bowl, the only coffee vessel to be standardized
- 11Contemporary shapes: what we buy is a well-drawn hypothesis
- 12Asia, and vessels made for the nose
- 13The disposable cup, which is a plastic object
- 14The largest survey ever made, and why it does not settle the matter
- 15What can be said in the end, and what cannot
The table of contents, with the first sentence of each section