# Why does a Pewter mug keep a beverage hot better than a foam cup?

I know my subject sounds improbable and that's why I posted it. I helped my daughter with a science project for school. We tested five different materials to determine which would keep hot water hot, glass, ceramic, plastic, pewter and foam. To may amazement, the pewter did the best, though only slighter better than foam. I was so surprised I re-did the tests for the foam and pewter and got the same results. We placed boiling water in the cup and measured the temperature over a five minute period. The temp in the foam cup dropped about 24 degrees and in the pewter it dropped about 23 over the five minute period. All the others were a degree or two over that. I can't explain this and I am a chemical engineer. Can't find much about it on the Internet either.

• Were the various cups of the same shape and size? It's likely not, and as explained in the good answers already given, this would mean the experiment wasn't controlled for surface area exposed to evaporation. So it's possible no firm conclusions can be drawn about the effect of the cup material. The measurement variation could be within experimental error limits. – paisanco Feb 9 '15 at 4:58
• Also what was the surface of the table? a wooden table wouldn't let the material affect much, while an ice block would let the isolation have much more effect. – ratchet freak Feb 9 '15 at 8:57
• Good questions. Yes, the containers were relatively the same size/shape, though not exactly so. And the surface was a glass stove top. I think I have my answer now, due to this and other websites, but thanks for contributing. – user72718 Feb 9 '15 at 16:23
• Are you sure the pewter mug has solid walls? I can't find a reference to one with hollow walls and possibly a vacuum inside. An easy way to find out is to fill it with cold water (thus avoiding burnt fingers) and see if the outside is not as cold as expected. Or it may be too thin for that possibility. – Andrew Morton Feb 9 '15 at 19:51
• Try covering the top of the cup with cling film (or anything else so long as you use the same thing for every experiment). – Tim B Feb 10 '15 at 12:47

## 3 Answers

The metal mug will equilibrate with the water much faster than the foam mug will— but after that the heat has no place to go$^\dagger$ except to be transferred away through radiation or be lost as steam via natural convection (which does not depend on the material of the mug). It turns out that radiation plays a very small role as shown below:

Say each mug is a cylinder with diameter $10\ cm$ and height $10\ cm$. Inputting the temperature of boiling water ($373\ K$) and the surface area of the mug ($150 \pi\ cm^2$) into the Stefan-Boltzmann Law gives an approximation of the heat radiated away by the cup of 15 Watts. 5 minutes at 15 Watts = 4,500 J of energy radiated away, which we will call $Q$. Assuming you filled the mugs to the top, there is $250 \pi\ cm^3$ of water or a mass $m$ of $250 \pi\ g$. Since water's heat capacity $C$ is $4.18\ J/g\cdot K$ you can calculate the temperature drop $\Delta T$ due to radiation using the definition of heat capacity:

$$\Delta T= \frac{Q}{mC} =\ \frac{4,500\ J}{\left(250 \pi\ g\right)\left(4.18\ J/g\cdot K\right)}=1.3\ K$$

That is much less than the 23 degrees temperature drop you report, so the majority of the heat loss comes from evaporative cooling as suggested by Martin Beckett. That means the cooling rate is relatively unaffected by the material of the mug and instead depends mostly on the area of the water surface exposed to air. A great teaching opportunity about the different mechanisms of heat transfer!

$^\dagger$This is assuming no additional conduction to the table. If the table was made of metal you might see the effect you were expecting, since the heat would be able to conduct quickly through the pewter mug into the table.

• This seems to ignore convection of air as a heat transport method too. This may be material dependent since the higher thermal conductivity material would maintain a higher temp at the external surface. Air currents would thus draw more heat away. – ZSG Feb 9 '15 at 6:21
• @Rick Good point. I've updated it for clarity – pentane Feb 9 '15 at 14:06
• @ZSG true; I did ignore forced convection as I assumed the experiment was done indoors (relatively still air). – pentane Feb 9 '15 at 15:52
• These were some great comments and exactly what I needed. I did find another sight last night that basically discussed the same thing. It seems I was completely forgetting about the heat capacity of the containers and focusing too much on radiation from the cup to the environment, which is very small in any container due to air being such a poor conductor. – user72718 Feb 9 '15 at 16:24
• So the foam cup probably did worse because it's wider near the top, creating extra surface area compared to a pewter mug with a cylindrical interior? – ruakh Feb 10 '15 at 6:53

The heat loss from an open cup was probably dominated by evaporation so the material didn't have very much effect and was within the limits of your experiment.

• Actually, we got a significant difference between some of the materials. For example, the glass cup lost the most heat of all in the allotted time span, significantly more than the pewter and foam. The ceramic was next and then plastic. And this was of course repeated through multiple runs with consistent results. So I feel very confident that there is a statistical difference between the materials, though I haven't done the statistical analysis. – user72718 Feb 10 '15 at 16:28

The cup that insulates the best will minimize convention and present the hottest liquid at the surface, where the delta T between liquid and air will determine cooling.

The cup that conducts heat the best will carry heat from the top to the bottom and cause convection currents. The heat will spread more evenly throughout the liquid and the surface liquid will have a slightly lower temperature than with the best insulating cup. The delta T between liquid and air will be lower, even though heat content of the two cups of liquid were the same.

I would expect the insulated cup to cool faster if the mouth is the same size and shape and the liquid level is the same. A small change in air currents will have a big effect. Can you test with a lid? A floating disk of foam to fit each cup would do, and make measurements for 30 minutes.

That's my theory and I'm sticking to it!

• A metal cup may also mean that the whole system acts as a heat reservoir at a lower temperature, due to the heat capacity of the mug. If I get time I might run some numbers. – Chris H Feb 9 '15 at 12:11
• More great comments! I suspected the same and I plan to repeat the test for a longer period and perhaps introduce a lid as well, if I can find one that works. Very interesting experiment for a middle school science project. Not as intuitive as I expected. – user72718 Feb 9 '15 at 16:27
• I had a pair of students who tested different lids using the same type of styrofoam cup ( styrofoam, plastic and aluminum foil lids) and obtained inconclusive results doing a similar controlled experiment. Their research showed that styrofoam should be the best insulator, but they did not receive satisfactory results for any of the lids. They made some errors, but I also agree with @user72718 that it is not as intuitive as I expected. – suse Mar 3 at 4:54