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.
[Physics] Why does a Pewter mug keep a beverage hot better than a foam cup
home-experimentthermodynamics
Best Answer
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.