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Some teapots, like this one

enter image description here

Are made from thin steel which conducts the heat of the teapot quite well, meaning that you can't comfortable hold the sides while they're full of hot water.

Tonight I was having a pot of tea, and I'd left it for a while, so I touched to the sides of the pot to feel how hot it was, discovered that it still felt quite hot, and so poured myself another tea from it.

Now my question is, is my assessment that 'because the teapot is hot, the water inside is still hot' correct, or is it possible that the water inside would be cooler the the metal?

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  • $\begingroup$ I don't have the time (or these days the knowledge) to do the calculations necessary to post an actual answer, but my educated guess is the metal, having very high thermal conductivity and much lower SHC than the water, would have a temperature extremely close to (but less than) that of the water. (If there was a nonzero temperature gradient in the water, I think the metal would take the temperature of the hottest bit of water in contact with it, and assist with equalising temperature throughout the water.) $\endgroup$ – IanF1 Jun 9 '15 at 11:06
  • $\begingroup$ I'll first note that steel isn't a great conductor of heat, particularly compared to copper or silver. Now, if the heating element is inside the pot, the water heats up, the steel heats up, and the steel loses heat to the outside world. Given that heat from the water has to be lost to the outside world through the steel (OK, a simplifying assumption), the steel will always be at a lower temperature than the water. Actual design of the tea pot may impact this (e.g. where the heating element is). $\endgroup$ – Jon Custer Jun 9 '15 at 14:27
  • $\begingroup$ Just to make sure I understand (I don't drink tea): You're pouring the water into the teapot after heating it somewhere else, right? $\endgroup$ – Javier Jun 11 '15 at 1:55
  • $\begingroup$ @Javier some tea pots you set on a burner, others if you do that it'll tin the metal. Others have electric heating elements.. $\endgroup$ – user273872 Jun 11 '15 at 2:23
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Let's assume that the water, teapot and air are each a single temperature, but the temperatures may be different. The water cools by passing heat through the material of the teapot and then into the air. But, heat always flows from warm locations to cold locations, so for the heat to move from water to teapot to air, the first must be warmer than the second, which in turn must be warmer than the third.

If you let the temperatures in each material vary, then it's possible that this could be violated in specific, small locations (e.g. driven by falling, cooled water), but on the whole the answer will be the same.

Edit: another way to look at this is think of the initial condition, with the water hotter than the teapot, and the teapot being warmed by the water. For the teapot to get warmer, or the water to get colder, heat must transfer from the water to the teapot. But, as the temperatures get closer and closer, the heat transfer gets proportionally less and less (ignoring convection), with the heat transfer approaching zero as the temperature difference approaches zero.

A better physicist than I could prove that the temperatures will never match. However, even ignoring that, you can show that the temperatures will never pass each other. Let's say there is a moment when the temperatures are equal; the heat flow at that point will be zero, so the water cannot heat the teapot any further, and the teapot cannot cool the water any further.

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