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I'm familiar with why water condenses on cool surfaces.

However, why does hot/warm food cause surfaces to sweat/condensate?

For example, if you put a warm (such as panini pressed) sandwich on a plate, then place the plate on the table that is cooler than the sandwich, water will collect in a liquid form under the plate/on the table.

What causes water to become liquid or to collect here? I would think that the heat would cause the water to evaporate...

Edit: Another way to perform this experiment yourself is with toasted bread or Pop-tarts. I have found the most success with a paper plate when using objects with a low specific heat. If you use food stuffs containing more water (with a higher specific heat) like lasagna and other pastas, the same effect can be achieved with stone, ceramic and glass plates.

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When water is close to the hot panini, it is in equilibrium as vapour. When that vapour reaches the cold plate, it is in equilibrium as liquid, and so condenses. That it condenses on the plate is to do with nucleation theory - it's hard for a droplet to condense freely, but with a nucleation site such as an imperfection on a plate, it can act as a seed for a water droplet.

Edit: I admit I misread the question at first, and didn't see you meant under the plate.
As for why droplets form under the plate, I suspect this is due to the energy cost of forming a droplet. In forming a droplet, you gain energy from being in the favorable phase, this scales with $r^3$. However you lose energy at the surface, which scales with $r^2$. Hence for small droplets, $r\rightarrow 0$, the energy cost scales with $1/r$.

So while you may have water vapour, that could reduce its energy by condensing into water, to get to that lower energy state, it must get past the nucleation barrier. By heating the water vapour, you give the water more energy, and hence it is more likely that it can jump over the barrier to forming droplets, and hence can lower its energy by condensing.

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