My bathroom tap has two seperate metal 'pipes' that supply the hot and cold water. After a while of using the tap, water starts to form on the cold water 'pipe' (which I understand) but it also forms on the outside of the hot water 'pipe'. Does anyone know why this happens? (The outside of the hot water pipe is hot and the cold one is cold- just to be clear that the pipes aren't insulators)
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In thermodynamics, most of the time, and also in this case, there are no absolute rules of what can happen and what cannot. Rather, thermodynamic systems behave statistically. This means, whenever you have some gas and a solid surface, there is always the chance that some gas particles will be in a bound state (condensated) on the surface, independent of the temperature. The probability of a bound forming is now determined by several factors, like the temperature of the gas and solid, the (partial) pressure of the gas, the energy of the bound state and probably some others which I did not think of.
The above means, that even if the pipe is hot, if there is enough water vapour in the air (meaning that the partial pressure of that vapour is high) and the air is warm enough itself, the chances of water condensating could be high enough that you can observe this process. On the other hand, the warmer the pipe is, the more thermal energy is available on it's surface and the higher becomes the probability of water evaporating, which is why condensation is more often observed on cold surfaces.
Remark: The same holds true for virtually every gas, like stated in the first paragraph. This means, you even have a certain chance of the nitrogen in the air condensating on your bathroom pipes, only this is very, very, very unlikely to happen. However, on a large enough metal surface, there will be, even at room temperature, single nitrogen atoms bound to the metal by adhesive forces.
