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I put some wet Polyester clothes outside for the night (the clothes were washed by hand with pretty cold water -maybe around 4°C- and wringed by hand so there was still water dropping of them when I put them outside). It was -4°C went I put them. One hour later I checked the clothes and they were totally frozen. In the morning (before sun rise) the clothes were dry : it was -6°C. The sky was clear (almost no clouds) and there was no wind.

I am quite surprise that my clothes can dry in less than 10 hours with such a low temperature. This answer explains that the process is called sublimation but it doesn't explain where does the energy needed for the water to sublimate comes from ? In my case there was no sun, no wind, no temperature above 0°C.

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The energy came from the surrounding environment at -6°C. Put microscopically, temperature describes the distribution of energies of the ice molecules within the frozen clothes and the air molecules interacting with the clothes. Through random collisions, ice molecules occasionally obtained sufficient energy to break their bonds with adjacent ice molecules and launch into the atmosphere. In general, everything around you is mixing because of these thermal fluctuations.

Put thermodynamically, a process occurring at constant temperature and constant pressure is driven by minimization of the Gibbs free energy $G=U-TS$, where $U$ is the internal energy, $T$ is the absolute temperature, and $S$ is the entropy. There's a tremendous entropy increase associated with an ice molecule leaving its rigid structure and entering the relatively low-humidity atmosphere, where there are many more potential configurations. This large value of $S$ is what drives solids and liquids to have a nonzero vapor pressure at nonzero temperatures even if their temperature is insufficient for boiling. In general, all condensed matter around you is evaporating/sublimating, although the rate may be minuscule.

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