Water from the clothes becomes a gas vapor. When clothes are hung, a greater surface of them is in contact with air and may be hit by a draft that brings dry air to them. Plastic fibers hold on to water poorly, and some of it will drain to the bottom because of gravity and drip out still in liquid form.
The water molecules are all vibrating randomly. They move around and bump into each other all the time. This molecular motion is the temperature. When it’s warmer, the molecules move and bump around faster. When it’s colder, they’re slower. If it gets hot enough, then the molecules move so fast that they can break free of the forces holding them and become lone molecules flying out on their own. That’s called evaporation. As for how this happens in your laundry without adding heat, remember that all these molecules are moving around randomly. Every so often, just by chance, a molecule will collide and get bumped in such a way that it comes away moving faster than it was before while the others are moving slower. That faster molecule can gain enough speed to break free and go off on its own. Over time, this eventually happens to each water molecule, and your laundry gets dry.
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