The people saying Maxwell's demon/"cannot separate" are mistaken. They've pattern-matched to the wrong concept. This is possible and is the way swamp coolers operate. They exploit the difference between ambient temperature and dew temperature of the liquid, say water. As long as relative humidity is below 100%, some water will evaporate, leaving your vat colder than environment. The separation is simple - the wind carries away the 100% humid water vapors, replacing it with fresh low-humidity air. You can then use the temperature difference to drive a stirling engine or something.
The point where your free energy ends is when you run out of water. You need to take your 100% humid air and cool it down somewhere else to get the water back by condensing it. In nature this happens automatically at nighttime when the heat radiates into the cold of space and air temperatures drop. If you are running a closed-loop cycle though, like on a spaceship, you need to provide your own source of environmental heat (the Sun) and your own heat sink (the cold of space), and at that point you should just be using a regular high-efficiency heat engine instead of this swamp cooler.