So, obviously there’s a mistake in my reasoning somewhere. Maybe I’ve pointed it out already I’m not sure.
You have a vat with some liquid. The ambient temperature X (which is low and not useful) keeps it at X temperature, a certain base level of energy. Through random collisions as temperature works some will get more energy than the average and get enough energy to evaporate. You separate those passively since it’s literally a phase change it could be done passively? (Leaving you with slightly less energy in the environment but which is in our case infinite since eventually you’d give the energy back before changing it a lot when doing useful things) with the now higher energy particles you have in a separate place?
It automatically turns high entropy useless environment thermal energy into higher more useful energy? (Cascade the same system many times for really high useful energy?)
This only works if the separation step can be done passively (or uses less energy than you gain from it) I guess but that seems maybe plausible considering the phase change?
Yep, that right here is the kind of pattern-matching you have to be careful about! Read what you wrote carefully:
The vat is literally cooler. You put a thermometer in it, will show a lower temperature than thermometer in air. This is not a fake effect “only shows lower because it’s wet”, it’s a real temperature. You put your stirling engine cool coil in the vat and hot coil in the air, you got yourself a temperature gradient. A small one, maybe 10 degrees C, but more than zero.