I have an idea for an energy source for a colony on a cold world with not enough solar power. Is my idea workable, or is it debunked as perpetual motion machine? Here is the set-up and my plan:
Scenario: Humanity has made giant steps since the landing on the moon. Better and faster space-travel allows travelers to reach Saturn and its moons in a month or less, and space colonies are emerging on Saturn's moons. One of those moons is Titan. Wind power is the main power source, since nuclear fusion has not yet been mastered, and solar energy is too scarce.
The problem: One of the colonies was established, out of necessity, in a location with little wind flow. As there is no other source of energy, and fusion has not yet been mastered, the colonists had to find an alternative.
The geography: The area is classified as a "desert": The air is dry. Yet, there is a river that flows, albeit too slowly for hydro-electric power. (The river is made of Methane, not water, and the humid air would contain Methane vapor). A similar set-up is the Red-Sea which crosses the rift between the Sahara and Arabian Peninsula: Although there is plenty of water, the air in the desert is dry.
The heat engine: The heat engine all by itself would be of no use, as no available heat sources were found in that location. In addition, coupling the engine to a heat pump which creates a heat gradient will not work either. That would classify the system as a perpetual motion machine which violates the second law of thermodynamics.
The work-around: The designer has realized the air is dry. If a heat pump will not work, then what about an evaporative cooler which takes Methane from the river? A cooler will use far less energy than a heat pump for the same cooling effect. It will create a heat gradient that may be sufficient to drive the heat engine. The heat engine will provide energy to drive the cooler and (hopefully) excess energy for the colony.
The energy source: In an enclosed system comprising a fluid and "dry" air above it, the fluid eventually evaporates until it fills the air above it and reaches the vapor pressure unique to each fluid, pressure and temperature. The overall temperature goes down because some heat becomes "latent heat" which made some fluid remain as vapor. Because all such systems end-up doing this, I can assume that a system with a fluid and dry air above it has some potential energy. At vapor pressure, the system is in equilibrium and has no potential energy, therefore energy is no longer extracted. On the other hand, the climatic set-up around the colony is not an enclosed system: Constant dry air is provided by the weather system. The river flows from a humid into a dry location. In other words, the set-up is still powered by the weather system.
Will my design solve the colony's energy crisis?