Would that heat-engine provide power to the colony on Titan?

Question

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?

Answer 1

Enthalpy of vaporization of methane is very low - 5 times less than that of water. You will get about 5 kJ from 1 kg of methane. Even with low temperatures (about 100K ) "boost" to efficiency, it would not be above ~25-30%. So only 1.5kJ of energy from kg of evaporating methane would go to colony.

One household (about 2-4 people) here on Earth need about 10 kWt*h ~ 3.5 MJ of eneregy per day. On Titan we can multiply it by 10 (heating, oxygen, science). So by this rough approximation you need to evaporate 30t of methan per "hosehold" or ~10t (~20 m^3) per person in a day. That will produce 200-2000 millons m^3 of "wet air" per person per day or about 2-20 L/s.

Thats a lot, but doable.

But there is a catch: to make this scheme work you need a place with strong and costant winds to remove this huge amounts of wet air from a vast cooling fields. But this wind would be a more convinient and powerfull source of energy by itself. It would be times more efficient to build wind generators in this area. And if place is bad for wind generators - evaporation would not work (for long) since "wet air" will accumulate and prevent futher evaporation. Thats why nobody uses this scheme here, on Earth.

P.S. And you have to have a realy good explanation why this river does not evaporate by itself at first place. Most rivers in Sahara (there are some!) do not last for long (both in distance and time) becase of that.

P.P.S. all approximations are wild!

Answer 2

If spacecraft can reach Saturn in a month, then you have some sort of energy source which renders the problem moot (even if it is not fusion as per your OP, it has equal or greater energy density in order to propel spacecraft that quickly). The craft can orbit Titan and beam energy down via microwaves or lasers focused on cooperative power targets if you handwavium requires that your system remain in space (i.e. artificial back hole drive).

As for actually operating on Titan, most conventional heat engines will work far more efficiently due to the extreme cold temperatures. The Carnot equation depends on the temperature differential between the "hot" and "cold" reservoir, and the greater the differential the higher the efficiency. Since on Earth the "cold" side is atmospheric or room temperature, the only way to really boost efficiency is to run the hot end at the maximum temperatures the materials can handle. On Titan , the "cold" side is cryogenic, where ice is as hard as granite and things like methane are liquids in the open, so the temperature differential is far higher.

In simple terms, a heat engine on Earth is about 25% efficient (1- 300k/400k; 1-3/4 = .25) while the same engine on Titan is about 75% efficient (1-100k/400k; 1-1/4 = .75)

Issac Arthur has a very interesting (if long) video where he describes how this fundamental principle could make Titan the economic hub of the outer Solar System since the cold temperatures and the presence of an atmosphere (which makes heat rejection far easier than radiation alone) makes industrial processes using the Carnot cycle far more efficient. This also translates to far more efficient computing as well. His key takeaway is that people will not actually live on Titan, but simply live in orbit and supervise the work of the machines below.

So the real answer to your question is there is no need to create strange contraptions on Titan to extract energy from the local environment. Humans have not done that on an industrial scale since the Industrial revolution, and there is no need to do so in space either. The sort of energy needed to travel across interplanetary distances at high speed already means there is a surplus of energy available, and Titan provides a convenient "cold sink" for high efficiency industrial and computing operations to take place.

Answer 3

It sounds like you're trying to reinvent the Stirling Engine. If so, then yes it will work.

To operate the stirling engine merely requires a greater temperature differential than is ambient in the environment. As soon as that occurs the engine will run and energy can be extracted from the system.

Answer 4

As other answers have said, given enough resources (Methane), your proposed heat engine could work, however I wonder if there could be a more elegant design - especially considering that humans have mastered travel through the solar system.

Since, in your world, humans are now expanding to other planets and moons I think it likely that through the development process engineers would be working on ways to either encapsulate energy for when it is scarce or ways to transmit energy long distances. Since humans are traveling around the solar system in months and spread throughout it there would likely be some sort of infrastructure in place for cargo transport, etc.

If there is no reason that the colony has to be 100% self-sufficient (the energy has to come from Titan), you could take advantage of these cargo routes to transport either fuel or large batteries to colonies with scarce energy along with regular resupply missions. This could be one solution, but the next one I like better:

Wireless Solar Energy Transmission So, you're on Titan. It's cold, dark, full of methane, and you need energy... bad. Luckily the engineers have been working on solutions to maintain a flow of energy to all the colonies.

In a close orbit to the sun, you have an array of large solar collection devices. The concentrated energy is used to generate a laser of a specific wavelength that transmits energy to satellite devices spaced along routes through the solar system. Mirrors/Optic systems could create a constantly unobstructed pathway to all of the satellites as they move through their orbit (or in stationary orbit around another planet). After passing through a relay of these satellite devices, the laser ends its journey at a receiver on the destination planet/moon.

Disadvantages of a laser system such as energy loss through atmosphere wouldn't be an issue transmitting to Titan, but you would certainly not get all of the energy back. This would require a receiver on Titan many hundreds of meters across, and a substantial battery to store the energy as it comes in. Ideally, an unmanned mission would prepare the required infrastructure so that the colonists arrive with several months worth of energy already having been transmitted and stored in the battery.

Similar energy transfer can be done with Microwaves, and to my knowledge the energy conservation is much more effective with Microwaves since you aren't losing so much energy to visible light. Current systems can achieve up to 85% efficiency. Microwave however runs the risk of RF interference (which could be a problem unless the system is positioned away from communication channels) and the receiver would have to be larger than that of a laser.

Here are some stats on current wireless space-solar power systems for reference: