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How do steampunk civilizations get lifting gas?

Inspired by the above question I was tempted to suggest collecting the gases rising from public toilets.

I know that human gaseous emissions contain varying proportions of oxygen, nitrogen, carbon dioxide, hydrogen and methane.

https://en.wikipedia.org/wiki/Flatulence#Production,_composition,_and_smell

Some of these are lighter than air and some are heavier than air.

Judging by answers to this question https://chemistry.stackexchange.com/questions/61140/why-dont-heavy-and-light-gases-separate-in-the-atmosphere it would be possible to engineer an environment that allows the gases to separate.

Question

By removing turbulence due to draughts, can I rely on the lighter gases such as hydrogen and methane rising from the toilets where they can be collected. Will the heavier sink to the floor where they can be drained away? If not, how can I most efficiently separate them in situ without using chemistry or endangering the clientele?

Not without any additional means.

In the chemistry question that you mentioned the selected answer discussed entropy as one of the reasons gases won't separate in the atmosphere. This means that even in the absence of turbulence gases in the atmosphere would remain mixed.

However, you can use non-chemical means to separate gases:

1. Gravity. Different gases are indeed distributed differently in the atmosphere. But you need to go a few kilometers higher to see any noticeable increase in concentration of lighter gases. You can put your gas mix into a fast centrifuge, and in the center of this centrifuge gas would be richer in hydrogen, helium and other light gases. By repeating the process you can get those gases reasonably clean.




2. Temperature. Different gases have different condensation points. In the extreme cold, only hydrogen and helium will remain gaseous. Methane, on the other hand, would condensate at a higher temperature (-161C) than the air (-194C).




3. Molecule size. Using membrane filter you can separate different gases. Fortunately, hydrogen and helium molecules and atoms are small and should be easy to separate.

Yes, it can be done but it's not especially easy.

For a mixture of gasses in a gravitational field there are two opposing tendencies: (1) Light gasses will tend to collect at the top of a container and heavier gasses at the bottom and (2) Entropy will tend to mix the gasses uniformly.

We can't control entropy, but we can control gravity. So, either start with a giant planet (Jupiter does much better at separating gasses than Earth) or use a centrifuge. The latter may be more practical in most cases, so let's look at that.

For example, here's an article Separation of carbon dioxide and methane in continuous countercurrent gas centrifuges that reports on doing exactly that. It's 100% physics and 0% chemistry and perfectly effective. They're separating carbon dioxide and methane, and the relatively large percentage difference in molecular mass helps, but this technique can be used to separate any pair of gasses.

In another example which is the separation of uranium isotopes using gas centrifuges. Here the uranium is made into a gas by making it into UF₆ and relying on the tiny percentage mass difference between U₂₃₅ and U₂₃₈. It works well enough that it's a major geopolitical hot issue.

So, bottom line: Yup. The Victorians could build equipment which will separate gasses using nothing but mechanical means.

To the question of toilets, it's even easier. Right now in many places we collect reasonably pure methane from garbage. Recipe: Take lots and lot of garbage (toilet waste would be great), seal it up in an airtight container (we pile a mountain of trash on a rubber mat and then cover the whole thing with rubber) and let anaerobic bacteria do their thing, releasing lots of methane in the process. The major gas evolved in the heap will be methane (the second most important is CO₂) and if you let it escape through a hose, you get a burnable mixture, though not a very light mixture. Using the separation method discussed above, you can get fairly pure methane.

How do steampunk civilizations get lifting gas?

What you want is "Synthesis gas". It's what all good fellows with a hunger for flight and adventure need. How shall I make this gas you ask? Well, since you're so inclined, then I'm inclined to tell:

[...] is made by passing steam over a red-hot carbon fuel such as coke:

Don't let the fact that I am able to explain the chemistry put you off good fellows, for 'tis simple in it's operation:

Both the products Carbon Monoxide and Hydrogen are positivley boyant in air, require no complicated spinning or cooling, just directley feeding into your dirigibles.

It has the virtue that it can be done with limited and primitive or even improvised equipment anywhere that water and fuel (eg coal/wood/charcoal) are to be found, you'll be able to take off from much of anywhere in the world with a little labour but no effort.

They're both a bit sensitive so "No Smoking or Naked Flames" in the vicinity would be a good rule by which your servants should abide.

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For them that needs to know, here's the chemistry:

C + H₂O => CO + H₂

_{The reaction is endothermic, so the fuel must be continually
re-heated to keep the reaction going. In order to do this, an air
stream, which alternates with the vapor stream, is introduced for the
combustion of carbon to take place.}

_{This means there'll be a percentage of nitrogen present, but not enough to worry overly. All handshakes and swearings are final, no liability for fires or third party, no refunds!}