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In this question, I asked about using living things as power sources for metabolism-based magic, and concluded that yeast (most likely bred specifically for the purpose) seem like a good candidate for the purpose.

I'm using a human (1 kW peak, 300 W mean) as a rough measure. I figure yeast are not as efficient as mammals, and as a very gross estimate, I am guessing that you would need 3-10 m³ of tankage (the volume of the yeast's environment, not just the yeast themselves) to equal one human... but I really have no clue how accurate this is.

How much energy per unit of volume could such yeast plausibly produce? In particular, I'm interested in what improvement is plausible over "natural" yeast, given that yeast will be bred specifically for this purpose. (For example, we want it to produce heat as efficiently as possible for the "food" we give it, while we don't care about producing alcohol or gasses. We'd probably want greater heat resistance also, but a production system could incorporate active cooling.)

p.s. It would be great to know both overall density, and also density per square meter under the assumption that all the energy generation happens in ~1 m of height with unlimited height above that for supporting equipment. For both cases, assume that "food" is tanked somewhere else. For the latter case, you may also assume that large, remotely located heat exchangers are available.

Edit: As AlexP points out in the comments, yeast and humans are comparable at the cellular level. What I'm really asking is how densely you can pack a yeast colony before overwhelming the necessary support infrastructure. For example, the density of yeast in a beer bottle or a loaf of bread is pretty low, but needs essentially no support machinery, whereas a human body is much more dense but has additional space and "equipment" dedicated to waste (both heat and chemical) management. So, really, what I'm asking is how dense can you pack yeast before you can't keep it alive, keeping in mind that the equipment to do so is also going to take up space.

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    $\begingroup$ (1) What do you mean exactly by "produce energy"? Do you mean thermal energy output? Mechanical energy output? What? (2) Both yeasts and humans are perfectly able to burn sugars completely, converting them into carbon dioxide and water; so that if what you are seeking is thermal output, then I don't understand why you would think that yeasts are less efficient than humans at burning sugar. Moreover, humans die if their temperature goes above 40° C. (3) But of course, yeasts can't produce mechanical energy at all, so that if mechanical output is what you are after, then you are out of luck. $\endgroup$
    – AlexP
    Commented Jan 15, 2021 at 15:49
  • $\begingroup$ Thermal. Magic can harness that output to do mechanical Work, but to keep things simple, just worry about thermal output. As to efficiency per volume, I might be wrong, but part of the question deals with how much support structure they need. One yeast may be as efficient as 'an equal mass of human', but can I pack a bunch of yeast together as tightly as a human body without the colony dying? $\endgroup$
    – Matthew
    Commented Jan 15, 2021 at 15:56
  • $\begingroup$ Yeasts do not live in colonies -- each cell is on its own. I have no idea if you can pack them as much as the say muscle cells in a human body, but on the other hand most cells in the human body don't burn much sugar -- adipose cells, connective cells, blood cells etc. don't use all that much energy. Most heat is produced by muscle cells and brain neurons, and those are only a small part of the body mass and volume. $\endgroup$
    – AlexP
    Commented Jan 15, 2021 at 16:04
  • $\begingroup$ "Mass", then? "Collection"? I don't know the word for a group of yeast. $\endgroup$
    – Matthew
    Commented Jan 15, 2021 at 16:10
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    $\begingroup$ (Continued) You really do want something like a cyclic process beer brewing, where you launch a batch, grow it, siphon off its magic energy (killing it in the process but who cares, it's yeast which would have died anyway), flush the tank, and start a new batch. (I've always meant to write a fantasy story where dark magic/necromancy has been reformed to be not-evil because the lifeforce used to power dark magic/necromancy comes as a byproduct of breweries rather than from killing animals/people.) $\endgroup$
    – GrumpyYoungMan
    Commented Jan 15, 2021 at 17:15

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In order to answer this, we need to answer several questions:

How much "fuel" (sugar) can we make available?

One source suggests a 40% solution is reasonable, or 1546 KCal/L. The same source suggests that some strains may tolerate as high as 60-75%. However, this also appears to have an inhibitory effect on yeast, with 20% being more amenable.

Let's start with 20%, keeping in mind that our final number might be as much as one third the actual potential limit. Sugar solutions are defined as the percent-number of grams in 100 mL of water. Conveniently, this means that a 20% solution is 200 g/L, or 1 cup, which is 773 kcal. This gives us a potential energy figure.

How fast can yeast, which have been bred for the purpose, convert this into heat?

This graph suggests that half of our 20% solution can be metabolized in about 5 hours. This gives us about 90 W/L, or 90 kW/m³. Not too shabby! Some of this needs to go cellular maintenance and reproduction, but it's plausible we can get this as "peak output" for short durations.

How much volume can be dedicated to the yeast-water-fuel mixture, and how much is needed for support equipment?

We need to feed the yeast and get rid of wastes, including excess heat. Diagrams of continuous brewing rigs suggest a need for about 50% air, plus some pipes to deal with material input and output. What this doesn't account for is getting rid of excess heat in order to avoid cooking our yeast.

So...?

If we go with a very conservative estimate that the actual yeast-water-fuel mix is no more than 6% of the total volume, this still gives us an impressive 5 kW/m³.

Realistically, it seems like heat dissipation is going to be the main limiting factor...

...Unless, of course, there is something wildly off in my logic. Please critique!

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The below is just a back of the envelope estimate and is at best only going to be accurate to within an order of magnitude.

From https://en.citizendium.org/wiki/Fermentation_(biochemistry), we get an estimate of 118 kJ of heat produced per mole of sucrose (342.3 grams) fed to a yeast solution.

If you look at concentration graphs vs time for fermentation over time (Google for image "fermentation of sugar concentration vs time"), you get the sense that 80%-95% of fermentation for sugars only occurs within the first 24 hours. The specific fermentation rates (and therefore heat output) will vary depending on the strain of yeast used and what it's being fed.

Plugging the numbers in for 90% of 118 kJ over 24h gives us a coarse estimate of 1.23 mW for every mole of sucrose (342.3 g) being reacted in parallel.

Since you want your yeast to act as a generator, you can use literature for continuous fermentation processes to help describe your system. A good starting point would be: https://en.wikipedia.org/wiki/Fermentation#Continuous

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  • $\begingroup$ This... isn't exactly an answer. Maybe a starting point... $\endgroup$
    – Matthew
    Commented Jan 17, 2021 at 14:23
  • $\begingroup$ Also, if I crank those numbers through some other info, I get a whopping... 1.4 W/m³ (before accounting for support equipment, need to set aside air volume, etc.), which is just pathetic. I really, really hope a system that's been bred for this purpose can manage better than that! If not, I'm back to (ab)using livestock instead... $\endgroup$
    – Matthew
    Commented Jan 17, 2021 at 15:40
  • $\begingroup$ @Matthew Yeast reproduce quite rapidly, e.g. 1 gram of yeast can grow to 100kg in less than 36 hours under optimal conditions (~16.6 doublings), which implies an efficient metabolization of food and low waste heat. Given that, it should be self-evident that using heat output as a stand-in for magical energy generated wasn't the correct metric to use. $\endgroup$
    – GrumpyYoungMan
    Commented Jan 18, 2021 at 4:57
  • $\begingroup$ ...which is why this is a world building question and not a biology question. These would be bred specifically to metabolize "fuel" (e.g. sugar) without reproducing... or more precisely, to be able to metabolize very quickly, but to normally metabolize (and reproduce) very slowly to minimize how much fuel they burn through when not being used. $\endgroup$
    – Matthew
    Commented Jan 18, 2021 at 14:15

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