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In my world, dragons are big, and require lots of energy just to support their massive bodies and huge brains - and of course, to fly, using enormous oversized wings. Rather than causing mass extinctions when they have breakfast, I want my dragons to gain part or all of their energy needs by other means.

I would like to keep these dragons as classic as possible, so I had the idea that they should make lairs inside of volcanoes, and have the ability to hibernate in these lairs. They would sustain their organism on the geothermal heat that's plentiful in their environment. Efficiency is not a huge concern, as the dragons can have a fairly arbitrary amount of heat in the lair, and equally arbitrary energy needs when hibernating.

But how do they turn heat into energy that their organism can use? As far as I can tell, even bacteria near hydrothermal vents don't use the heat for energy, but rather "eat" sulfur compounds ejected by the vent. I do not particularly care if these dragons are warm-blooded, cold-blooded, reptilian, mammalian, whatever, so long as they are organic beings and don't require magic or particularly intense hand-waving.

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    $\begingroup$ You're trying to make sense of something that doesn't. Your entire problem can be solved by simply stating that "the dragon fed off the heat". As things stand, this question is asking us to completely make up a mechanism, thus rendering this question opinion based. $\endgroup$ – AndreiROM Jan 12 '18 at 14:45
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    $\begingroup$ @AndreiROM Wouldn't an explanation that is theoretically possible, but not yet observed be an objectively correct answer? $\endgroup$ – Szega Jan 12 '18 at 14:58
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    $\begingroup$ @AndreiROM So the problem is that it is not falsifiable? If we did not know of bacteria that produce lactic acid and someone asked "how could a single cell organism produce lactic acid" you would call that opinion based? Even is someone then produced the metabolic description of a Lactobacillus out of his genius? The reactions there do make sense and could be tested. $\endgroup$ – Szega Jan 12 '18 at 15:12
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    $\begingroup$ I honestly still don't understand the close votes. Nobody's given a satisfactory explanation as to why it's impossible; y'all are just saying that it's not possible without actually backing that statement up. $\endgroup$ – HDE 226868 Jan 12 '18 at 15:14
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    $\begingroup$ @AndreiROM Because the question has been tagged science-based, feel free to write an answer challenging the premise. Explain why converting heat energy to stored energy isn't possible, that no such mechanism can exist. The concept not being possible is not grounds for closure. $\endgroup$ – Frostfyre Jan 12 '18 at 15:19
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Try thermosynthesis.

Thermosynthesis is a hypothetical mechanism, usually applied to the RNA world theory for the rise of life on Earth. In a nutshell, it states that an organism could function as a heat engine, where thermal energy is gained from a heat reservoir - in this case, a volcano.

Thermosynthesis allows you to synthesize molecules via anabolic pathways; it's not too far a conceptual leap to imagine that this organism could store chemical energy through thermosynthesis in the form of sugars, and from there, use a mechanism similar to respiration to unlock the energy from those sugars. More specific details can be found in an answer by Dubukay.

Would it be evolutionary feasible? Well, that's another question entirely. From an evolutionary perspective, it would be unlikely that thermosynthesis would be selected as an animal's method of energy generation, because a primarily thermosynthetic organism would need to stay close to the source of heat. Thus, it doesn't make sense for the creature to be mobile. So you'd probably see something less complicated - like, say, a fungus - evolve first.

Perhaps an animal of sorts would arise to use thermosynthesis, but only on a world where most other forms of energy generation are impractical or impossible. It has been suggested that thermosynthesis could be handy on a world that's cold, where the creature would take advantage of the temperature difference between the atmosphere and frozen ground. This is sort of the reverse scenario; the ground is hot and the air is comparatively cold.

I think thermosynthesis is the closest you can get to what you're looking for. The odds are against such a creature, but it's not impossible at all.

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    $\begingroup$ "Overgrown reptile? Don't be silly, I'm a kind of fungus." -- Dragon, probably. $\endgroup$ – SPavel Jan 12 '18 at 15:28
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    $\begingroup$ Since the evolutionary leap from fungus to dragon is pretty significant, perhaps the dragons live in symbiosis with the fungi/single-cell thermosynths? Imagine a fantasy ecosystem where "volcanic caves are covered with thermosynthetic slime"-->"heat-loving big lizard crawls into volcanic cave"-->"big lizard eats slime, which takes up residence in the dragon's gut"-->"big lizard evolves to be even bigger thanks to extra calorie source, becomes dragon". The thermosynths could live in the gut or be incorporated into the dragon's very cells like ancient mitochondria. $\endgroup$ – The Walrus469 Jan 12 '18 at 17:09
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    $\begingroup$ The problem with is that it needs a temperature gradient, not just a hot temperature. It has to extend from hot to cold in order to work. The temperature gradients across a micro-organism are too small to drive life. You need something at least as big as the distance from the heat source to a significant heat sink. $\endgroup$ – Paul Sinclair Jan 12 '18 at 18:46
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    $\begingroup$ @PaulSinclair All I'm hearing is evolutionary pressure that drove dragons to be big and good reason to have attached external facing caves for plot relevant confrontations :P $\endgroup$ – Lunin Jan 12 '18 at 19:54
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    $\begingroup$ 1. If the dragon exploits the gradient by itself, it will inevitably have huge heat exchangers on opposing sides of the body. i.e. a multitude of thin fins. 2. It might be easier for the dragon to eat aforementioned thermosynthetic funghi. 'Traditional' animals don't have to photosynthesize to exploit the solar radiation, they can just as well eat some plants, or each other. $\endgroup$ – Earwin Jan 12 '18 at 22:09
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You cannot actually gather usable energy from heat directly (that's a law of thermodynamics). You need a heat differential. The movement of heat from a hot reservoir to a cold reservoir is required in order to actually gain energy.

There are many ways to build a heat-engine to transfer heat from hot to cold in this way, but I would recommend two processes.

The first is for use in the lair. While in the lair, you have limited access to cold objects to transfer heat to. However, the lair itself is going to have some heat differential from top to bottom. We can leverage that. In fact, the dragon may intentionally make the top of their lair cooler (by adding things like metals to conduct heat to the surface... and Gold just happens to be a very good heat conductor). This won't generate much energy, because the temperature differential is minimal within the lair. However, it could generate enough energy to keep the dragon alive and functioning if they have to stay in their lair for long periods.

The second approach is neater. Some reactions favor one direction or another at different temperatures. For example, CaO(s)+H2O(l)⇌Ca(OH)2(s)+heat, the conversion of quicklime to slaked-lime, is tremendously exothermic. It's a great energy source. However, at high temperatures, the reaction reverses, taking slaked-lime and converting it to quicklime and water. You can use this to form a heat engine within your dragon. While it is in its lair, it stores slaked-lime in its body, which gets converted naturally into quicklime. Later, when the dragon emerges to fly, needing substantial energy to stay in the air, it can decrease the temperatures of these quicklime stores (using the outside air to cool them), and convert them back to slaked-lime using an enzyme which captures the energy of this conversion rather than just wasting it as heat.

This energy is now in a "usable" form, so can be used immediately or stored in compounds which can be used for metabolism both inside the lair and outside, and can be used on a moment's notice (if your dragon doesn't have time to air-cool a bunch of quicklime)

I'm not sure if the slaking of lime will be an acceptable reaction for you (it's hard to tell if dragon metabolism can balance that equation correctly for volcanic temperatures), but it's an example of the kind of reaction which lets you draw energy from the volcano.

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The big issue with your concept is that life, the universe, and everything does not run on energy. Instead, we run on the flow of energy. The universe has been going for billions of years, but the total energy content in the universe is the same now as it was at the very beginning - this is known as "conservation of energy". However, the energy is not equally distributed. There are places (in atomic bonds, for example) where the energy density is high and other places where it is lower. As it has opportunity, the energy flows to disperse itself. It is this flow of energy that is the actual driver of processes, including life.

Heat itself is a form a energy, so the literal answer to your question of how to convert heat into energy is "it already is". What you really want is "how do you make use of that heat to live". And there is the problem. Your dragon is surrounded in a high concentration of heat energy. But that energy has to flow before it can used, and in environs where everything is the same temperature, there is no where for it to flow. There is no way for your dragon to survive simply off of living in a hot environment. Even with magic, it is magic that the dragon would be using to survive, not the heat.

There are two possible solutions. The sessile solution is for the dragon to physically bridge the gap between the hot environment near the volcano to cooler surroundings. Then it can make use of the flow of temperature from the hot environment to the cooler.

The other solution is to make use of the mobility of the dragon. The dragon has both heat-reservoir and heat-sink organs. The reservoirs are exposed while in its volcanic lair, allowing the external heat to flow freely into them, while the sinks are kept insulated, allowed to heat up slowly from the internal processes keeping the dragon alive. When the sink gets too warm, the dragon must leave the lair and move to someplace colder, where the sink is exposed and the reservoir is insulated. The sink sheds its heat quickly while the dragon uses the flow of heat out of the reservoir to live.

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    $\begingroup$ That could add interesting ramifications to the classic dragon's fire breath. Sure it's a gout of devastation, but it also uses up precious reserves from the last time they "fed" from the heat at a volcano and could result in a dragon "starving" if overused. Though fires started by dragons away from said volcanoes could be an initeresting way of attempting to scavenge some heat (use small amount of energy to start fire that burns external fuel, use external blaze to gain more than initial ignition breath) $\endgroup$ – Lunin Jan 12 '18 at 19:57

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