## How to calculate energy in humans?

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liberonscien
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### How to calculate energy in humans?

How would someone go about calculating the total amount of energy in a person?
I'm not just talking about how long a person could work but the amount of energy that could be extracted from a human.
I'm trying to determine how much energy a person could get out of a human.

In a series I'm creating a mage ends up accidentally draining a human of all of its energy to power a spell and the spell starts converting the human's mass to energy to power itself.
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### Re: How to calculate energy in humans?

It depends. In terms of food calories, it's about 120,000 kcal or so.
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Thesh
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### Re: How to calculate energy in humans?

If you are talking the entire mass into energy, that's given by E = mc^2, and it turns out that the Hiroshima explosion has the energy of approximately 0.7 grams of matter. An average male has around 100,000 times that energy.

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Tub
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### Re: How to calculate energy in humans?

liberonscien wrote:How would someone go about calculating the total amount of energy in a person?
[..]
I'm trying to determine how much energy a person could get out of a human.

Those are two very different questions. "Energy" and "usable energy" are two different concepts often mixed up by non-physicists (and even physicists). For example, a very hot plasma in thermal equilibrium is a high-energy system with zero usable energy, i.e. with no way to do useful work like casting a spell.

The amount of energy in a person has been answered (the mass-energy is the dominating form of energy, so we don't need to worry about a bit of kinetic energy etc).

The amount of usable energy you can extract from a human to do useful work is a lot lower. You can let the human turn a dynamo until the human dies of exhaustion, you can burn the human to power a steam generator, you can try to use the temperature gradient between the human and its surroundings to extract energy.. neither is particularly efficient. There is no way to convert a human's mass into another form of energy without investing a lot more energy than the human contains, and then you'll need even more energy to contain and direct all that energy into a spell.

Another approach is to recognize that a human, on average, produces about 100W of heat. And that can be kept up for at most a few weeks before starvation. So your typical human has maybe 35 kW/h stored in a way that can be used to do useful work without killing the human. If released at once, that's plenty for a decent spell.
Burning the corpse would release additional energy. I'm not sure how much; but it's going to be in the ballpark of burning 80kg of other organic material like wood. Numbers for wood should be easier to find.
After that, you're left with a pile of ash, and no more energy can be extracted from that.

As an aside, I don't see the point in trying to get physics half-right. Either get them right (but then it's going to be difficult to incorporate magic), or make up your own rules around magic that fit the story you're trying to tell.
Using the correct amount of energy, but ignoring the fact that there's no way to extract that energy, is not physically correct, and you've gained nothing over just claiming "magic did it". You've just created new problems that you need to explain away.
If your mage can convert matter to energy, there's no reason why they would convert a human instead of a stone or simply the air around them. There's really nothing special about the atoms in a human.
If your mage can convert matter into energy, then their magic must be able to create tremendous amounts of energy at will, and then you need to explain why that energy is used to extract a lot less energy from a human instead of using the energy to fuel the spell directly. You also need to explain how the mage is able to handle these energies without disintegrating themselves and everything for miles around them.
If your mage can readily access and use any form of energy around them, then your mage has godlike powers, and that's bad for the story unless you want to tell the story about a person's power trip into madness.

Consider an alternative: the mage is casting a giant fireball by extracting heat energy from their surroundings. Another human ends up standing too close and gets turned into a popsicle. This variant is about as physically incorrect as the other (we're just replacing mass energy with heat energy), but it'll give much better visuals for storytelling, it's a lot easier to make consistent (the mage can direct energy, but not convert it. Draining heat for a fireball is fine, draining mass for a lightning strike is not, thus giving you a device to limit their power), and you avoid entering the uncanny valley of physical correctness where you're getting it kinda right, but not quite.

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### Re: How to calculate energy in humans?

liberonscien wrote:a mage ends up accidentally draining a human of all of its energy to power a spell
You need to first specify what kind of energy this is. And if it's something mystical like "life energy" (i.e. the mage uses magical energy until the human dies), then you can just decide for yourself how much of that there is.

The problem with using up "all" a body's energy and then moving onto matter conversion, is that you haven't specified all of what kind of energy, because without qualification I might take that to include mass-energy, but even if it's not that, you can extract chemical energy from a person's body by burning (or metabolizing) it but then there's less remaining matter to extract energy from.
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### Re: How to calculate energy in humans?

You could release an awful lot of energy by throwing a person down a very deep well

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### Re: How to calculate energy in humans?

Thesh wrote:If you are talking the entire mass into energy, that's given by E = mc^2, and it turns out that the Hiroshima explosion has the energy of approximately 0.7 grams of matter. An average male has around 100,000 times that energy.

This is doing wonders for my self-image!
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speising
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### Re: How to calculate energy in humans?

Tub wrote:but it's going to be in the ballpark of burning 80kg of other organic material like wood.

Pretty wet wood, though. Humans don't really burn well.

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### Re: How to calculate energy in humans?

BlackSails wrote:You could release an awful lot of energy by throwing a person down a very deep well

Hmm idea for a superpower, someone who can freely turn his potential energy from the earth gravity field into other energy but the effect of earths gravity on them gets weaker and if they use all their potential energy it won't affect them at all and well I guess they will drift into space or something. But before that it will make them super light so that is nice.

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### Re: How to calculate energy in humans?

It seems reasonable that a typical spell would use 1 Planck energy. Maybe the mage didn't realise quite how much this was.

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### Re: How to calculate energy in humans?

quantropy wrote:It seems reasonable that a typical spell would use 1 Planck energy. Maybe the mage didn't realise quite how much this was.

It seems even more reasonable that a typical spell would use 1 plank. It could probably be any form of wood, but planks have a good surface-to-volume ratio. (and of course trees have bark and people paint their wooden houses to make them unattractive to magic users)

And it turns out the person that got drained was actually Pinocchio.

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### Re: How to calculate energy in humans?

Flumble wrote:
quantropy wrote:It seems reasonable that a typical spell would use 1 Planck energy. Maybe the mage didn't realise quite how much this was.

It seems even more reasonable that a typical spell would use 1 plank.

Well wood has an energy density of a few planck energies per cubic meter, so if it's a large enough plank then it is much the same.

WibblyWobbly
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### Re: How to calculate energy in humans?

Flumble wrote:
quantropy wrote:It seems reasonable that a typical spell would use 1 Planck energy. Maybe the mage didn't realise quite how much this was.

It seems even more reasonable that a typical spell would use 1 plank. It could probably be any form of wood, but planks have a good surface-to-volume ratio. (and of course trees have bark and people paint their wooden houses to make them unattractive to magic users)

And it turns out the person that got drained was actually Pinocchio.

I'm guessing, then, that the amount of usable energy contained in an average human (say, for instance, a witch) is equal to the wood plank-equivalent of that person (witch), which is itself equivalent weight of the person (witch) in units of ducks?

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### Re: How to calculate energy in humans?

speising wrote:
Tub wrote:but it's going to be in the ballpark of burning 80kg of other organic material like wood.

Pretty wet wood, though. Humans don't really burn well.

Just need to get them hot enough, actually. Fat burns very well.
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Jorpho
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### Re: How to calculate energy in humans?

I find myself thinking of the end of Heaven Sent, from the previous season of Doctor Who. (What a smashing good episode that was. Didn't make a lot of sense, but smashing good.)

Tub wrote:As an aside, I don't see the point in trying to get physics half-right. Either get them right (but then it's going to be difficult to incorporate magic), or make up your own rules around magic that fit the story you're trying to tell.
Make up new physics. Like, say there's a certain amount of energy required to put an atom in this universe from Somewhere Else, and that energy can be liberated by returning an atom to Somewhere Else.

liberonscien
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### Re: How to calculate energy in humans?

Tub wrote:
liberonscien wrote:How would someone go about calculating the total amount of energy in a person?
[..]
I'm trying to determine how much energy a person could get out of a human.

Those are two very different questions. "Energy" and "usable energy" are two different concepts often mixed up by non-physicists (and even physicists). For example, a very hot plasma in thermal equilibrium is a high-energy system with zero usable energy, i.e. with no way to do useful work like casting a spell.

The amount of energy in a person has been answered (the mass-energy is the dominating form of energy, so we don't need to worry about a bit of kinetic energy etc).

The amount of usable energy you can extract from a human to do useful work is a lot lower. You can let the human turn a dynamo until the human dies of exhaustion, you can burn the human to power a steam generator, you can try to use the temperature gradient between the human and its surroundings to extract energy.. neither is particularly efficient. There is no way to convert a human's mass into another form of energy without investing a lot more energy than the human contains, and then you'll need even more energy to contain and direct all that energy into a spell.

Another approach is to recognize that a human, on average, produces about 100W of heat. And that can be kept up for at most a few weeks before starvation. So your typical human has maybe 35 kW/h stored in a way that can be used to do useful work without killing the human. If released at once, that's plenty for a decent spell.
Burning the corpse would release additional energy. I'm not sure how much; but it's going to be in the ballpark of burning 80kg of other organic material like wood. Numbers for wood should be easier to find.
After that, you're left with a pile of ash, and no more energy can be extracted from that.

As an aside, I don't see the point in trying to get physics half-right. Either get them right (but then it's going to be difficult to incorporate magic), or make up your own rules around magic that fit the story you're trying to tell.
Using the correct amount of energy, but ignoring the fact that there's no way to extract that energy, is not physically correct, and you've gained nothing over just claiming "magic did it". You've just created new problems that you need to explain away.
If your mage can convert matter to energy, there's no reason why they would convert a human instead of a stone or simply the air around them. There's really nothing special about the atoms in a human.
If your mage can convert matter into energy, then their magic must be able to create tremendous amounts of energy at will, and then you need to explain why that energy is used to extract a lot less energy from a human instead of using the energy to fuel the spell directly. You also need to explain how the mage is able to handle these energies without disintegrating themselves and everything for miles around them.
If your mage can readily access and use any form of energy around them, then your mage has godlike powers, and that's bad for the story unless you want to tell the story about a person's power trip into madness.

Consider an alternative: the mage is casting a giant fireball by extracting heat energy from their surroundings. Another human ends up standing too close and gets turned into a popsicle. This variant is about as physically incorrect as the other (we're just replacing mass energy with heat energy), but it'll give much better visuals for storytelling, it's a lot easier to make consistent (the mage can direct energy, but not convert it. Draining heat for a fireball is fine, draining mass for a lightning strike is not, thus giving you a device to limit their power), and you avoid entering the uncanny valley of physical correctness where you're getting it kinda right, but not quite.

They are different questions?
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Tub
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### Re: How to calculate energy in humans?

We know about conservation of energy, so energy cannot be created or destroyed. But every day, we "use" energy, don't we? At least the bills from my power company seem to imply so. If energy is conserved, why can't we plug in our laptop until it's full of energy and use it indefinitely?
If you're saying "because it's radiating light and sound waves", that's just part of the reason we need to refill its energy. Most of the energy that enters via the power cord leaves as heat from the fan exhaust. Why does it do that? I spent money putting that energy in there, stop leaking it!

And that's where entropy comes in. You can transfer energy, shuffle it around, you can convert energy into another form. But all those things are only possible in ways that increase the entropy of the system. If you're putting medium-entropy electricity into a laptop, and you want to convert it into low-entropy light signals on the display, you must be increasing entropy somewhere else. In many mechanisms, that high-entropy energy you're creating is heat. And because it's now high entropy, the energy is "used"; you cannot feed the heat back into your laptop's battery and use it again. (Though apparently samsung phones try to do it anyway )

Transfer that knowledge to your mage. You need low-entropy energy. The human body has quite a bit of that, but most of the mass is in a high entropy state. Even if you could instantly convert that mass into energy, you'd just get a high-entropy fireball that transforms the human, the mage and the neighbourhood into a high-entropy state, i.e. everyone dies in something that looks suspiciously like a nuclear explosion. If that's what your spell is supposed to look like, fine. If you want to actually direct the energy into doing something useful, then my advice is to stop converting regular matter. Either find a low-entropy source, or stop worrying about physics in a fantasy story.

Oh, and make a mental note that "entropy" and "disorder" are really different things. Describing entropy as a measure of disorder is the best intuitive description we have, but that correlation won't survive past the first few theoretical examples. If you want to estimate the entropy of a system, never reason about order. You will need to count microstates and macrostates for that.

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### Re: How to calculate energy in humans?

It should be noted that "get out" means "get out at less cost than we put in" - you can convert all matter to pure energy simply by compressing it into a black hole, so it evaporates and radiates heat. It's just that the energy it takes to compress, for example, a gram of lead into a black hole is going to exceed that 1 gram of mass energy that it contains (by an approximately huge multiple).
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### Re: How to calculate energy in humans?

Thesh wrote:you can convert all matter to pure energy simply by compressing it into a black hole, so it evaporates and radiates heat.

Ignoring the lack of experimental evidence for hawking radiation, does it say anywhere that hawking radiation has to be exclusively massless particles? I've always understood it to produce all kinds of particles; certainly favouring low-energy particles, but also emitting more energetic or massive particles if the black hole gets hot (small) enough. Several google results agree, though neither me nor those results count as experts.

I wouldn't even bet on any special conversion taking place until someone describes the mechanism for it. The original idea was that the radiation is made of freshly created particles, created as random pairs on the horizon, thus being independent from the original infalling matter. But according to that thing I read on the internettm, you can also derive hawking radiation via the uncertainty principle - you cannot confine a particle into a space smaller than its compton wavelength, not even in a black hole. The low energy/long wavelength particles are the first to leave; as the black hole shrinks the high energy/short wavelength particles follow, making the radiation look thermal. This may or may not allow black hole evaporation to work without introducing any new particle interactions, e.g. without any new ways to convert matter to energy.

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### Re: How to calculate energy in humans?

Tub wrote:
Thesh wrote:you can convert all matter to pure energy simply by compressing it into a black hole, so it evaporates and radiates heat.

Ignoring the lack of experimental evidence for hawking radiation, does it say anywhere that hawking radiation has to be exclusively massless particles?

I'm no expert, but I've always heard it as black body radiation, so I assume EM. Doesn't really matter, though, since from the wizard's perspective fire is just energy, not EM-emitting gas.

That said, hypothetically you could throw someone into the gravity well of an anti-matter-Jupiter (which, we could hypothetically either find or make). I'd recommend against it, but you could. Wouldn't even be that interesting of an invent to astronomers. Except for the whole antimatter planet thing.
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### Re: How to calculate energy in humans?

Tub wrote:created as random pairs on the horizon

That was not the original idea, that is a lie told to children. Bogolyubov transformations are much too scary, so a little picture where a particle goes one way and the anti another sounds fun, but this is not what happens or how the derivation works.

You could radiate other things too, but it'll all be highly suppressed. Maybe when the black hole finally kaputs, but then you need some quantum gravity help.
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### Re: How to calculate energy in humans?

doogly wrote:That was not the original idea, that is a lie told to children.

By no other than mr hawking himself But alright, I'll try to erase that lie from my mind.

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### Re: How to calculate energy in humans?

Tub wrote:Start by learning about entropy.

We know about conservation of energy, so energy cannot be created or destroyed. But every day, we "use" energy, don't we? At least the bills from my power company seem to imply so. If energy is conserved, why can't we plug in our laptop until it's full of energy and use it indefinitely?
If you're saying "because it's radiating light and sound waves", that's just part of the reason we need to refill its energy. Most of the energy that enters via the power cord leaves as heat from the fan exhaust. Why does it do that? I spent money putting that energy in there, stop leaking it!

And that's where entropy comes in. You can transfer energy, shuffle it around, you can convert energy into another form. But all those things are only possible in ways that increase the entropy of the system. If you're putting medium-entropy electricity into a laptop, and you want to convert it into low-entropy light signals on the display, you must be increasing entropy somewhere else. In many mechanisms, that high-entropy energy you're creating is heat. And because it's now high entropy, the energy is "used"; you cannot feed the heat back into your laptop's battery and use it again. (Though apparently samsung phones try to do it anyway )

1.Transfer that knowledge to your mage. You need low-entropy energy. The human body has quite a bit of that, but most of the mass is in a high entropy state. Even if you could instantly convert that mass into energy, you'd just get a high-entropy fireball that transforms the human, the mage and the neighbourhood into a high-entropy state, i.e. everyone dies in something that looks suspiciously like a nuclear explosion. If that's what your spell is supposed to look like, fine. If you want to actually direct the energy into doing something useful, then my advice is to stop converting regular matter. 2.Either find a low-entropy source, or stop worrying about physics in a fantasy story.

Oh, and make a mental note that "entropy" and "disorder" are really different things. Describing entropy as a measure of disorder is the best intuitive description we have, but that correlation won't survive past the first few theoretical examples. If you want to estimate the entropy of a system, never reason about order. You will need to count microstates and macrostates for that.

Alright.
1. I see.
2. I am trying to make this as realistic as I possibly can.
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