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The Law Of Conservation Of Mass
watchmen, who will watch the watchers
spiderspun
I have some questions of the theoretical science type. The current one is this: if you had to replace an average human male's total mass with an equivalent amount of air (i.e. one hydrogen atom for one hydrogen atom, one helium for two hydrogen... maybe some extra electrons - but mass not weight), what would the volume of said air be?

It's for a new (semi)superheroic character - The Pixie.

Scenario:
Pixie can teleport. Process of teleportation takes Pixie at Point A and replaces him with an equivalent amount of matter at Point B. Point B is a position in the air at sea level. What volume of air at Point B would be required to replace Pixie at Point A?

I suppose the other way to approach the question is: if you were turn an average male into gas, what volume would it take up at sea level?

I'm trying to get an idea of how small a room he can 'port into. How much air will be sucked out of a room he 'ports into/how much air will billow out when he 'ports out. That sort of thing.

My problem is that I don't know who to ask even for a rough idea. And everyone on the internet knows that when you don't know who to ask you ask the internet. I have a vague memory of highlyeccentric mentioning a forum/community in which writers could ask questions for writing purposes and receive relatively reliable answers... does that sound at all familiar?

:s

I'm really happy with what I've got for Pixie so far: he's got a suit (black, with a pink shoulder cape thing), an almost-definitive logo, a lair/batcave (or whatever pixies call home)/HQ, and some basic laws surrounding his ability. By no means is he complete yet - while I think he has a wife, and I think he's an architect when not being The Pixie, I don't know his name nor where he was able to source all his materials and funds nor how he was able to build his underground HQ nor where it is exactly. Nor am I sure if he's a loner or a team player; I'm not even sure if he's in the same universe as Cassie (Cassiopeia) and James (Scythe).

Anyway, please help if you can. Muchos appreciados!*


*Worst Spanish ever.

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I'm a bit confused as to what is happening.

If he teleports into a room, does the volume of his body just replace the air? Or does his body displace the air like a body going into a bath?

If his body replaces the air and you want to find the mass of the air, you find the volume of the body. The density of a person is probably slightly more than water. So let's say 1.2kg/L or 0.8L/kg. So you can work out the volume by multiplying that by the mass. So he's 100kg, then it takes 80L of space. The density of air is about 1.2g/L so that's like 96g of air that could fit in a human adult's space.

If the body just displaces the air, then if the room is closed then the only thing that will increase will be the pressure of the air in the room. The equation we use here is PV=nRT that is, the pressure in the room times the volume in the room is equal to the number of moles (ignore that) times some constant and temperature. Assuming the temperature doesn't change. (Which it probably will, but that's tricky to calculate) then basically you can work out the new pressure in the room with this formula: P1/P2=V1/V2 or P2/P1=V2/V1 where P1 is initial pressure and P2 is final pressure and V1 and V1 are the same etc.

So P2=P1*V2/V1 So if the room is 1000L and the body is 80L and the room is at 1 atm (or 103kPa) then V1 = 1000, V2 = 1080 and P1 = 1 atm = 103 kPa.

So P2 = 103*1080/1000 kPa = 111 kPa.

Now, you could probably look up stuff which says how much air pressure is tolerable for a human. I think 111 kPa is fine, since humans can take hyperbaric conditions (look that up, that will be a good upper limit.)

You can also use this to work out the decrease in pressure when he leaves a room, just make V2 the volume minus the volume of the person.

Super bonus awesome points if you can like work out the amount of energy it would take to either remove or create that amount of pressure in the room. Since if you wanted to make his power like thermodynamically accurate it would be required. (That is to say, it should require some form of energy for him to transport somewhere, where that energy comes from doesn't matter as much. Like I assume the teleportation itself will require a base amount of energy, but if you want to be cool with science it should take more energy to teleport into or away from small spaces, since you will be creating a greater pressure increase. (Leaving small spaces would be more energy intensive since "nature abhors a vacuum") )

So yeah, that's my overly long explanation. Does that make sense? Feel free to ask for clarification/ other questions!

Ah ha! Now we're getting science!

Unfortunately, it's option 3 - he replaces the same number of atoms as he has. So say his body has 100 atoms (I know it's ridiculously small, it's just an example), he needs to replace 100 atoms of air. The difference between density of a body and density of air means that the volume of air required takes up more physical space than his body. It's 100 atoms of body spread over one square inch, versus 100 atoms of air spread over one square foot. That sort of replacement. Which means that differences in atmospheric composition affect the volume of particles at the destination required for teleportation - if he were 'porting into a liquid, the density being far greater than that of a gas, the volume would be much smaller. And if it were into a solid it would require a volume roughly equal to that of his body - a replacement of your Option Number One above kind.

This means he'd be 'porting into a quickly-filling vacuum every time he 'ports into a substance less dense than his body.

Does that make any sense? :s How does that affect the equations?

oh wait! So if you make a container the shape of a human body, you're saying it can hold either 96 grams of air, or 100 000g of body?

Which means that the density of a body is about 1041 times greater than that of air? Which means it would take 1041 of those containers filled with air to hold as much matter as one container full of body? Which, at 80L a pop, would take up 83 280L of space?

That's massive. Please tell me I'm wrong.

I started replying, but then saw you're reply so I will answer that first then go to my other reply.

Yes, the density difference is huge, about a thousand times, but we are talking numbers of particles which is slightly different and I will go through the calculations for that. But it might be similar...

Ahh, I see. Interesting.

Though a bit scientifically silly, :P but still interesting and cool.

Ok. So this will be a bit more tricky to work out. You need to convert everything to moles. Actually, it's not that tricky to work out.

So like the formula for converting from mass to moles is n=m/FM Where n is the number of moles, m the mass and FM the molecular weight. Now the body is like 75%(?) water and the FM of water is 18. But it has other shit there too so lets make it an even 25. So a 75kg would basically be 3 kmoles or 3000 moles (since the FM is in units of g/mol or mol/g I can't remember). So there are 3000 moles of particles in a human body, and avogadro's number tells us that a mole of anything contains 6.022*10^23 of that thing. But that doesn't matter since we know that a mole of anything is constant.

So if there are 3000 moles of particles in a body then that will require 3000 moles of air. Now I remember a mole of air taking up about 22L (might be 24) so that's about 60 000L for the body. That's 60 m^3 which is close to 64 which is 4^3. So that's like a cube with dimensions 4 x 4 x 4 (or 2 x 8 x 4) etc. I'm in my TV room and a quick look around seems to show that there's probably a bit more than that. So the actual amount of air that is required is ok.

But that means if he ports into a room that's 100 m^3 of air, there will only be 40 m^3 left. Which will mean P2 = 40/100 P1 so like he will more than halve the air pressure. But in bigger rooms, the effect will be less noticeable.

Hmm, I know feel like graphing this on excel... If you add me on msn or give me your email, I can send you a file showing the effects of the size of the room. Though, I might be missing the point a bit...

Oh, my msn is neotaco@hotmail.com

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