air displaced from the point you teleport to is instantly moved to form a monolayer (1 molecule thick) on your surface.
The displacement of air is adiabatic (no heat is transferred, which will be true if the displacement is instantaneous)
Volume of displaced air: ≈ 100L = 0.1m^3
At atmospheric conditions: ≈ 4 mol
Surface area of cylindrical human: ≈ 1.58 m^2
Diameter of nitrogen molecule (which is roughly the same as for an oxygen molecule) : ≈ 3 Å
Volume of monolayer: ≈ 4.7e-10 m^3
Treating the air as an ideal gas (terrible approximation for this process) gives us a post-compression pressure of ≈ 45 PPa (you read that right: Peta-pascal) or 450 Gbar, and a temperature of roughly 650 000 K.
These conditions are definitely in the range where fusion might be possible (see: solar conditions). So to the people saying you are only “trying to science”, I would say I agree with your initial assessment.
I’m on my phone now, but I can run the numbers using something more accurate than ideal gas when I get my computer. However, this is so extreme that I don’t really think it will change anything.
Edit: We’ll just look at how densely packed the monolayer is. Our cylindrical person has an area of 1.58 m^2, which, assuming an optimally packed monolayer gives us about 48 micro Å^2 per particle, or an average inter-particle distance of about 3.9 milli Å. For reference, that means the average distance between molecules is about 0.1 % of the diameter of the molecules (roughly 3 Å) I think we can safely say that fusion is a possible or even likely outcome of this procedure.
I feel like a mathematician would go a step further and not even assume a specific geometry. Maybe a human is just a subset of points in a measure space, with a measure fixed at 1 human-unit.
To be fair, the result of this calculation only depends on the area/volume ratio of the human. I used the specific cylinder, because humans are roughly cylindrical, and have a volume of roughly 100 L. The surface area of a regular human is probably a bit larger than that of a cylindrical one though.
That’s true, and in this case where the layer is a single molecule thick, pores and even cellular structure will add to it quite a bit. Hell, at that scale it’s probably hard to define any solid boundary to the body at all, since you’ll have things like the surface of evaporating sweat. Once again, we need to know a bit more about how the magic works to give a single answer.
Our mathematician would have to add a measure on subset boundaries I guess. Or maybe just hand the problem off to a big boy who can handle things in the real world (zing!).
Oh, you’re assuming a monolayer. Yeah, you’re right then. I thought you were talking about the vacuum end and the air was magic-ed out in a more orderly fashion at the other end.
Assuming
Volume of displaced air: ≈ 100L = 0.1m^3 At atmospheric conditions: ≈ 4 mol
Surface area of cylindrical human: ≈ 1.58 m^2 Diameter of nitrogen molecule (which is roughly the same as for an oxygen molecule) : ≈ 3 Å Volume of monolayer: ≈ 4.7e-10 m^3
Treating the air as an ideal gas (terrible approximation for this process) gives us a post-compression pressure of ≈ 45 PPa (you read that right: Peta-pascal) or 450 Gbar, and a temperature of roughly 650 000 K.
These conditions are definitely in the range where fusion might be possible (see: solar conditions). So to the people saying you are only “trying to science”, I would say I agree with your initial assessment.
I’m on my phone now, but I can run the numbers using something more accurate than ideal gas when I get my computer. However, this is so extreme that I don’t really think it will change anything.
Edit: We’ll just look at how densely packed the monolayer is. Our cylindrical person has an area of 1.58 m^2, which, assuming an optimally packed monolayer gives us about 48 micro Å^2 per particle, or an average inter-particle distance of about 3.9 milli Å. For reference, that means the average distance between molecules is about 0.1 % of the diameter of the molecules (roughly 3 Å) I think we can safely say that fusion is a possible or even likely outcome of this procedure.
How to spot a mathematician/physicist.
I’m actually a chemist, thankyouverymuch
#Chemistry Is When There’s Too Many Electrons For The Physicists
;)
I feel like a mathematician would go a step further and not even assume a specific geometry. Maybe a human is just a subset of points in a measure space, with a measure fixed at 1 human-unit.
To be fair, the result of this calculation only depends on the area/volume ratio of the human. I used the specific cylinder, because humans are roughly cylindrical, and have a volume of roughly 100 L. The surface area of a regular human is probably a bit larger than that of a cylindrical one though.
That’s true, and in this case where the layer is a single molecule thick, pores and even cellular structure will add to it quite a bit. Hell, at that scale it’s probably hard to define any solid boundary to the body at all, since you’ll have things like the surface of evaporating sweat. Once again, we need to know a bit more about how the magic works to give a single answer.
Our mathematician would have to add a measure on subset boundaries I guess. Or maybe just hand the problem off to a big boy who can handle things in the real world (zing!).
Can confirm, as a cylindrical human, 2m tall, 25 cm diameter.
Thank you for taking the time to do the actual calculations, you are a legend!
Oh, you’re assuming a monolayer. Yeah, you’re right then. I thought you were talking about the vacuum end and the air was magic-ed out in a more orderly fashion at the other end.