PDA

View Full Version : incompressible fluid vs indestructible container



ross
2018-09-11, 07:01 PM
I've just posted a thought experiment over at https://rpg.stackexchange.com/questions/131539/cup-of-water-versus-cube-of-force which will probably be deleted; reposted here 'cause I thought it might have potential to generate interesting discussion, at least for people who are in to thinking about such things.

Here's the full post in case you don't feel like clicking on links



Create a magic item - the specifics don't matter, but say it's a cup - which is enchanted with the effect "Produces 1 liter of water each second, as long as the pressure at the cup's location does not exceed 10 atmospheres."

Create a cube of force, one meter on each side.

Teleport the cub inside the cube. What happens?

The cup is indestructible
The cube is indestructible
The cube is impermeable to all substances in any phase
The cube's interior when first created is perfect vacuum
With the exception of violations caused by the above premises, all standard physical laws apply. Gravity and (external) atmospheric pressure is the same as that at Earth's surface. Initial ambient temperature is 25 C.
For reference, ten atmospheres is the pressure exerted by a column of water about 91 meters tall, and is roughly equal to 1 megapascal.

My initial hypothesis was that the water would undergo a phase change, but https://i.stack.imgur.com/n6LXj.gif indicates that 1 MPa has no appreciable effect on water's freezing point. On the other hand, water is basically incompressible: according to https://water.usgs.gov/edu/compressibility.html, even at 150 atmospheres (far greater than the point at which the cup would have stopped producing water), compression is less than 1 %. So the naive assumption is that the cup continues to produce water, which can't be compressed, and can't go anywhere.

It may be that there is no answer, or that there is an obvious one that I simply don't see because I don't know enough about the physics involved. If the former is the case, I would like to hear how people would rule such a situation in their own games.

halfeye
2018-09-11, 07:35 PM
I've just posted a thought experiment over at https://rpg.stackexchange.com/questions/131539/cup-of-water-versus-cube-of-force which will probably be deleted; reposted here 'cause I thought it might have potential to generate interesting discussion, at least for people who are in to thinking about such things.

Here's the full post in case you don't feel like clicking on links



Create a magic item - the specifics don't matter, but say it's a cup - which is enchanted with the effect "Produces 1 liter of water each second, as long as the pressure at the cup's location does not exceed 10 atmospheres."

Create a cube of force, one meter on each side.

Teleport the cub inside the cube. What happens?

The cup is indestructible
The cube is indestructible
The cube is impermeable to all substances in any phase
The cube's interior when first created is perfect vacuum
With the exception of violations caused by the above premises, all standard physical laws apply. Gravity and (external) atmospheric pressure is the same as that at Earth's surface. Initial ambient temperature is 25 C.
For reference, ten atmospheres is the pressure exerted by a column of water about 91 meters tall, and is roughly equal to 1 megapascal.

My initial hypothesis was that the water would undergo a phase change, but https://i.stack.imgur.com/n6LXj.gif indicates that 1 MPa has no appreciable effect on water's freezing point. On the other hand, water is basically incompressible: according to https://water.usgs.gov/edu/compressibility.html, even at 150 atmospheres (far greater than the point at which the cup would have stopped producing water), compression is less than 1 %. So the naive assumption is that the cup continues to produce water, which can't be compressed, and can't go anywhere.

It may be that there is no answer, or that there is an obvious one that I simply don't see because I don't know enough about the physics involved. If the former is the case, I would like to hear how people would rule such a situation in their own games.

It seems to me that the cube fills with water, then the cup stops, because the pressure inside the cube goes above 10 atmospheres? Why do you not think that's what happens? Is the cup supposed to be measuring the pressure outside the cube for it's stopping state? that might get you to a very high pressure, but then you have indestructible versus indestructible, and that depends on which definition of indestructible is more accurate.

ross
2018-09-11, 07:49 PM
It seems to me that the cube fills with water, then the cup stops, because the pressure inside the cube goes above 10 atmospheres? Why do you not think that's what happens? Is the cup supposed to be measuring the pressure outside the cube for it's stopping state? that might get you to a very high pressure, but then you have indestructible versus indestructible, and that depends on which definition of indestructible is more accurate.

Assuming the cup is denser than water, and is therefore at the bottom of the cube, then when the cube is full, the pressure on the cup is 1.1 atm ( or 2.1 atm if we take the outside air in to account ). Therefore, the cup continues to produce water. However, the cube is already full, the water can't exit the cube, and the water is still incompressible ( even at 150 atm, water only compresses by less than 1 % ). This appears to lead to a contradiction.

By "indestructible" I mean no amount of force or pressure will damage the cube or the cup in any way.

Glimbur
2018-09-11, 08:17 PM
Sounds like you will have to test it and find out :P

More seriously, this is an example of how you can't mix magic and real physics. It works however the rules of the game you are playing says it does.

ExLibrisMortis
2018-09-11, 08:40 PM
If you say "this cubic metre is filled with water compressed sufficiently to fit what would be 1200 litres under standard conditions", can't you calculate the required pressure? (And then keep increasing until you hit 10 atm on the cup?)

ross
2018-09-11, 09:55 PM
If you say "this cubic metre is filled with water compressed sufficiently to fit what would be 1200 litres under standard conditions", can't you calculate the required pressure? (And then keep increasing until you hit 10 atm on the cup?)

As stated above, a cubic meter of water can exert a maximum of 1.1 atm on an object. So we need about 10 times as much water to shut off the cup; so water is still being produced; but there is no more room for more water; the water can't be compressed to make room; and the existing water can't move anywhere to make room, because the cube is totally impervious to all force.

exelsisxax
2018-09-11, 10:37 PM
You start making new and interesting forms of matter, because 'incompressible' is an imaginary trait. Molecular oxygen and hydrogen if they compress more, or maybe hydroxides and free protons. Probably not enough to make metallic hydrogen, but maybe liquid hydrogen or oxygen? Physicists would like to conduct this experiment.

NichG
2018-09-11, 11:02 PM
As stated above, a cubic meter of water can exert a maximum of 1.1 atm on an object. So we need about 10 times as much water to shut off the cup; so water is still being produced; but there is no more room for more water; the water can't be compressed to make room; and the existing water can't move anywhere to make room, because the cube is totally impervious to all force.

The mistake is that this statement is wrong. A cubic meter of water can exert any arbitrary amount of pressure on an object, based on how much the cubic meter of water is itself compressed. That 1.1atm figure is from the weight of a 1m column of water. When you compress the water into a cube, the dominant contribution to pressure isn't the weight of the water, its the fact that you've placed slightly more than 1 cubic meter of water into a 1 cubic meter space. The compressibility of water is the slope of that curve - for each percentage point of reduction in volume, how much does the pressure increase? Since water is almost incompressible, the curve is very steep.

So the cube will fill with water, and then the cup will almost instantly stop, and you'll have a cubic meter of water compressed to 10atm.

LibraryOgre
2018-09-11, 11:59 PM
"They surrender". (https://youtu.be/6uwnRz1z9iY)

Knaight
2018-09-12, 12:05 AM
The mistake is that this statement is wrong. A cubic meter of water can exert any arbitrary amount of pressure on an object, based on how much the cubic meter of water is itself compressed.

Up until the point where it would cease to be water anyways. To go to a ludicrously far extreme you eventually just get neutronium.

That said the general point of liquids being technically compressible and thus able to exert pressure absolutely applies, as does that technical compressibility leading to them being able to exert massively more pressure with a minor increase in quantity relative to a gas.

jayem
2018-09-12, 12:40 AM
That said the general point of liquids being technically compressible and thus able to exert pressure absolutely applies, as does that technical compressibility leading to them being able to exert massively more pressure with a minor increase in quantity relative to a gas.

So what you'd have assuming the field let gases through would be that the pressure would slowly rise to 2.1Atm (from the water and the air above it) exerting 1.1 Atm on the walls (which has air pressure acting in both directions).
At this point you'd rapidly get the force from trying to compress coming in and by the time you added an extra 1% mass you'd get 152 Atm (assuming the numbers you gave earlier).

If it were truly incompressible the first extra molecule would cause the pressure to jump to infinity and it would it would be pushed back into the extruder.


What would be a problem would be if it produced a fixed volume of room temp/pressure water.

NichG
2018-09-12, 01:40 AM
So many of the world-breaking properties of magic are just because someone didn't think it was necessary to add the addendum 'at standard temperature and pressure' to each and every magical item and spell...

Khedrac
2018-09-12, 02:22 AM
If this is 3.5 D&D then the rule that spells fail when they cannot be made to work properly kicks in - so the cup stops creating water as soon as the box is full.

TBH for me the red flag is the item having an effect depending on Real World physics - namely the "pressure exceed 10 atmospheres" clause - as soon as you try to mix 3.X D&D and RW physics the rules break. AD&D can potentially cope with this because the rules were a lot looser (it becomes DM's call) and I cannot speak for 4th Ed or later.

With other systems the answer will vary depending on the system in questions, but one important question (even for D&D 3.X) for this is "how are you determining the pressure?

NichG
2018-09-12, 02:36 AM
If this is 3.5 D&D then the rule that spells fail when they cannot be made to work properly kicks in - so the cup stops creating water as soon as the box is full.

TBH for me the red flag is the item having an effect depending on Real World physics - namely the "pressure exceed 10 atmospheres" clause - as soon as you try to mix 3.X D&D and RW physics the rules break. AD&D can potentially cope with this because the rules were a lot looser (it becomes DM's call) and I cannot speak for 4th Ed or later.

With other systems the answer will vary depending on the system in questions, but one important question (even for D&D 3.X) for this is "how are you determining the pressure?

Honestly, specifying a pressure cutoff is what saves it from being a situation where things break. It's equivalent to saying e.g. that the cup works by opening a portal to an infinite, gravity-less plane of water which is uniformly pressurized at 10 atm, where the portal radius adapts to the pressure differential within the geometry of the cup so as to limit flow through the portal to no more than 1 liter per second. So when the environmental pressure is 10atm, no fluid flows through the portal; and if the environmental pressure were, say, 20atm then you'd get back-flow; and so on.

On the other hand, a magic item that says 'this cup produces 1 liter of water per second' can produce e.g. pressures equal to those at the core of the earth (you'll be waiting a long time for that neutronium...) when combined with the force cage setup, because it doesn't recognize that the amount of energy needed to inject a liter of water into a situation isn't constant or specify that the effect is limited in the size of the forces and energies it could produce.

Of course, forgetting about the cup, you can certainly get yourself in trouble by having two force cages collide with each-other (by e.g. being anchored to different reference frames, or by being in a reference frame where the geometry of the force cage would be distorted such as the surface of a 2 meter radius rapidly rotating asteroid). So it's always good to have cutoffs in mind for these things.

Rabidmuskrat
2018-09-12, 03:02 AM
The water does not compress due to the weight of water on top of it, it is compressing because there is more stuff inside a fixed space than what would fit at 1 atmosphere.

What would happen is the following:
If the cube was a vacuum, the initial water would immediately vaporize due to the low pressure, turning into a gas.
Regardless of whether there was a vacuum or not, the pressure would increase as more water is added and the gas starts to be compressed.
At the time the water fills the cube, the pressure would spike upwards. Water is being compressed as more water is added and the pressure inside the cube can be calculated based on how much the water has compressed.
It would not spike very far, however. After very little compression, the inside of the cube would reach 10 atm and the addition of more water would stop.

You have the equation backwards. You are not solving for compression, based on pressure, you are solving for pressure, based on compression.

Frankly, if you have such cool things like indestructable containers and spontanuous (magical) generation, experiments like these are kinda tame compared to how you COULD be trying to break physics.

Satinavian
2018-09-12, 03:46 AM
Yes, as many others have said, "nearly incompressible" is not the same as "incompressible". And that is one of those cases where it does matter. The pressure would rise and the inflow of watr would stop when the cube is full.

Knaight
2018-09-12, 04:35 AM
So what you'd have assuming the field let gases through would be that the pressure would slowly rise to 2.1Atm (from the water and the air above it) exerting 1.1 Atm on the walls (which has air pressure acting in both directions).

No. Incompressible fluids can be pushed up in pressure. The difference is that cranking up their pressure doesn't cause their volume to decrease. Nearly incompressible real fluids are similar, except the volume does technically decrease, slightly.

ross
2018-09-12, 08:06 AM
If this is 3.5 D&D then the rule that spells fail when they cannot be made to work properly kicks in - so the cup stops creating water as soon as the box is full.

TBH for me the red flag is the item having an effect depending on Real World physics - namely the "pressure exceed 10 atmospheres" clause - as soon as you try to mix 3.X D&D and RW physics the rules break. AD&D can potentially cope with this because the rules were a lot looser (it becomes DM's call) and I cannot speak for 4th Ed or later.

With other systems the answer will vary depending on the system in questions, but one important question (even for D&D 3.X) for this is "how are you determining the pressure?

I'm not referring to any particular system. Pressure is determined by total force applied over total area.

ross
2018-09-12, 08:09 AM
The water does not compress due to the weight of water on top of it, it is compressing because there is more stuff inside a fixed space than what would fit at 1 atmosphere.

What would happen is the following:
If the cube was a vacuum, the initial water would immediately vaporize due to the low pressure, turning into a gas.
Regardless of whether there was a vacuum or not, the pressure would increase as more water is added and the gas starts to be compressed.
At the time the water fills the cube, the pressure would spike upwards. Water is being compressed as more water is added and the pressure inside the cube can be calculated based on how much the water has compressed.
It would not spike very far, however. After very little compression, the inside of the cube would reach 10 atm and the addition of more water would stop.

You have the equation backwards. You are not solving for compression, based on pressure, you are solving for pressure, based on compression.

Frankly, if you have such cool things like indestructable containers and spontanuous (magical) generation, experiments like these are kinda tame compared to how you COULD be trying to break physics.

I am not "trying" to break physics, I was just curious about what would happen in this specific situation.

aldeayeah
2018-09-12, 08:41 AM
I am not "trying" to break physics, I was just curious about what would happen in this specific situation.

You would end up with a cube full of water at a 10atm pressure, comparable to a depth of 100 meters in the ocean. That's not nearly enough to crush a freediver, but enough to give them decompression sickness should you dismiss the forcecage!

But that's only because of that wussy pressure limit. If you removed that pressure limit, you'd have increasingly dense, high-pressure liquid water, followed by increasingly dense, exotic forms of ice, followed by a series of exciting phases of degenerate matter, all the way to neutron matter and beyond. Needless to say, any non-indestructible object inside the forcecage would be crushed by the overwhelming pressure.

Midway through the process, you'd also get nuclear fusion, the resulting gamma radiation obliterating the surrounding area (since forcecage doesn't stop electromagnetic radiation from getting through).

Man, this should totally be a xkcd "What if" scenario. (https://what-if.xkcd.com/1/)

Delta
2018-09-12, 09:06 AM
...and finally, if you kept adding mass infinitely, you'd create a black hole that would get heavier and heavier until pretty much all of the universe begins collapsing into it, but since no matter can get inside the forcecage either (I think it works both ways?) all of the matter in the universe would gather around the edges of the forcecage until that becomes dense enough to collapse into singularities themselves, basically the whole thing would become a cube-shaped black hole with an even more massive black hole in its center (which doesn't really matter since from the outside it would be indistinguishable from a "normal" supermassive black hole) that continues to gobble up the universe.

halfeye
2018-09-12, 09:35 AM
Assuming the cup is denser than water, and is therefore at the bottom of the cube, then when the cube is full, the pressure on the cup is 1.1 atm ( or 2.1 atm if we take the outside air in to account ). Therefore, the cup continues to produce water. However, the cube is already full, the water can't exit the cube, and the water is still incompressible ( even at 150 atm, water only compresses by less than 1 % ). This appears to lead to a contradiction.

The idea that the pressure doesn't increase when more water is added to a full cube is mistaken. Imcompressible means that when you apply pressure to water, the size of the water doesn't go down very much. Incompressible does not mean that pressure cannot be applied to water.


...and finally, if you kept adding mass infinitely, you'd create a black hole that would get heavier and heavier until pretty much all of the universe begins collapsing into it, but since no matter can get inside the forcecage either (I think it works both ways?) all of the matter in the universe would gather around the edges of the forcecage until that becomes dense enough to collapse into singularities themselves, basically the whole thing would become a cube-shaped black hole with an even more massive black hole in its center (which doesn't really matter since from the outside it would be indistinguishable from a "normal" supermassive black hole) that continues to gobble up the universe.

Eventually, you would reach stasis, with the black hole emitting Hawking radiation at the same rate that the water was coming in, which since black holes emit less radiation as they get bigger, would be as a very big black hole indeed (I'm kind of assuming that that's per surface area, otherwise it would stop nowhere before universe mass, and maybe not then).

Pilo
2018-09-12, 09:46 AM
The Paradox kills you (Mage the Awakening) and both spells end.
If D&D 3.5, it does not works because you cannot teleport or conjure something inside something else :
A creature or object brought into being or transported to your location by a conjuration spell cannot appear inside another creature or object, nor can it appear floating in an empty space. It must arrive in an open location on a surface capable of supporting it

Anyway the cub dies by suffocation because of the typo.


Teleport the cub inside the cube. What happens?

https://media.gettyimages.com/photos/lion-cub-south-africa-picture-id177314345?b=1&k=6&m=177314345&s=612x612&w=0&h=EViPJ70BkjQEIw-BuxrVT0vR0VFNzFz2zF31K8Ufdb8=

Delta
2018-09-12, 09:56 AM
The idea that the pressure doesn't increase when more water is added to a full cube is mistaken. Imcompressible means that when you apply pressure to water, the size of the water doesn't go down very much. Incompressible does not mean that pressure cannot be applied to water.

Yeah, this. That water compresses so little just means that when the container is full, there's only very little water you could add until the pressure rises above the magical cutoff limit. Feels a bit like Zeno's Paradoxon to me, the problem is that OP is looking at it from a weird point of view.


Eventually, you would reach stasis, with the black hole emitting Hawking radiation at the same rate that the water was coming in, which since black holes emit less radiation as they get bigger, would be as a very big black hole indeed (I'm kind of assuming that that's per surface area, otherwise it would stop nowhere before universe mass, and maybe not then).

Yeah, I gotta admit my physics lessons in college were quite a while ago and I never really got that far into it to be able to call out specific numbers for Hawking radiation here, but I guess that's a possibility especially since the matter being "fed" to the black whole is so consistent. But yeah, this might actually be a fun question to submit to xkcd, unfortunately a) Randall rarely posts new what-ifs these days and b) he doesn't really like "infinity" questions for obvious reasons.

Nifft
2018-09-12, 01:59 PM
The incompressible water compresses into a bose-einstein condensate, where bosons behave like bozos and element zero crystallizes.

As we all know, a sufficient quantity of element zero immediately animates as a Void Elemental, and will therefore ignores the cube of force by teleporting somewhere fun.

LibraryOgre
2018-09-12, 03:16 PM
So, in the Guardians of the Flame series, a group of modern college students get inserted into their game world. One of them is an engineer, and they start developing gunpowder and taking on the slaver's guild. The slavers are allied with the Wizards guild, and so the Wizards create an approximation of gunpowder. IIRC, they do so by taking an iron sphere filled with water, and heating the water until the sphere would normally explode... but they also prevent the sphere from exploding.

The result is that it condenses into a powder that explodes when it gets wet.

Now, there's more involved than that. But, there you have it. Another option.

Psyren
2018-09-12, 03:24 PM
I'm not referring to any particular system. Pressure is determined by total force applied over total area.

But you have to, because the system is what will determine what happens when two magical elements (in this case, a spell and a magic item) of that system interact. That's why Khedrac's answer is the right one for D&D 3.5, while another system may have a different answer.

Deophaun
2018-09-12, 03:27 PM
If a material is incompressible, that means vibrations travel through it instantaneously, faster than the speed of light. Exert a force on one end, and that force is immediately transferred to the opposite end.

As nothing can go faster than light, incompressible materials do not exist inside physics.

kyoryu
2018-09-12, 04:47 PM
Water can absolutely exert stronger pressures than that.

That's how hydraulics work.

Delta
2018-09-12, 05:42 PM
Reading the OP again, I think the "paradox" he thinks of is indeed simply based on his choice of magic, so looking the question in a scientific way is meaningless. The problem is that he doesn't specify how the water is "produced". How exactly does that mechanism work? Is it like a portal to another plane filled with an unlimited amount of water at exactly 10 atmospheres of such size that exactly one liter per second can pass through? Then water would flow in until the pressure is equalized and the water inside the cage would of course be under 10 atmospheres of pressure. That's the most scientifically valid interpretation of the magical item you described.

If that's not what you meant, then it all boils down to you asking "I have a magic item that works by rule A and by rule B. What happens when rule A contradicts rule B?" to which to only answer can be "No one can tell you that, you made up the rules, so you have to make up the answer"

gkathellar
2018-09-12, 08:06 PM
We discover Ice XVII.

Satinavian
2018-09-13, 03:21 AM
You would end up with a cube full of water at a 10atm pressure, comparable to a depth of 100 meters in the ocean. That's not nearly enough to crush a freediver, but enough to give them decompression sickness should you dismiss the forcecage!

But that's only because of that wussy pressure limit. If you removed that pressure limit, you'd have increasingly dense, high-pressure liquid water, followed by increasingly dense, exotic forms of ice, followed by a series of exciting phases of degenerate matter, all the way to neutron matter and beyond. Needless to say, any non-indestructible object inside the forcecage would be crushed by the overwhelming pressure.

Midway through the process, you'd also get nuclear fusion, the resulting gamma radiation obliterating the surrounding area (since forcecage doesn't stop electromagnetic radiation from getting through).

Man, this should totally be a xkcd "What if" scenario. (https://what-if.xkcd.com/1/)
Well, if the forcecage really let's through gases, there might be a state where the added energy from pressing even more water into the cube is enough to force water through the the forcecage in the form of steam so that you end up with a cube of constant steam streams puring out from all sides.