I probably didn't stress enough the distance between Plasmas and Electron Degenerate matter; suffice it to say that I can make a small amount of plasma in the microwave youtube.com/watch?v=G7lfzA7WzVI and it takes stellar cores to make Electron Degenerate matter and would obliterate a generous amount of anything around it violently if we made it (unconfined magnetically) on Earth. In a graph it would be quite far away from Plasma.

What if the substance being compressed was connected to a heat sink, so that the compression was isothermal? If the system's temperature wasn't increasing as it became more compressed, would any of these stages change?

Yes. At some pressure, even with no heat increase (you'd need one hell of a heat sink here, or enlist some physical-law-defying deity to help) the crystalline structure that makes it a solid would be unable to resist the pressure (crystalline degenerate matter, if you will), which may form a liquid but more likely would jump straight to a gas (would depend on the material). Then, at some even higher pressure, if it was liquid it would eventually give to make gas, then give to make a Plasma, and so on to electron degeneracy pressure.

Even suppose it was some material that refused to exist in any of the states between, such as liquid or gas or plasma, it WOULD eventually get to Electron Degeneracy pressure (likely as a Plasma before that) with infinite force and infinite material strength, and continue the chain.

At sufficiently high pressures, the distinction between solid and liquid becomes vague. Isothermal compression of ordinary materials will go from solid to a sort of "flowing solid" state to electron degenerate matter without ever passing through a gas or plasma phase.

Why does it take divine intervention to have no heat increase? Other than the divine intervention needed to manufacture this piston in the first place, I mean. Can't you just press the piston extremely slowly, that is to say as slowly as it needs to go to let things cool to ambient? Not that we can know much about cold neutronium from observation, of course :-)

Sorry, but this is wrong. While it is possible under some circumstances to compress a solid and end up with a liquid, you will never get a gas by compressing a liquid. You're mixing up the effects of heating at constant pressure with the effects of adiabatic compression, which are different.

So, at what point will the inter-molecular bonds break? Presumably that is where the state will change from solid/liquid to gas? Also, when will the molecular bonds break, so that the atoms become separated?

I don't like this answer because it oversimplifies compression. When you're compressing a gas, you can do it isothermally, adiabatically, etc and this answer does not make those distinctions. I also agree with an above comment that compressing a liquid will not make a gas. In fact, Pressurized Water Reactors (PWR) at nuclear power plants exploit the fact that the opposite is true. Water above 100 degrees Celcius can remain in the liquid phase if pressure is sufficiently high.

@SteveJessop - It takes one hell of a heat sink to displace the heat of compressing ordinary room temperature matter through electron degeneracy and into a (room temperature) black hole.

@Nathaniel - I did offer up that it might skip a few states, I'll make that more clear. The adiabatic came in the comments after the question, but wither way it will eventually get to electron degeneracy pressure somewhere in that, and likely have some sort of plasma-ish states with ionized nuclei before that.

@Sean - I am oversimplifying compression. A piston/housing that's "infinitely strong, infinitely dense, has infinite compression" allows it. PWR reactors get nowhere near Electron Degeneracy pressure, and we aren't given that the substance is water - do you know with certainty all types of matter can be compressed to Electron Degeneracy pressure without entering gas or plasma states? (also you'd pretty much need an infinite heat sink to do so without heating).

@Ehryk: Considering just one step: suppose I have some room-temperature high-pressure matter that's just short of electron degeneracy. Suppose I don't attach one hell of a heat sink to it, but I do compress it a little bit more and then stop. I presume it gets hotter, perhaps much hotter, but does it ever cool down to a room temperature electron-degenerate state, or does it do something different? For the overall process (all states), what's the difference between one hell of a heat sink vs. a crummy heat sink and one hell of a lot of time?

@SteveJessop - sure, just like I said, bring in the physics bending deity to keep temperature constant, or infinite heat sink, or a regular heat sink and lots and lots and lots of time (astronomical time, depending on the amount of source matter) and you could have room temperature electron, proton, neutron, quark, and (preon) degenerate matter. However once you cross the Schwarzschild radius, the singularity would then take it from really, really dense matter to infinite density and thus produce infinite heat out of your room temperature degenerate matter.

... thus the need for an infinite heat sink, or the help of a deity or just allowing it for the sake of a thought experiment. The singularity itself couldn't be brought to room temperature, I don't think (but the infalling matter could).

Heh, yes, I'm happy to let the inside of the event horizon be any temperature it likes, although I suppose we might have to contend with the temperature of the Hawking radiation. I think "astronomical time" fully answers my original question, and leaves "how fast?" as an issue the questioner doesn't address and that (in the extreme) affects the answer.

For what it's worth, for single atoms, or perhaps one gram, and large heat sinks, it might be doable within a human lifetime. I wonder if there's a way I could calculate the heat for a given amount of source material compressed to room temperature electron degeneracy...

@Ehryk A singularity aka Black Hole ...yes, and then what happens?! Don't keep me in suspense.

@BadHorsie ... and THEN... the black hole of the matter would then merge with the piston and it's cylinder walls and head / other end of the piston (infinite density, remember) and because physics has been so bent as to allow an infinite density non-zero-volume piston, it would contain infinitely more matter than the entire universe (which may have singularities with infinite density but over zero volume)...

... the compressed matter making little difference to the infinimassive black hole / singularity that is the piston, which would reverse the expansion of the universe, sucking all matter into it gravitationally including you and I and everything we can see, like bathwater down the drain but more hot and violent and full of death. Even on the way down it would send gamma ray jets out to obliterate all life as we know it.

@Ehryk ...bummer.

Hey, at least we'll all go out close together bathed in warmth just like we started out this journey instead of being forever thrust into the lonely expanse of nothingness, forever alone, until the eventual heat death of a cold, cold universe.

@Ehryk it's not a case of "it might skip a few states", it's a case of your sequence being in completely the wrong order. Under adiabatic compression virtually all substances will go from gas to liquid to solid, not the other way. Just look at the Earth's core - the inner core is solid because the pressure is higher.

@Nathaniel - that's all well and good, but the question as stated does not make any reference to adiabatic compression; thus my answer does not, either. Compression would produce heating; heating would (likely, depending on substance) produce the phase changes in that order perhaps skipping a few. In the comments someone else asked about adiabatic compression with an infinite heat sink, and at which case I have since mentioned they many not follow that order until electron degeneracy - but only in the comments, because this wasn't the question as asked.

@Ehryk: You should look up the term "adiabatic". I'm not quite sure what you think it means, but "adiabatic compression with an infinite heat sink" is a contradiction in terms.

So if you compressed air, and allowed said compression to heat the air correspondingly, you would expect it to compress into a solid? Where's your source on this? (I thought it meant 'without heating the substance')

@Ehryk, when oxygen is compressed (diamond anvil cell) first it turns blue, then red, then shiny metal indistinguishable from steel. Where's all that in your description?

@alancalvitti It's decidedly missing, because the OP did not specify the material or phase, let alone oxygen when they wrote "some type of matter", nor did I make any claims on coloring. If you'd like to give an in depth treatment to a specific material, but you may do so in your own answer if you like.

@Ehryk "adiabatic" means without allowing heat to pass in or out of the system. When you talk about things being "compressed, resulting in lots of heat", you're talking about adiabatic compression. But you're wrong about its effects. Compression releases heat but it also increases pressure, and the phase of a substance depends on that as well. It's simply impossible to compress a liquid into a gas, and rare to compress a solid into a liquid - it's usually the other way around. For a reference, take a look at the phase diagram for any substance.

@Ehryk - Adiabatic means energy doesn't enter or leave the system spontaneously as heat, but compression will still do work on the system and add energy to it (if the compression is reversible so there's no change in entropy, you should be able to integrate -P(V) dV to get the change in energy according to the fundamental thermodynamic relation). And according to the equipartition theorem, increasing its internal energy should increase its temperature.

@Nathaniel when an internal combustion engine compresses an air/fuel mixture, the temperatures increase greatly; so greatly that in standard gasoline like compression ratios of ~10:1 or so, you can have a ~400 degree F air charge from ambient. What compression 'releases' heat? If I have a certain volume of matter, and with infinite force and infinite strength make it occupy half of that volume and don't heat sink it away, the temperature of the substance would increase.

This would indicate a positive slope on the phase diagram; pressure is increasing, causing temperature to also increase likely in some proportionate ratio (though perhaps not linear), in which case at some point a solid would melt or sublimate, and a liquid would boil (due to the resulting temperature increase, not directly from the pressure itself).

@Nathaniel also note that internal combustion engines are NOT adiabatic then; they allow energy to enter the system in the form of fuel and ambient air; and exit the system via exhaust gas and heat transfer via a cooling system. Despite being non (completely) adiabatic, the compression of the fuel/air mixture in the cylinders heats the charge greatly; thus by talking about "compressed, resulting in lots of heat" you MAY NOT BE talking about a completely adiabatic system.

@Ehryk Internal combustion engines are a bad example, the vast majority of the energy/heat released is due to the combustion of the gasoline, not compression. Look at the phase diagram for water (www1.lsbu.ac.uk/water/water_phase_diagram.html), starting at the circled E (STP conditions), unless the slope of our line is extremely small (a very large amount of work giving a very small pressure change), then the water won't ever go from liquid->gas or solid->gas.

The reason why people keep bringing up the process being adiabatic is that at least for the relatively boring pressure ranges (i.e. gas->liquid->solid), the amount of heat generated by compression can easily be dissipated in a reasonable time frame.

@cartographer I tune internal combustion engines, and have to select compression ratios and boost levels that don't predetonate my fuel because the fuel/air charge, without a spark or combustion, would heat so much it would detonate on it's own; even without fuel entirely you have a non-completely adiabatic process that is compressing matter and in doing so producing a large amount of heat (say, 70F -> 400F).

Are you saying that if I took frozen ice at -10C, and pushed on it with infinite force and unbreakable materials, I would get all the way to electron degeneracy pressure before the ice melted, sublimated, or melted and then boiled? Do you have a source on this?

For reference, according to this wikipedia article Copper's electron degeneracy pressure is $ ~40 GPa $, and Neutron star cores, past Proton degeneracy, are $0.3-16\times10^{34} Pa$. I'd be interested in phase diagrams that extend this high in the pressure direction. The hitch of my argument here is, I suppose, with infinite force all matter would compress (to infinite density), and this would produce some amount of heating, which may cause phase changes depending on the substance.

Perhaps I have overestimated said temperature change, so I'd also be curious to see how much temperature would be involved in pressurizing something to electron degeneracy pressure from STP if there are sources on doing so.

@Ehryk I'll defer to your expertise for the pre-detonation issues, but the majority of the energy/heat released in a combustion engine is still from the actual combustion. Actually, this is actually a perfect example of why the time scale + whether the process is adiabatic or not matters.

I think you would agree that the fuel/air mixture is being compressed very quickly relative to the normal time scales a person deals with, and that if you compressed it from 10:1 (non-adiabatically) over a period of 30 seconds it would probably not heat up nearly as much.

@Ehryk I apologize, I think I was unclear. I don't have any problem with the answer starting at electron degeneracy pressure, simply because its such a different case (and I have no idea, nor does it seem like there is a definite consensus on how exactly that happens in the literature anyway). The only problem I had was the adiabatic thing for the (boring) transitions, and the liquid->gas and solid->gas possibilities.

On second thought, I think it really depends entirely on the temperature increase due to the compression and whether or not the process is adiabatic.

@cartographer I'd agree that it is 'somewhat' adiabatic in both internal combustion engines and compressing a solid; heat leaves the system (cooling system) but relative to the speed of the compression, not much of it and certainly not enough to keep the substance at a constant temperature (vertical line/undefined slope on the phase diagram). Air compressors are another example; they dissipate the added heat over the surface area of the container.

All I'm trying to argue is that SOME temperature increase would happen as you kept applying your infinite force, and thus you have some positive slope (perhaps high, perhaps a low fractional one), and when I look at phase diagrams starting from solids if you take a positive sloped path through the diagram you either melt, sublimate, or boil the substances I looked at.

Thus, from my reasoning (which may be flawed, for sure) it appears as though if you started with ice cubes at -10C, and applied infinite force (increasing the substance's temperature), most ranges of positive slopes indicate the answer I provided. Even if the slope is at a 89 degree angle, and you only have a slight temperature increase with LOTS of pressure increase, by the time you get to degeneracy scale pressures of 40GPa + (which I have yet to find a phase diagram that goes this high)...

The temperature would be well past solid and liquid temperatures for standard pressure. Wait, here's one: upload.wikimedia.org/wikipedia/commons/thumb/0/08/…

I guess it completely depends on temp:pressure slope; my mistake. How can I include this in my answer while still staying generic enough for 'all matter'?

With water you could even get solid->liquid-solid with a ~45 degree slope, or perhaps even solid->liquid->gas->liquid->solid, assuming a linear relationship; but I can't really assume linear relationships, either, or that this diagram is representative of ALL matter. Suggestions for how to edit my answer to properly treat solid/liquid/gas/plasma phases universal to all substances are welcome.

Yeah, I'm trying to think. Really you just need a good idea of the amount of energy you need to compress a normal liquid or solid a significant amount. I think the magnitude of that number will entirely determine the high pressure solid/liquid steps.

Pretending the process is adiabatic for a second, I think you can look at from the point of view of the en.wikipedia.org/wiki/… of a solid, just in reverse. In that case it looks like the temperature increase might actually be so much so that basically everything goes straight to gas.

I think this makes sense from an atomic standpoint because as you force the atoms together, as long as energy is not lost (aka its adiabatic) then they will always have enough energy to break any sort of attraction between them (barring chemical reactions), will always fill the space they are in, and would thus be a gas.

Actually I take that last part back, since it depends on any energy barriers.

That was my initial sentiment on it: the slope would essentially be ~1-5 degrees and thus go solid->liquid->gas->plasma or solid->gas->plasma depending on the substance. I mentioned 'crystalline degeneracy pressure' earlier in this comment thread, at which point the 'structure' that makes them a solid can no longer withstand the pressure thus making it a liquid or gas.

Are there sources we can cite for this to convince the naysayers, or find some sort of pressure:temp ratio that applies to this sort of thing?

@Ehryk I think you can use phase diagrams for the solid->liquid argument since even water can do this with no temperature change as seen in your link. For the liquid/solid->gas->plasma transition I think you can argue that since the atoms end up being "pushed" up the slope of the repulsive potential between atoms (e.g. en.wikipedia.org/wiki/Lennard-Jones_potential), so in terms of energy alone you can see that once the distance between atoms is small enough,

they would have enough potential energy to overcome any energy barriers that would (depending on the substance) stop them from acting as a gas and filling whatever volume they are in.

It's still pretty vague though, and the exact behaviour wouldn't be easy to determine. I think as long as you have some sort of argument that the temperature increase is high enough to assume the process is adiabatic once you are at the solid/liquid point, it should be ok.

Do you know of any sources I could use to back my assumptive intuitions on the temperature increase?

Well as a first approximation, the thermal expansion coefficient can be used to get an idea of the magnitude, since the walls of whatever we're compressing this stuff in are immovable. For example, water only expands by 0.1% if you heat it ~5K, if you assumed this was valid for large changes (probably not but its a decent approximation I guess), then you would need to heat it 550K to expand it by 10%.

For steel, assuming you can extrapolate the thermal expansion coefficient to large changes like that (and ignore temperature initially), you would need to heat it by ~3300 K.

On a second note, it would ALWAYS run through a plasma phase, would it not? Electron degeneracy doesn't happen as an all or nothing proposition (other than for hydrogen): before the nuclei lose all their electrons (electron degeneracy) they lose their outermost orbital, and then the next one, and then the next one... am I correct in this being Plasma? en.wikipedia.org/wiki/Plasma_%28physics%29

Does that thermal coefficient work in reverse? If I compress water 0.1% will it heat ~5k, and compress steel 10% will it heat 3300K?

For small changes, like 0.1% and if you assume the walls of the container are immovable and infinitely strong and all that, yeah I'm pretty sure.

The 10% is a huge approximation though, but I think it should be representative of the scale of energy needed.

Mathematically you can say that you can apply it in reverse if the process is adiabatic and the walls are immovable. And so you just say, ok so since the increase in temperature would be this much if we treated it adiabatically, then we can basically just say it is, since the temp is that high.

If this were indeed the case, then basically EVERY substance would go solid -> (liquid) -> gas -> plasma -> electron degeneracy, with some having brief states in the liquid phase and most going straight to gas, correct?

Well.... hmm.... except percent of material compressed varies greatly with respect to Pa of pressure, so it's not a straightforward relationship between Pa and Temperature.

Am I correct on my use of plasma here? (fractional electron degeneracy)?

I don't think so

Electron degeneracy pressure is the "pressure" due to the pauli exclusion principle, which doesn't have much to do with plasmas. Additionally, according to wikipedia at least, proton degeneracy pressure is LESS than electron degeneracy pressure, so you might want to reorder that.

Actually I think I'm mixing up electron degenerate matter and electron degeneracy pressure. I think you're right with plasma being a necessary step before electron degenerate gases. The proton thing still stands though.

Ok so ignore me on the proton thing, electron degenerate matter is defined as the point where the degeneracy pressure is greater than the pressure due to thermal movements. Since the pressure is lower for protons, and our material presumably isn't 100% protons/electrons, I'm not sure "proton degenerate matter" would ever exist on its own, which is probably why wikipedia says "proton degeneracy is usually modeled as a correction to the equations of state of electron-degenerate matter."

Of course, our temperature isn't low either, so if the pressure due to the temperature is greater than the electron degeneracy pressure, will we even have electron degenerate matter? Or go straight to combining electrons and protons to form neutrons? Pretty much all of the info I see is related to astronomy, and is non-adiabatic, so I'm not so sure about the proton/electron/neutron stages either.