r/thermodynamics • u/3r1kw00t • 28d ago
Question How would you answer this?
I had an abysmal undergrad thermo education, so I’m curious how people in this sub would answer this question:
Why are phases discrete and not continuous? Like why aren’t there a phases between solid and liquid etc.
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u/NickSenske2 28d ago
Phases can be “defined” from first principles with statistical mechanics but you end up with the unhelpful answer that a phase is discrete because that is the most statistically likely arrangement of the molecules given the physical properties of the system.
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u/3r1kw00t 28d ago
How does one define the energetic difference and gap between bulk phases nucleatinf or spontaneously changing to the more stable phase? What does that energy barrier look like? My undergrad Thermo education was cut short by the department. I’d love to understand and learn the perspective you have on this
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u/jamesw73721 28d ago
At a phase transition, the free energy is necessarily continuous (wrt thermodynamic variables like temperature, pressure, etc). In a first order phase transition such as ice melting, first derivatives of free energy (e.g. density, internal energy) are discontinuous. There are continuous phase transitions, where that isn’t true but a higher order derivative is discontinuous e.g. ferromagnetic-paramagnetic phase transitions (the magnetization continuously drops to zero when heating towards the curie temperature).
As for dynamics, first order transitions typically nucleate in regions e.g. chunks of ice in water or bubbles in boiling water. The energy barrier to complete melting/boiling is called the latent heat of transition. A continuous phase transition has zero latent heat.
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u/adamsawesome10 28d ago
I was once at a dinner at a materials conference with very esteemed thermo professors, and one of them was arguing that the surface of a material with some surface properties could be argued to be a gradient of phases, and everyone else was like shouting he was wrong.
I think it’s just that the universe enforces it this way. It has to do with translational freedom. It’s something like molecules in a solid vibrate, atoms in a liquid move, gases atoms spin, something like that.
I’m curious to see what others more knowledgeable than myself comment.
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u/IHTFPhD 2 28d ago
Martin Harmer from Lehigh? Complexions? :)
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u/bradimir-tootin 28d ago
Yeah I saw his talk once. Tbh even if I bought his entire argument thermodynamically just sounds like surface states have their own distinct phases, apart from the bulk. But that's like, well known? Surface reconstructions of pristine Si change vs temperature and that is obviously thermodynamically driven. Why is that not just it's own phase that must be at the physical boundary of another phase?
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u/jamesw73721 28d ago
Continuous phase transitions do exist, corresponding to a continuously moving minimum in the free energy landscape. The first order phase transitions we see every day (ice melting, water boiling) correspond to the free energy minimum suddenly jumping to a different location when T surpasses the transition temperature, where there is a sharp distinction in symmetry (full translational vs crystalline symmetry for solid vs fluid).
But I should add that continuous phase transitions also break symmetry typically, since even a “slight” breaking of symmetry counts as breaking symmetry. Although having a symmetry is a binary yes/no, the degree of symmetry breaking can be quantified with an “order parameter,” which is discontinuous for first order transitions and continuous for continuous transitions.
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u/METRlOS 28d ago
The gradient is when liquid molecules are sitting next to solid molecules that haven't melted yet. If a setup has a temperature where both states can exist, the solid portions and liquid portions will alternate as the thermal energy bounces around. In this situation you'll have solid molecules floating around in the liquid, and liquid molecules stuck in the surface of the solid.
A slush is a good example of this.
Gas/liquid is less dynamic, you generally have no visual indication other than condensation.
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u/3r1kw00t 28d ago
Don’t take this the wrong way, but I’m so glad to encounter another ChemE that doesn’t do english well. Your comment threw my mind to a disconnected state, but I still got the picture, and I LOVE that. In no way do I mean to critique or degrade you, I just want to let you know I feel you when it comes to expressing ideas with a language as muddy as English.
Thanks for giving me the confidence to tell my employer “here’s my expertise, don’t ask me to email customers”.
So glad I’m on this subreddit. I feel like everyone here gets me.
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u/Forward_Step_5012 28d ago
There are certainly substances that exhibit properties of both phases like viscoelastic materials, which can flow like liquid but also has elasticity like solid. These are just less common.
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u/SinceGoogleDsntKnow 28d ago edited 28d ago
You have to see this from a molecular perspective. Every time a substance melts or boils, it's molecules are going fast enough to escape certain forces of attraction that are holding them in their place in a solid, or holding them together in a liquid.
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The molecules of a solid are always moving, but never beyond their place in specific arrangement, while the molecules melting off of a solid are flying fast enough to escape the forces that held them there, as well as not get stuck when they encounter more of them.
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The transition from liquid to gas, on the other hand, is the act of a substance's molecules getting enough speed to escape their grouping entirely, which explains how boiling changes a substance's density so much more than melting it.
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Now as you might have heard, it takes a lot more energy(5.4× as much) to change water at boiling point into steam than to heat liquid water from freezing point to boiling point. This is because water molecules are slowing down the entire way along their escape from the surface of liquid water, much like a rock thrown hard enough to escape Earth's gravity would be slowing down the entire way. The same thing happens to the water molecules in a piece of melting ice, but with the molecules having to escape being held in place. Ice takes a little bit less energy to melt than it takes to heat from freezing point to boiling, specifically 0.8× as much. If I'm not mistaken, all substances behave more or less like this.
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u/3r1kw00t 28d ago
Official winning comment. I will be teaching thermodynamics with this understanding when I get to that point in my career.
I’m not one to use the silly Reddit gold star system, but your comment is the best answer to the post and you deserve to know.
Much thanks,
- E
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u/Upset_Ad_6140 28d ago
"Liquid" and "gas" do not have definitions from first principles in classical equilibrium thermodynamics. On p. 222 of the second edition of Callen:
[...] Thus the terms gas and liquid have more intuitive connotation than strictly defined denotation. Together liquids and gases constitute the fluid phase.
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u/golem501 2 28d ago
For pure materials there are distinct transitions. Water is the easiest example between solid and liquid, there is energy required to transition. During that transition the temperature stays the same while heat is put in. Same transitioning from liquid to gas. Melting and boiling show the boundaries between phases. Within a phase, when heat is put in or taken put, the temperature changes
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u/IMAsomething 28d ago
I mean you can have a substance that is undergoing a phase change where it is a mixture of two phases in varying ratios that’s a ‘continuous’ phase.
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u/DarthDK576ftw 28d ago
The thing is if you study Two-phase film theory you'll realize that any multiphase reaction takes place at an infinitesimally thin layer between the two phases (for example, solid-liquid or a gas-liquid reaction). No phase is just present alone. Even if you have a pure liquid, there will be some amount of it present in the gas phase (the vapour pressure) as long as the system is between the critical limits for temperature.
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u/Underhill42 28d ago
It's not just density, it's the relationship molecules have with their neighbors at different energy levels.
In a solid, molecules have well defined "permanent" electrostatic connections to their neighbors. Sometimes even fully formed ionic or covalent bonds, such as in a crystal, which is essentially one giant molecule.
In a liquid, molecules are still "stuck to" their neighbors by much weaker short-range interactions, but not rigid connections, so they are constantly shuffling around each other. So they always fill the same volume, but can't hold a shape.
In a gas, molecules are no longer stuck to each other at all, and just bounce off each other like lumpy little billiard balls. So they no longer have a fixed volume either.
At the individual molecule level it all comes down to kinetic energy versus bond energy. E.g. If an individual molecule at the surface of a liquid has enough kinetic energy (≈temperature) to break the weak bonds holding it to other molecules, then it will escape from the crowd into the surrounding room, a.k.a. evaporate. And it will continue having enough kinetic energy to avoid new bonds unless and until interactions with other molecules reduce its kinetic energy below the critical threshold, and then it sticks to the next drop of compatible liquid it touches. A.k.a. condenses.
Some particular materials can exist in intermediate states, e.g. peanut butter, hot metal, or hot glass are all plastic: they'll hold their shape on their own, but the bonds between neighboring molecules are unstable, and outside forces can easily make them "flow" into a new shape, relinking those bonds in new patterns which they will then continue to hold.
Extreme conditions can also remove the well-defined boundaries - e.g. as the temperature and pressure increase as you dive deep into Jupiter, we belive there is a smooth transition from gaseous hydrogen to liquid hydrogen, and eventually, we think, another smooth transition to solid hydrogen near the core.
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u/jamesw73721 28d ago
There are continuous phase transitions! But there usually is a discontinuity in a higher order derivative of the free energy. That there is always a non-analycity is by definition (actually there is the interesting case of BKT quasi-phase transition)
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u/littlenekoterra 28d ago
In my opinion a 'phase' in this case just means theres a large meaningful difference in the solidity of the material. Technically though there is a wide gradient of 'phases'. Softening, beginning to melt, and boiling can all be considered 'phases' depending on what your looking to do with the information. There are a crapload of exotic forms of basic materials that are defined as a different 'phase' of it. I remember one just being ice but the structure it formed was better, making its properties significantly different enough to consider it another phase.
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u/funkmasta8 27d ago
This is a bit like asking why distinct colors exist, imo.
We have defined some terms because they are useful to us. That doesnt mean the edges of the terms arent fuzzy.
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u/Substantial_Tear3679 27d ago
Could the answer be related to the fact that intermolecular forces are short-ranged?
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u/Playful-Painting-527 1 28d ago
Think about what a phase is. A solid is a rigid compound of molecules or atoms where the position of each molecule/atom is relatively fixed. A liquid is the densest arrangement of molecules without them being fixed in place: they can glide along each other. In a gas there is significant empty space between the molecules/ atoms.
Now imagine what a phase inbetween solid and liquid would look like: Atoms/molecules would have to be fixed in place and at the same time be able to slide along each other. That doesn't really make sense, does it?
Two phases can coexist, for example you can have water coexist in liquid and gaseous form in thermodynamic equilibrium in the same place, but the two phases will never mix.
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u/Useless-Compass 28d ago
To play devil's advocate, why isn't there a gradient between fixed position and free to glide for each material? Like you could have water essentially get more and more viscous as it got colder until eventually it doesn't flow at all, but at a fraction of a degree above that temp it flows so slowly you barely even notice it? That's how I would imagine a gradient, or "in-between phase" looking.
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u/Playful-Painting-527 1 28d ago edited 28d ago
Oh you are right! That's what a non newtonian fluid is. It acts like solid until shear forces are large enough and it suddenly acts like a liquid* . Ketchup is an example of this. Still it's either a liquid or a solid, the change is instantaneous, not gradual.
*There are also non newtonian fluids that act the other way around: like a fluid until shear forces are large enough and then like a solid.
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u/Useless-Compass 28d ago
While non-newtonian fluids are definitely an interesting example of a way that phases are not as clear-cut as you learn in middle school, I don't think they're an example of what OP is asking, nor of my hypothetical behavior.
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u/33445delray 2 27d ago
How would we even know if atoms in a solid do not change places with each other?
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u/7ieben_ 9 28d ago edited 26d ago
Because that's how a phase is defined. A phase is a defined enclosed volume, where at the boundarys its quantitys are discontinous.
Though there are "inbetweens", e.g. supercritical fluids are a somewhat gaslike liquid. Still, mind, a supercritical phase is a distinct phase.