Thermodynamics of solids under extreme pressure

[dBrandon/dC]

I was wondering - when pressure is applied to solids, do they heat up? Not pressure like an impact - I'm not talking about conversion of kinetic energy. But suppose a piece of iron is put in a hydraulic press and the pressure increases slowly. More specifically, I'm wondering about the rocks deep inside the earth. Do solids generate heat simply by being under pressure? It seems like high pressure could restrict the thermal motions of the molecules, causing them to generate heat simply by their vibrations. But since solids are generally incompressible, I didn't know if this would happen. Actually, I guess that's another question - are solids really incompressible, even under giga-Pascals of pressure?

 

[A. Neumaier]

I was wondering - when pressure is applied to solids, do they heat up? Not pressure like an impact - I'm not talking about conversion of kinetic energy. But suppose a piece of iron is put in a hydraulic press and the pressure increases slowly. More specifically, I'm wondering about the rocks deep inside the earth. Do solids generate heat simply by being under pressure?

It depends what you can assume to be constant. Assuming a reversible process, the laws are dU=TdS-PdV and SdT=VdP; the term TdS is the heat. This tells it all.

 

[Andy Resnick]

Actually, I guess that's another question - are solids really incompressible, even under giga-Pascals of pressure?

*everything* is compressible.

http://www.jstor.org/pss/84446
http://adsabs.harvard.edu/abs/1992ZhETF.102.1433T
http://prb.aps.org/abstract/PRB/v32/i12/p7988_1

Some materials even have a negative compressibility- they expand under pressure:

http://www.sciencemag.org/content/281/5374/143.full
http://www.sciencemag.org/content/331/6018/742.abstract
http://prl.aps.org/abstract/PRL/v68/i5/p674_1

In any case, as Arnold wrote, whether the material heats (or cools) during compression depends on the process and what is held constant.

 

[RedX]

Some materials even have a negative compressibility- they expand under pressure:

http://www.sciencemag.org/content/281/5374/143.full
http://www.sciencemag.org/content/331/6018/742.abstract
http://prl.aps.org/abstract/PRL/v68/i5/p674_1

So if you put such material in the chamber of a cylinder, and push down on it with a piston, what exactly happens? It can't exactly expand since the piston is in the way, yet pressure is increasing as the piston pushes down harder on the material.

Anyways, I believe the compressibility of a solid is manifest in the finiteness of the speed of sound in solids, which I think is the maximum speed that a material can compress.

 

[Andy Resnick]

So if you put such material in the chamber of a cylinder, and push down on it with a piston, what exactly happens? It can't exactly expand since the piston is in the way, yet pressure is increasing as the piston pushes down harder on the material.

Interesting question- I'm not sure. If you contact these folks, you may get a response:

http://silver.neep.wisc.edu/~lakes/sci87.html
http://www.mrsec.wisc.edu/MR--Nugget.php?ID=33
http://onlinelibrary.wiley.com/doi/10.1002/pssb.200777708/pdf

 

[AlephZero]

You seem to have a basic misunderstanding about "compressibility". Almost all materials are compressible even with "small" applied forces. For eaxmple when you bend a cantilever beam, the material on one side of the neutral axis is compressed and the material on the other side expands.

The only isotropic materials where this is not true are the small number of materials with Poisson's ratio = 0.5. Rubber is one common example.

So if you put such material in the chamber of a cylinder, and push down on it with a piston, what exactly happens? It can't exactly expand since the piston is in the way, yet pressure is increasing as the piston pushes down harder on the material.

Most likely, the same would happen as if you did the experiment with a "normal" material. The cylinder would expand as far as necessary, to maintain equilibirum of the forces. Of course for a negative compressible material, the expansion (and stress in the cylinder) would be higher, so it would probably burst for a smaller piston movement.

Anyways, I believe the compressibility of a solid is manifest in the finiteness of the speed of sound in solids, which I think is the maximum speed that a material can compress.

You are right that the speed of sound is related to the elastic modulus of the material. The speed of sound is always of the order of sqrt(modulus/density), whatever type of wave is propagating through the material.

This does represent the "maximum speed that compression can propagate through the material from one point to another" (measured by the wave propagation speed), but the "maximum speed the material can compress at a fixed location" (measured by the rate of change of strain at the location) is something different.

 

[RedX]

This does represent the "maximum speed that compression can propagate through the material from one point to another" (measured by the wave propagation speed), but the "maximum speed the material can compress at a fixed location" (measured by the rate of change of strain at the location) is something different.

Can the maximum speed of the material can compress at fixed location be infinite? The speed should be the amplitude of the wave times the frequency?