# Which Phase of Matter has Largest dV/dT?

• gatztopher
In summary: And, hopefully, an explanation. Thanks!In summary, the ideal gas law does not apply to liquids or solids, and the coefficient of thermal expansion can be used to determine which phase has the greatest change in volume per change in temperature. However, this information is not readily available for phases in general, and further research is needed for a complete understanding of this concept.
gatztopher
Friend just asked me this question. I came to a conclusion using the ideal gas law (figured I could go off of different N/V for different phases), and it didn't make any sense. Then I realized, ideal gas law doesn't apply to liquids/solids! Gaaah!

Question: how do I empirically answer this? I could just say gas because that's intuitive, but then I wouldn't be a better physicist!

gatztopher said:
Friend just asked me this question. I came to a conclusion using the ideal gas law (figured I could go off of different N/V for different phases), and it didn't make any sense. Then I realized, ideal gas law doesn't apply to liquids/solids! Gaaah!

Question: how do I empirically answer this? I could just say gas because that's intuitive, but then I wouldn't be a better physicist!

See http://en.wikipedia.org/wiki/Coefficient_of_thermal_expansion, especially http://en.wikipedia.org/wiki/Coeffi..._expansion_coefficients_for_various_materials.

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Hmm... this is interesting. Some materials have a negative coefficient of thermal expansion, so that means that lowering the pressure also warms the material (Joule-Thompson effect). Exposing ice water to vacuum will warm the slurry. But where does that energy come from?

Andy Resnick said:
Hmm... this is interesting. Some materials have a negative coefficient of thermal expansion, so that means that lowering the pressure also warms the material (Joule-Thompson effect). Exposing ice water to vacuum will warm the slurry. But where does that energy come from?

Why do you think that? Why would the slurry warm up? Generally pumping on a liquid or volatile solid under it's own vapor pressure causes cooling ... you can actually freeze water this way if you pull a vacuum fast enough. Anyway, the coefficient of thermal expansion for ice is positive. I guess you were thinking that since the ice/water phase transition involves a positive change in the molar volume, then there is a thermal effect as well? I don't think that is correct.

That Wikipedia entry is great, but I still have inquiries. My question was weirdly stated to begin with, so let me restate it:

Between the gas, solid, and liquid phases, how can I determine which has the greatest change of volume per change in temperature?

The wikipedia entry lists change of volume per change in temperature, but by material - I want that same information, but for phases. And, hopefully, an explanation. Thanks!

SpectraCat said:
Why do you think that? Why would the slurry warm up? Generally pumping on a liquid or volatile solid under it's own vapor pressure causes cooling ... you can actually freeze water this way if you pull a vacuum fast enough. Anyway, the coefficient of thermal expansion for ice is positive. I guess you were thinking that since the ice/water phase transition involves a positive change in the molar volume, then there is a thermal effect as well? I don't think that is correct.

If you put an ice water mixture under pressure, the melting point will become lower, this means the temperature will also become lower, the energy will melt some of the ice.
You need about 10^8 Pa to get to about 255K however. At higher pressures some other form of ice will form

If you remove the pressure again, the melting temperature will go up and the energy for this comes from some of the water freezing. Of course lowering the pressure to below the vapour pressure of water will cause evaporation and cooling.

SpectraCat said:
Why do you think that? Why would the slurry warm up? Generally pumping on a liquid or volatile solid under it's own vapor pressure causes cooling ... you can actually freeze water this way if you pull a vacuum fast enough. Anyway, the coefficient of thermal expansion for ice is positive. I guess you were thinking that since the ice/water phase transition involves a positive change in the molar volume, then there is a thermal effect as well? I don't think that is correct.

If you put an ice water mixture under pressure, the melting point will become lower, this means the temperature will also become lower, the energy will melt some of the ice.
You need about 10^8 Pa to get to about 255K however. At higher pressures some other form of ice will form

If you remove the pressure again, the melting temperature will go up and the energy for this comes from some of the water freezing. Of course lowering the pressure to below the vapour pressure of water will cause evaporation and cooling.

willem2 said:
If you put an ice water mixture under pressure, the melting point will become lower, this means the temperature will also become lower, the energy will melt some of the ice.
You need about 10^8 Pa to get to about 255K however. At higher pressures some other form of ice will form

If you remove the pressure again, the melting temperature will go up and the energy for this comes from some of the water freezing. Of course lowering the pressure to below the vapour pressure of water will cause evaporation and cooling.

Sure, but that is not what was proposed. The exact statement was, "exposing ice/water to a vacuum, will warm the slurry". I don't see how that could happen if you start from room temperature ... actually, as long as both phases are present, then the temperature should remain constant, right? However, I took Andrew's statement as you did, that there would be a *net* release of energy into the mixture upon exposing it to vacuum. I guess that might be true if there were a way to do that without allowing any vapor to escape, but it definitely seems to go against what I have observed experimentally.

gatztopher said:
That Wikipedia entry is great, but I still have inquiries. My question was weirdly stated to begin with, so let me restate it:

Between the gas, solid, and liquid phases, how can I determine which has the greatest change of volume per change in temperature?

The wikipedia entry lists change of volume per change in temperature, but by material - I want that same information, but for phases. And, hopefully, an explanation. Thanks!

Clearly it is the gas .. just think about it. If you double the temperature of an ideal gas sample at constant pressure, you double the volume (Charles' Law). Incompressible condensed phases have much much less volumetric variation with temperature.

You can also think about it from the molecular point of view. Temperature is a measure of the average kinetic energy. In a gas sample, the molecules are free to move, so most of the extra kinetic energy of a hotter sample is in translation .. i.e. the molecules are moving faster, and thus take up more space (at constant pressure). In a condensed phase, the molecules are held quite closely together by intermolecular forces, and so the extra kinetic energy in a hotter sample just makes the molecules "wiggle" a bit more inside the condense phase. Once this thermal energy is high enough (on average) for molecules to break free of the intermolecular forces, you have reached the boiling/sublimation temperature for the condensed sample.

SpectraCat said:
Why do you think that? Why would the slurry warm up? Generally pumping on a liquid or volatile solid under it's own vapor pressure causes cooling ... you can actually freeze water this way if you pull a vacuum fast enough. Anyway, the coefficient of thermal expansion for ice is positive. I guess you were thinking that since the ice/water phase transition involves a positive change in the molar volume, then there is a thermal effect as well? I don't think that is correct.

Ok, so it's not ice; liquid water, from 4C to 0C, has a negative coefficient of thermal expansion: cooling the water increases the volume. Therefore, water from 4C to 0C has a negative Joule-Thompson coefficient. That means decreases to the pressure result in increases to the temperature.

Consider a well-insulated pipe of liquid water which exits through a porous plug. When the water exits the plug, because the pressure has dropped and the device is isoenthalpic, the temperature of the water must increase.

This sounds like a good undergrad lab...

## What is dV/dT and why is it important?

dV/dT is the rate of change of volume with respect to temperature. It is important because it helps us understand how different phases of matter behave under different temperatures.

## Which phase of matter has the largest dV/dT?

The liquid phase typically has the largest dV/dT because the molecules are more loosely packed compared to solid phases, allowing for more movement and expansion when heated.

## Is dV/dT constant for all phases of matter?

No, dV/dT varies for different phases of matter. Generally, gases have the highest dV/dT, followed by liquids, and then solids.

## How does dV/dT affect the behavior of matter?

dV/dT affects how matter expands or contracts with changes in temperature. It also plays a role in phase transitions, such as melting and boiling, as these processes involve changes in volume.

## Can dV/dT be negative?

Yes, dV/dT can be negative when a substance contracts as temperature increases. This is known as anomalous expansion, and it occurs in some liquids and all solids.

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