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Can pressure be negative?

Ziggurat said:
I've already explicitly stated that no infinite energies are involved here.
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Then no infinite temperatures are involved here either.

Of course it starts out at low temperature. This is to ensure a large magnetization. The lower energy you START at, the higher the energy will be once you reverse the field.
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Did the temperature jump to an INFINITE state, yes or no?

It does everything for my infinite temperature claim. You cannot have negative temperatures without infinite temperatures. Proof of negative temperatures IS proof of infinite temperatures.
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No. I can/will accept a definition of "negative temperature" if all you mean by the statement is an *INTERNAL ATOMIC ARRANGEMENT* that ultimately requires *finite external energy* to change that state. I can live with that concept. I can't live with our claim about 'infinity"+ temperatures however because nothing in that experiment ever achieved anything other than a "finite" energy state. PERIOD.

You'd know this if you understood what temperature is. But you obviously don't. Infinite temperature does not require infinite energy for all systems.
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If it's a finite amount of energy involved, then by necessity it's a FINITE temperature as well. In fact you own experiment *DEMONSTRATES* that point very clearly. If we add just a "tiny" bit of energy, the internal atomic arrangement returns to zero. There's nothing *INFINITE* about it!
 
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Ziggurat said:
The fundamental obstacle is the 3rd law of thermodynamics. There are a number of equivalent formulations of the 3rd law (though with some of them, it's tricky to figure out why they're equivalent). For our purposes, perhaps the simplest way to think about it is to note that the efficiency of a refrigerator approaches zero as you approach zero temperature. That vanishing efficiency means that it would take forever to cool something to zero temperature. The problem is that you're not just extracting energy, you have to decrease the entropy of the system.

But no such restrictions apply to increasing entropy. We can do that whenever we want to. So as long as adding energy doesn't decrease entropy, I have no thermodynamic restrictions on adding energy. And I can add energy to a paramagnet (by, for example, changing the direction of the applied field) without any decrease in entropy. And there's nothing actually special about the entropy at infinite temperature.
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That's what I thought, but what is the fundamental reason why the 3rd law is apparently so inviolable?

And also, does the ability to heat to infinite temperature in this case then imply that the energy required to produce a unit increase of temperature goes to zero as the temperature goes up (Otherwise it would indeed take infinite energy)? Perhaps that is the source of Mozina's lack of understanding here. He might be only thinking in terms of things like gases, plasmas, and so on that you can't get infinitely hot without infinite energy. He assumes that every system that can be assigned a "temperature" must behave like those, with nonvanishing heat capacity at infinite temperature (or at least not falling off fast enough to make the AUC finite).
 
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mike3 said:
That's what I thought, but what is the fundamental reason why the 3rd law is apparently so inviolable?
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It will probably take a bit to explain. I may come back to that if you don't find a satisfying answer, but I can't give you something very concise that's likely to answer this to your satisfaction.

And also, does the ability to heat to infinite temperature in this case then imply that the energy required to produce a unit increase of temperature goes to zero as the temperature goes up (Otherwise it would indeed take infinite energy)?
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Yes, it absolutely implies that. That's the heat capacity, and it does indeed go to zero.

Perhaps that is the source of Mozina's lack of understanding here. He might be only thinking in terms of things like gases, plasmas, and so on that you can't get infinitely hot without infinite energy. He assumes that every system that can be assigned a "temperature" must behave like those, with nonvanishing heat capacity at infinite temperature (or at least not falling off fast enough to make the AUC finite).
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Quite likely, but since he won't even tell us what he thinks temperature is, there's no way to be sure. There was a thread quite some time ago where we struggled for pages and pages to get him to give us a definition for pressure. And he repeatedly tried to assert that the ideal gas law defined pressure. I don't expect any better results here.
 
Michael Mozina said:
If it's a finite amount of energy involved, then by necessity it's a FINITE temperature as well.
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It's become quite clear that whatever your concept of temperature is, it's not correct. But you won't actually tell us what you think temperature is, even when challenged. Which is too bad, because that mistaken understanding of what temperature is in the first place is what's standing in the way of you understanding why infinite temperatures are possible.
 
Tubbythin said:
Nope, its based on a derivative.
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:)

You guys consistently ignore that fact that your mathematical formulas relate to REAL PHYSICAL PARTICLES. In the experiment cited, those particles are ATOMS. There are a finite number of them in the experiment and they only ever achieve a FINITE temperature that can be changed with FINITE amounts of energy! Hoy Like I said, you only recognize the math, and you ignore the physics entirely.
 
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Michael Mozina said:
:)

You guys consistently ignore that fact that your mathematical formulas relate to REAL PHYSICAL PARTICLES. In the experiment cited, those particles are ATOMS. There are a finite number of them in the experiment and they only ever achieve a FINITE temperature that can be changed with FINITE amounts of energy! Hoy Like I said, you only recognize the math, and you ignore the physics entirely.
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Meh. Can you just state your definition of temperature? What does the statement: "this system is at temperature T" mean to you? In all your posts, when you use the word "temperature", what do you consider this word to mean?
 
Michael Mozina said:
You guys consistently ignore that fact that your mathematical formulas relate to REAL PHYSICAL PARTICLES. In the experiment cited, those particles are ATOMS. There are a finite number of them in the experiment and they only ever achieve a FINITE temperature that can be changed with FINITE amounts of energy! Hoy Like I said, you only recognize the math, and you ignore the physics entirely.
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If your so certain this is the case then you'll be happy to provide us with a definition of temperature, won't you?
 
Ziggurat said:
It's become quite clear that whatever your concept of temperature is, it's not correct.
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I would have to say the same thing Zig. You're ultimately ignoring the fact that the experiment you cite does NOT achieve an INFINITE state of ANYTHING. In terms of a "less then zero" temperature, they are actually discussing *INTERNAL SPIN ARRANGEMENTS* of the atoms. There is no INFINITE temperature going on there, because the finite numbers of atoms are all at a zero temperature state with a LOWERED internal entropy state. No INFINITE energy state is achieved, and no infinite temperatures are achieved either. The experiment did not jump from cold to hot by adding a magnetic field, it never changed external temperature of the atoms in fact. All that actually changed was the ENTROPY of the spin in atomic lattice, and they changed by FINITE and measurable amounts of energy.
 
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Even though I have Mozina on ignore (life is too short), I see that he is still insisting that I must read Alfven's papers. I have tried to explain many times that I am certain that he does not have the educational background to understand Alfven's papers and neither do I. So reading Alfven's papers -- other than the thrill of touching sacred texts -- is a useless exercise.
I find these science threads a wonderful vehicle to learn, discuss and debate things where I do not the have the opportunity to do so in my personal life. Reading a wikipedia article, Scientific American or some other source is a great starting off point but a dialog with Ziggurat and many others can be an invaluable assist to understanding.
We have some people here with a strong knowledge of plasma physics, thermodynamics, QM, GR, etc, which allows me to better understand the universe as I slip into my dotage. Why would I waste my time reading Alfven and listening to an EU groupie instead of engaging those knowledgeable people?
As I said, Mr. Mozina, life is too short!
 
Michael Mozina said:
I would have to say the same thing Zig. ...
All that actually changed was the ENTROPY of the spin in atomic lattice, and they changed by FINITE and measurable amounts of energy.
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Michael Mozina, try reading the Wikipedia article Negative temperature, especially the definition of temperature:
A definition of temperature can be based on the relationship:
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That change in the ENTROPY of the spins in an atomic lattice was the negative temperature!

The lattice starts in a state where there are more atoms in the spin-down state than the spin-upstate. Adding energy takes the mixture of states closer to equal up and down states. This means that the entropy is increasing. That means that the temperature is positive.

After the 50/50 mix is achieved though, adding more energy puts more spins in the spin-up state. Entropy increases. That means that the temperature is negative.

So the question is what was the temperature during the transition from positive temperatures to negative temperatures?
Look at the temperature scale in the article. To go from positive temperatures to negative temperatures you have to pass through
  1. infinite positive temperatures
  2. infinite negative temperatures.
Consider a lattice that has one more atom in the in the spin-down state than the spin up state. Add the tiny amount of energy that swaps that spin. The entropy decreases by a very small amount. That means that the temperature is high and positive. The spin mixture is now 50/50.
Now add add the tiny amount of energy that swaps another spin. The entropy increases by a very small amount. That means that the temperature is high and negative.
IMO this looks like a phase transition rather then a continuous change in temperature. So the infinite temperatures are never reached.
 
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