Can pressure be negative?

[Tim Thompson]

Nonscalar Temperature

Since both S and U are scalar quantities, you'd need something other than the standard thermodynamic definition to get a nonscalar temperature. I've never seen such a thing, and I don't know why it would be of any use. Perhaps you can tell us a little more about what you have in mind here.

I could have been more clear about that. In this case I am reverting to the notion of temperature as particle kinetic energy. I disagree with the idea that it is wrong to think of temperature as kinetic energy because, after all, that is what thermometers actually measure. There is more than one way to define temperature, so it's just a matter of being sure that the physics & definition are all mutually consistent. In any discussion of infinite temperatures, we do need to be clear about which temperature we are using.

Now, if we go back to the Boltzmann distribution or Maxwell-Boltzmann distribution, when we speak of temperature as an average over some such distribution of particle velocities, we assume that the velocity distribution is isotropic, and in the usual cases, such as air temperature, it is. However, in some cases, such as a stellar corona, it is not. The kinetic temperature measured in the radial direction is in the millions of Kelvins, while the kinetic temperature measured in a direction orthogonal to that is zero, or close to it. Of course this is an average, ignoring flow in a loop for instance, and ignoring the radiative temperature.

For me, it comes from the habit of converting energies to temperatures making use of the units (i.e., E = k_BT) which I learned when I started out in radio astronomy, when papers annoyingly tended to publish antenna temperatures instead of fluxes. But it strikes me as a valid though unusual and probably non-standard concept. I have seen the temperature of the solar corona referred to in this manner, though I cannot produce a specific example at the moment.

 

[Ziggurat]

I could have been more clear about that. In this case I am reverting to the notion of temperature as particle kinetic energy.

OK, I think I understand better what you're saying. But I think it's more accurate to say that there are quantities which one expresses as a matrix of energies expressed in a temperature scale, not that temperature itself is a matrix.

I disagree with the idea that it is wrong to think of temperature as kinetic energy because, after all, that is what thermometers actually measure.

It can certainly be useful to express temperature and kinetic energy in terms of each other, but viewing them as actually the same can be quite problematic, particularly in regards to measurements.

Generally, most thermometers measure some state variable of the thermometer itself. That variable is rarely kinetic energy. Traditional alcohol and mercury thermometers measure the volume of a liquid. Thermocouple thermometers measure a voltage. These state variables are connected to temperature in some known way, so if you know the value of the state variable, you know the temperature. But the temperature that you've measured is the temperature of the thermometer itself, which you can take as being the temperature of the system you're measuring if they're in thermal equilibrium, because temperatures are equal at equilibrium.

If the case of something like an ideal gas or even a high-temperature fluid, then the temperature is rather directly connected to the kinetic energy. And if you're doing astronomy, then you're pretty much always dealing with such cases. So the distinction between kinetic energy and temperature becomes unimportant most of the time, and you probably won't get in trouble substituting one for the other most of the time. But even in astronomy, there are cases where the distinction is critical (ie, degenerate white dwarfs and neutron stars).

And that's often not the case in condensed matter physics. For many condensed matter systems, the temperature does not represent the kinetic energy. This isn't just a matter of different definitions, though. If one tries to apply the definition of temperature as being the average kinetic energy, then one will find that two systems can be in thermal equilibrium at different temperatures. That's a real problem: among other things, it means that you can't measure temperature with a normal thermometer anymore, since your thermometer temperature no longer represents your system temperature. So if one ever wants to work with a system where energy doesn't scale linearly with temperature (and they abound in condensed matter, even if they're rare in astronomy), you pretty much MUST use the thermodynamic, entropy-based definition, not a kinetic energy definition.

There is more than one way to define temperature, so it's just a matter of being sure that the physics & definition are all mutually consistent. In any discussion of infinite temperatures, we do need to be clear about which temperature we are using.

That's just it: there's really only one definition which IS consistent in the sense that all systems in thermal equilibrium will always have the same temperature. Pick any other definition, and that's no longer true. If you happen to be working only with systems where kinetic energy scales with temperature, then one can certainly use kinetic energy to represent temperature and vice versa, but you shouldn't be defining temperature that way. You don't need to, and it can get you in trouble if you venture beyond those systems.

For me, it comes from the habit of converting energies to temperatures making use of the units (i.e., E = k_BT) which I learned when I started out in radio astronomy, when papers annoyingly tended to publish antenna temperatures instead of fluxes. But it strikes me as a valid though unusual and probably non-standard concept. I have seen the temperature of the solar corona referred to in this manner, though I cannot produce a specific example at the moment.

One should probably still think of that as energies mapped to a temperature scale, not as actual temperatures.

 

[Perpetual Student]

Oh, I've definitely made mistakes here. I'm not going to tell you what they are, but they exist.

This next part is addressed to Calrid, not sol:

But when I've made those mistakes, I've also accepted correction, and learned from them. Which is more important in the long run than not making mistakes. So for example, from our exchange in this thread it's clear that I know more about thermodynamics than Perpetual Student does. But he's clearly expressed his opinions, he logically outlined his objections so that they could be directly addressed, and when those objections were addressed, he learned. He lived up to his name, quite admirably. He may not know as much about the subject as I do, but one could not ask for more gentlemanly conduct than he displayed.

At the end of the day, it's not really very important if you learn from me what temperature actually is. But it is important that you learn from Perpetual Student how to behave in a debate.

Nice comments, but I have not always lived up to that standard. The problem laymen have with modern physics is that so much of it is not intuitive. This notion of temperature not being a surrogate for the average energy of an object is a good example. I have struggled mightily with QM and GR, and still do battle from time to time and find it difficult to simply yield when intuition is so strong in the counter direction.
I do know that the amount of training and accumulation of knowledge within the various fields of physics is quite considerable (even daunting) and that a casual familiarity with something can be a very deceiving thing, a fact that helps me stay humble -- sometimes.
I believe the problem with Calrid, Mozina and many others is that they have not accepted the truth that their intuition will simply not work in some areas. Coupled with what seems to be a narcissistic leaning, they go on their rants in these forums, not making even the slightest attempt to learn.

 

[Michael Mozina]

What he's trying to do is infer that a maths model does indeed really simulate what happens in real world experiment.

How would you ever measure an infinite temperature in experiment? Ask yourself that?

He actually claimed it was a *HIGHER* than infinite temp.

The basic problem IMO is that this group relies upon math and *ONLY* math to support all their beliefs. I can't even get them to explain what they would physically add or subtract from a "pure" vacuum (no particles or kinetic energy of any sort) to create a "negative pressure."

They tend to ignore the physics and the physically difficult questions. Instead they go off on a dozen of more "tangents" (in this case infinity+ temps) and ignore the tough questions entirely. We could ask them in which physical experiment did ANYONE actually achieve "infinite temperatures", but of course it will never get answered.

 

[Ziggurat]

He actually claimed it was a *HIGHER* than infinite temp.

Indeed I did. And what's the problem with that? The only objections I've seen so far are based on an incorrect understanding of what temperature is. Given the problems you've had with even simple definitions like pressure, I would be positively shocked if you actually understood what temperature is, given that it's actually a fairly sophisticated concept. But go ahead, prove me wrong. Tell me what temperature is, and then tell me why infinite and negative temperatures are prohibited.

They tend to ignore the physics and the physically difficult questions. Instead they go off on a dozen of more "tangents" (in this case infinity+ temps) and ignore the tough questions entirely. We could ask them in which physical experiment did ANYONE actually achieve "infinite temperatures", but of course it will never get answered.

No, Michael. I already answered that. I gave you a link to a famous negative-temperature experiment. Pretty much any negative-temperature experiment (including that one) is also an infinite-temperature experiment. This is yet another example of your endless dishonesty.

 

[mike3]

No, rwguinn. Negative absolute pressures DO occur in such experiments. Your intuition misguides you. While equilibrium would involve the creation of vapor and/or solid states, metastable negative pressures can be and are obtained experimentally.

So what is the key difference between these experiments and throwing water out in the vacuum of space? How come that you cannot get a stable or meta-stable liquid phase in absolute pressure zero in free space?

 

[mike3]

No, Michael. I already answered that. I gave you a link to a famous negative-temperature experiment. Pretty much any negative-temperature experiment (including that one) is also an infinite-temperature experiment. This is yet another example of your endless dishonesty.

I've got another curiosity question. If there is some exotic kind of system for which infinite temperature can be reached with finite energy, why can't the same be done with zero temperature? What is the deep reason in the laws of nature, and how much would be upset if we were to find out such a thing were really possible?

 

[Michael Mozina]

Tell me what temperature is, and then tell me why infinite and negative temperatures are prohibited.

For starters it would require *INFINITE* amounts of energy to achieve an *INFINITE* temperature and you don't have infinite energy to work with, now do you?

 

[mike3]

Indeed I did. And what's the problem with that? The only objections I've seen so far are based on an incorrect understanding of what temperature is. Given the problems you've had with even simple definitions like pressure, I would be positively shocked if you actually understood what temperature is, given that it's actually a fairly sophisticated concept. But go ahead, prove me wrong. Tell me what temperature is, and then tell me why infinite and negative temperatures are prohibited.

How do you know he's having a problem with the definitions, vs. understanding the ramifications and applications of those definitions?

 

[Michael Mozina]

No, Michael. I already answered that. I gave you a link to a famous negative-temperature experiment. Pretty much any negative-temperature experiment (including that one) is also an infinite-temperature experiment. This is yet another example of your endless dishonesty.

If that is your *EXAMPLE* of infinite energy, you have giant problem. The whole experiment was conducted near ABSOLUTE ZERO. You're at the wrong end of the energy scale in terms of total energy Zig. While such experiments might be useful in your "negative temperature" argument, it does absolutely nothing for your "infinity and beyond" claim.

 

[Ziggurat]

So what is the key difference between these experiments and throwing water out in the vacuum of space? How come that you cannot get a stable or meta-stable liquid phase in absolute pressure zero in free space?

Liquid water in space is metastable. It doesn't all instantly evaporate. But it will evaporate from the surface.

If the water is in a sealed piston, there is no free surface, and creating a free surface costs energy (surface tension). In fact, if the negative pressure isn't too large, a small enough bubble will actually collapse because of this energy cost. Without such a surface, evaporation won't take place, and the metastable state can persist.

 

[Tubbythin]

For starters it would require *INFINITE* amounts of energy to achieve an *INFINITE* temperature

No you don't.

 

[mike3]

Liquid water in space is metastable. It doesn't all instantly evaporate. But it will evaporate from the surface.

I thought it started boiling, which means evaporating on the interior (thus forming surface inside to evaporate from.).

 

[Ziggurat]

I've got another curiosity question. If there is some exotic kind of system for which infinite temperature can be reached with finite energy, why can't the same be done with zero temperature? What is the deep reason in the laws of nature, and how much would be upset if we were to find out such a thing were really possible?

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.

 

[Michael Mozina]

No you don't.

Then your definition of "infinite" is really "finite". Finite isn't "infinite".

 

[Ziggurat]

I thought it started boiling, which means evaporating on the interior (thus forming surface inside to evaporate from.).

If it's disturbed (by impurities, internal turbulance, or temperature gradients), it might well do so. The actual stability of a metastable state can depend quite a lot on precise details.

 

[Tubbythin]

Then your definition of "infinite" is really "finite". Finite isn't "infinite".

Nope.

 

[Ziggurat]

If that is your *EXAMPLE* of infinite energy, you have giant problem.

I've already explicitly stated that no infinite energies are involved here. Once again, we find you being dishonest. And ignorant, since you still clearly haven't figured out what temperature is.

The whole experiment was conducted near ABSOLUTE ZERO.

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.

While such experiments might be useful in your "negative temperature" argument, it does absolutely nothing for your "infinity and beyond" claim.

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.

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.

 

[mike3]

If it's disturbed (by impurities, internal turbulance, or temperature gradients), it might well do so. The actual stability of a metastable state can depend quite a lot on precise details.

I kind of thought so. Does this also apply to the neg. pressure experiments in a container? If it was disturbed somehow, a break (bubble) would occur?

 

[Ziggurat]

I kind of thought so. Does this also apply to the neg. pressure experiments in a container? If it was disturbed somehow, a break (bubble) would occur?

Yes, if something nucleates a bubble, then the whole thing can rapidly collapse into the stable state (water + vapor/ice, depending on temperature and volume).