Well, actually, if you squeeze the jar (maybe a better image is pushing down on a piston in a cylinder), you’re adding energy to the system. Temperature is more like ‘kinetic energy per individual molecule’ than ‘kinetic energy per volume’.
Again, the theoretical definition of temperature allows you to establish a temperature for an individual molecule, atom, or I suppose free electron; it’s just that there’s nothing useful to do with it, because the whole point of ‘temperature’ is that it allows you to make predictions about what groups of molecules will do, without having to know what each individual molecule is up to. With the info you’d need to determine the “temperature” of a single molecule, you’d have enough info to predict what the molecule will do directly; going through a temperature calculation would just add steps and probably be less accurate.
I’m guessing Planck should figure in here somewhere, as the Planck temperature is the upper bound.
I don’t see why you need two particles: surely any single particle that has mass or energy has a temperature, simply by virtue of existing? Energy is temperature, and mass is an equivalence of energy.
I’m sure the physicists will shortly fight my ignorance.
A hydrogen atom by itself then theoretically has some temperature as it is made up of paticles that are moving … even if that hydrogen atom is not moving relative to any other atoms?
If so, then a bunch of hydrogen atoms, all not moving relative to each other, but each with some finite temperature of their own internal particles … is at absolute zero?
I get confused easily I guess!
So what if you have a single particle zipping along through an otherwise-vacuum? By its mass and velocity, it has kinetic energy. Yet nobody calls that “temperature” that I know of. That’s where I get the idea that the concept of “temperature” must necessarily involve particles bumping into one another, or interacting somehow. And isn’t this, likewise, why Chronos specifies that you need at least two particles in order to have temperature?
Now my mind is back on Ellen Page.
I’ll be in my bunk.
Heat is radiated into space from the earth (or any other given body) in EM, or photons. Photons derive from electrons moving from a higher energy level to a lower one, typically due to their atomic bound states. So, by combining E[sub]K[/sub] with electrical potential, one could in theory assign some temperature to at least an atom. After all, the temperature of a thing that is made of a bunch of atoms is essentially a sum of kinetic energy vectors combined with the associated EM potential. The lonely, moving atom will probably slam into something, sooner or later, at which point some of its E[sub]K[/sub] will be exchanged with that other thing. Or it might affect or be affected by some magnetic field, transferring energy one way or the other by that means.
And, personally, I find the smallest unit of hotness most likely to be defined in terms of the Rauch (Melissa), the things the costumiers do with her bust make even a leg/butt man take notice.
Ellen Page standing next to co-star Alexander Skarsgard at the premiere of The East. And she’s wearing high heels.
Two would be at the boiling point.
Normal atoms in a given mass are going to move randomly and “bump” into each other all the time. But suppose you could get all the atoms to move in the same parallel direction? They could then still have a lot of kinetic energy but there would be no “bumping”. Would the temperature of such a mass be the same as a equivalent mass with normal atomic movement? In other words, is temperature solely the product of the atoms’ collective kinetic energy or is it partly the product of the interaction between atoms?
Would a fair comparison be to measure the temperature of our solar system? Or Galaxy?
I just read a book called The Dinner by Herman Koch and I hated it. If I were to rate it, I’d give it 1 star. You could, if you wanted, do the math. 1 star plus nothing else divided by the number of ratings being added (1) gives you 1. But if my opinion is the only one you care about, it’s easier to just use the rating itself.
Well, so this is where what few neurons I have left were going with the question…“absolute zero.”
I’m sort of assuming, without pretending to know squat, that the concept of “temperature” (as in “hotness”) can apply to a couple–or a handful?–of (adjacent) atoms since it’s meaningful (isn’t it?) to say that their enthalpy and entropy are as close to zero as it’s possible to get along an asymptotic approach to “absolute” zero. It’s intuitive to me (and therefore probably wrong) that the more atoms you have near enough to bounce off one another, the more likely you are to have a hotter system…
And so what I think I was struggling with is whether or not there are components (elementary particles, e.g.) smaller than an atom which in the same sort of way can be said to be hotter than a different group of subatomic components.
It sort of seems to me, Chronos, that you think of a individual (elementary) particle as having a temperature of sorts because even an individual particle has an energy value…?
But if, by the various comments above, we say that you have to have at least two items to have “hotness” --i.e. a temperature greater than a different “system”–then would those two items be the weakest interacting particles (such as a couple of electron neutrinos)? (And I realize considering two neutrinos as a “system” is more or less a thought experiment since it might be tough to keep them in the same vacuum tube while we mess around with them 
)
It’s problematic to speak of a single particle with no internal components (or at least, no components we care about) having a temperature, because the kinetic energy of the particle depends on the reference frame you look at it in, and you’d really like to have an invariant definition of temperature. With two or more particles, though, you can do all of the measurements in the center-of-mass reference frame (that is, the reference frame where there is no momentum) and call the average of kinetic energies in that frame the temperature.
Some degree of interaction between particles is convenient, since it lets us get all sorts of other useful things from the temperature, but it’s not actually necessary to define the temperature itself.
I was wondering this too. I think, at small scales, temperature, sound and motion might not be entirely separate.
as opposed to the entire Ellen Book?
sorry, but it made me laugh.
Thanks to all for the helpful replies. I had a bunch more stupid questions (I have always held there are no stupid questions; only stupid people) but I’ll try to distill it a bit:
If we assume that any useful concept of “hotness” (i.e. a temperature greater than any value one might assign to a single particle) needs a reference frame (and therefore more than one particle), then is there a smallest amount of stuff that can have hotness?
For example, could any amount of photons or gluons ever have hotness?
Do you have to have at least some mass to have hotness, and if so, is it the case that more mass generally gives a hotter system?
And if so, then is the theoretically least hot system two electron neutrinos? Or does it only make sense to talk about hotness if you have composite (or larger) particles?
(This will be my last annoying question(s) from the back of the room, and it’s OK if the bell has already rung to end the class.)
My also back of the room guess waiting for someone who knows to speak up …
I think you need mass to have hottness because it it a statisitical property of kinetic energy. Hence photons have no temperature.
Being based on kinetic energy a group of objects of larger mass at the same average velocity would have a higher temperature but it is more velocity than mass dependent (related to the square of velocity).
My additional questions - in particle accelerators (if I understand close to correctly) groups of particles are made to all move in one direction at about the same speed (including protons in the proton accumulator ring). Relative to each other do they then have a very low temerature at that time? And is there any temperature oddness in relation to Bose condensates?
Collections of photons can and do have temperature. For instance, the photons of the cosmic microwave background have a temperature of about 2.7 K. They are, in fact, the most perfectly thermal phenomenon known in the Universe (Science: It works, bitches).
One could, however, still say that temperature requires mass. Even though an individual photon is (so far as we’re able to determine) massless, a collection of multiple photons does have mass.
A collection of photons might have an energy distribution that fits the emissive profile of a blackbody radiator at a particular temperature, but does the collection of photons itself actually have a temperature?
Also, how can a collection of photons have mass if each photon itself does not have mass?
Yes. It behaves in every way exactly the same as temperature for any other substance.
Mass is not additive. It may seem so in our everyday experience, but that’s just an approximation, and one that breaks down for things like photons. The “mass” of a system is defined to be that portion of a system’s energy which cannot be translated away by going to a different reference frame. Take a single photon, and you can get its energy arbitrarily low, by chasing it with ever-faster reference frames, so we say that the mass of an individual photon is zero. However, if you have two or more photons traveling in different directions, then after a while, when you’re redshifting one photon by changing reference frames, you’re blueshifting another, and so there’s some lowest total energy that you can’t get below. Thus, a system of multiple photons generally does have mass.