Talk:Temperature

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Thermodynamics

Looking in here because it's mentioned on Peer Review. Not being much of a peer on questions of thermodynamics, I make only one fairly obvious comment: how should this relate to the Thermodynamics article? There seems to be a good deal of overlap, with perhaps a lot of detailed information here that could fit better in the other article. This one might take a seriously simple-minded approcach (not a pejorative term in a popular work), as it does in places, with an invitation to go to the more technical article for more technical information. Most of the section on the second-law definition would be a candidate for a transfer. Then again, maybe not. But surely the division of labor wants discussion. Dandrake 07:01, Aug 10, 2004 (UTC)

Agreed. Much of the material under the second law definition of temperature really belongs in an article about the second law of thermodynamics and/or entropy. It is redundant to argue the second law here and in another article where such an argument naturally belongs. BlackGriffen 10:52, 13 June 2007 (UTC)

Regarding internal and external temperature, black-body radiation, and other concepts

LeBofSportif. You should be more humble before acussing others of inventing concepts just because you've nevery heard of them before. The following article http://physicsweb.org/articles/world/18/3/5/1 is about the quantum behavior of C60 Buckyballs. About half-way down it describes the notion of "internal temperature." It is well-known in physics. Previous versions of this temperature page and similar pages have wrestled with this concept. Before you go back and revert the page—which is childish when done the way you do it —PLEASE read the above-referenced article. I've got twelve patents to my name and many are related to thermodynamics. What are your qualifications? Greg L 22:27, 6 June 2006 (UTC)

I already had a section at the bottom for this discussion. Qualifications are irrelevant, understanding of physics is what is important.

Firstly, the phrase "external temperature" does not enter into that article you cite. Secondly, the article is about a specific experiment where "internal temperature" is introduced in quotation marks since it is relevant to the experiment in question. "Internal temperature" does not enter main stream discussions about temperature. The vibrational, rotational and translation d.o.f will be at the same temperature in most sensible gases worth talking about in the wikipedia article. Introducing internal temperature is just confusing for readers. LeBofSportif 22:33, 6 June 2006 (UTC)

How would you like to write about how a single, hot molecule emits black-body radiation due to its internal temperature?? Readers should know that not only do molecules move about, but they internally vibrate.

Of course readers should know that molecules have internal degrees of freedom. But in thermal equilibrium, each degree of freedom will be at the same temperature. It's only in funny experimental situations, or at very cold extremes where the degrees of freedom will have different temperatures, and these are not worth mentioning in an overview section of an encyclopaedic article. And I really cannot allow you to leave the phrase "This motion is known as its “internal energy” or “internal temperature.”" in the article - it's just plain wrong. energy and temperature are not the same thing, and moreover, internal energy is a totally different concept, which includes translational motion. LeBofSportif 22:48, 6 June 2006 (UTC)

That's exactly the concept that should be conveyed by the article, that internal temperature of molecules is the same the same as its external temperature. Nothing in the article says otherwise. All the energy is shared as equaly as possible. How would you propose to write that the molecules themselves have internal kinetic energy that diminishes when all the other forms of thermal energy diminish? An earler version of the "Temperature" article stated as follows:

"Temperature in respect to matter is a property only of macroscopic amounts and serves to gauge the average intensity of the random actual motions of the individually mobile particulate constituents. Intraparticle motions apparently contribute only to the heat capacity.

This is a way-wrong way of thinking abou the subject. The intraparticle motions contribute to heat capacity becuase heat energy went into them. It is therefore inescapable that the molecules themselves have an intraparticle temperature as a result of “intraparticle motions.” The German researches used a perfectly sensible term (internal temperature) that's been used before elsewhere. The term perfectly describes how heat energy is distributed in a molecular system. If the "intraparticle-motions temperature" is the same as its "actual translational motions-temperature", then a substance comprising molecules is in perfect equilibrium.

A single molecule does not have a temperature. Nor does a single atom. Temperature is an emergent property of collections of thermally interacting constituents. It is totally unnecessary to talk about a seperate temperature for the internal degrees of freedom. One can simply observe that they contribute to the heat capacity. LeBofSportif 23:19, 6 June 2006 (UTC)

You are presupposing that each degree of freedom is coupled to its own kind significantly stronger than to the other degrees of freedom. This is a bad presupposition.LeBofSportif 23:24, 6 June 2006 (UTC)

Your first sentence two paragraphs up is wrong. That is precisely what Arndt et all were doing; they shot individual hot molecules. The article as I wrote it specifically singled out molecules as a unique class for having internal temperature. Your last sentence seems to be a very weak argument: (let's just observe that something happened but not talk further about why). But WHY do molecules contribute to heat capacity? Because they're vibrating due to all the kinetic energy they've internaly absorbed. How does one talk about and accurately describe this energy so the reader can understand the complete nature of the vibrations in matter?

As regards your next paragraph. I don't think anything I wrote suggests the presupposition that any of the degrees of freedom are unique or special in some way that permits them to have a different temperature. Each vibrational and rotational degree of freedom will have its own frequency and amplitude such that after achieving equilibrium (due to kinetic energy sharing via collisions and thermal photons), all forms of vibration will have the same temperature. That's why I wrote As a substance cools, all forms of heat energy simultaneously decrease in magnitude.

"Temperature" is the average heat energy in a substance. Individual molecules can be agitated in a variety of ways; that's why there is evaporation and sublimation: individual molecules can achieve more than their fair share of kinetic energy and get kicked entirely out of a particular phase. The important point that should be conveyed to the reader is that the intraparticle motions of a molecule—its energy— is shared by the rest of the system. An individual molecule can momentarily be internally agitated, but once it spends any time in contact with other molecules, it will come back into equilibrium.

Temperature is NOT the average heat energy in a substance.

I repeat. A SINGLE MOLECULE DOES NOT HAVE A TEMPERATURE. Temperature is a parameter describing the distribution of energies across a population. A population of 1 does NOT have a temperature. In a gas at thermal equilibrium, the molecules have different energies, according to maxwell-boltzmann distribution.

As for "How does one talk about and accurately describe this energy so the reader can understand the complete nature of the vibrations in matter?" You can talk about the vibrational and rotational energies of molecules all you want in the article. Also you said: "Each vibrational and rotational degree of freedom will have its own frequency and amplitude such that after achieving equilibrium (due to kinetic energy sharing via collisions and thermal photons), all forms of vibration will have the same temperature." EXACTLY. The same temperature. No distinction between external and internal temperatures because there is only one temperature.LeBofSportif 23:47, 6 June 2006 (UTC)

Of course individual molecules have an internal temperature. They can do so because they are comprised of a plurality of atoms that are thermally agitated with respect to one another. An individual molecule is a "population" of atoms. An individual atom can't have an internal temperature. Arndt and his associates (quoting from the article I referenced) Indeed, when we increased the internal temperature of carbon-70 molecules to above 1000 K, the contrast between the interference fringes slowly disappeared. These guys were firing individual molecules through a diffraction gratting. If there is a 1000 K flame, the CO2 molecules in it will have intraparticle motions (due to absorption of kinetic energy) that are most easily described as having an average temperature of 1000 K. Greg L 00:05, 7 June 2006 (UTC)

Your confidence in your error is baffling. An individual molecule cannot have a temperature since temperature is a property of an ensemble of thermally interacting constituents. I frankly don't give a damn what Arndt and his associates report but if they said the temperature of the molecules (plural) was 1000K then I've got no problem with that. It is irrelevant to the fact that a single member of an ensemble does not have a temperature. LeBofSportif 00:15, 7 June 2006 (UTC)

You have edited your comment since I replied. When I use "molecule" I am not considering giant covalent structures, like graphite, which do have a temperature on account of their macroscopic scale. An oxygen molecule does not. Nor does a nitrogen molecule. Buckyballs presumably come somewhere between. LeBofSportif 00:23, 7 June 2006 (UTC)

Please stop editing the main article while this discussion is progressing. We are not in agreement, and I will just revert you. LeBofSportif 00:26, 7 June 2006 (UTC)

Are you suggesting than a diatomic molecule does not have internal vibrations? If you concede that it does, then this is the vibrations of a population. It is why a molecule (a plurality of particles) has a temperature. Greg L 00:32, 7 June 2006 (UTC)

Have you asked anyone you trust what they think of this dispute? Greg L 00:34, 7 June 2006 (UTC)

I trust myself and my ability to understand simple thermal physics. A diatomic molecule has a vibrational degree of freedom. It may be excited, or it may not be. This is insufficient to be able to say "the molecule has temperature X". A diatomic molecule does not have a temperature. LeBofSportif 00:38, 7 June 2006 (UTC)

I have edited the article to remove the references to internal and external temperatures. Before reverting these changes (if you intend to), please find support for what you are saying and discuss it here. LeBofSportif 17:09, 7 June 2006 (UTC)

So… after researching the issue, you acknowledge that heat energy CAN go into even simple molecules. But even if a molecule is excited, you are unwilling to call that a "temerature,” right? And also, when you say "may be excited, or it may not" you are apparently suggesting that the translational energy (from bouncing around) doesn't necessarily have to excite the internal degrees of freedom of a molecule and the atoms it is comprised of can remain still with respect to one another even though their translational temperature is substantially above absolute zero and the molecule is constantly being impacted.

There are other smart people in the world besides you and I. Many have Ph.D's on thermodynamics but you are unwilling to allow them a chance to edit my article. Have you considered actually leaving my prior version there for more than a few hours? It would be interesting to give others a chance to weigh-in but you are unwilling to permit this to occur—to allow others to weigh-in. Things that are factually incorrect (particularly on a fundamental subject like temperature) would soon be corrected by others. Squatting on an article as if you consider it your own private domain and immediately deleting others’ contributions because you refuse to accept notions like "the internal temperture of molecules," is not what Wikipedia is about. You could have waited a week for my contribution to be considered and weighed by the rest of the world's community but you have taken it upon yourself revert any edit you disagree with because of your fabulously high self-assesment of your ability to so thoroughly understand the issue.

I am going to do exactly as you suggest. I am going to run what I wrote by an authority of some sort, (probably a local University). I don't have time for tit-for-tat reverting. Such behavior is the playground of people who can't let go of things and (an may well have other “issues”). Wikipedia is a place for everyone to contribute and the behavior you've been exhibiting is the sort that just makes people throw up there hands and go elswewhere rather than put up with the frustration of having the "community" nature of Wikipedia subverted by a single individual who acts as an article's policeman.

It may be some time before you see my contribution again here. If you do, first try swallowing a small "humble pill," and then come back here to see why I put it there. And even then, you might give the contribution some time. Just sit back for a while and see how others handle it. You might actually find the process intresting to watch. Greg L 18:33, 7 June 2006 (UTC)

Firstly, I only edited the article because you continued to edit without responding to any of the points I made at the bottom of this talk page, which predate my decision to remove some of the content you added. I could only assume you were ignoring the talk page and so I changed back some of the points in your edits to draw attention to it.

Secondly, I am not squatting on the article as if it's my private domain. All I am doing is monitoring it, and removing inaccuracies when they occur. Leaving them in as a social experiment to see who else might edit the article does not interest me and that is why I see no point in leaving some of your contributions untouched for others to assess. As you say "Things that are factually incorrect (particularly on a fundamental subject like temperature) would soon be corrected...". Indeed, I correct many.

Thirdly, I do not have a "fabulously high self-assesment of [my] ability to so thoroughly understand the issue" but rather a realistically high self-assessment.

Fourthly, I do not have "other “issues”".

Fifthly, these are some of the reasons I edited the article:

• Temperature is not a measure of the average kinetic energy, or if it is, it is a different measure for each material. Thus I changed the article back to saying related to average kinetic energy.
• Use of the phrases subatomic particles and elementary particles is misleading. Quarks have no place in an introductory article about temperature.
• I do not feel that specifics about metals and metallic thermal conductivity are appropriate in the overview for temperature, especially when the classical theory of metals is totally inadequate and a quantum theory of the harmonic crystal and electron gasses is required for an accurate description. This is too detailed for this section.
• External temperature is not a common notion or phrase in physics.
• Internal temperature is not a common phrase in physics.

Sixthly, you said:

So… after researching the issue, you acknowledge that heat energy CAN go into even simple molecules. But even if a molecule is excited, you are unwilling to call that a "temerature,” right? And also, when you say "may be excited, or it may not" you are apparently suggesting that the translational energy (from bouncing around) doesn't necessarily have to excite the internal degrees of freedom of a molecule and the atoms it is comprised of can remain still with respect to one another even though their translational temperature is substantially above absolute zero and the molecule is constantly being impacted.

I am absolutely saying that! The vibration energies of a diatomic molecule are quantised, and they are unlikely to be excited unless the typical thermal energy is greater than the vibration energy. Give me a hydrogen molecule from a gas at 300K and give me a hydrogen molecule from a gas at 200K and you will most likely find that there is no vibrational excitation. So how do you propose to assign an internal temperature to the molecule, given that a single molecule in equilibrium at 200K and a single molecule in equilibrium at 300K can be the same, i.e. not vibrationally excited? I shall repeat what I have said many times: temperature is only meaningful for a large number of thermally interacting constituents. Otherwise, energy is the only thing worth talking about. LeBofSportif 23:53, 7 June 2006 (UTC)

I'm having the temperature article reviewed by two Ph.D.s. One is an expert in thermodymanics and teaches at a university. The other is a chemist with whom I worked on fuel cells for seven years. Let's see what these two have to say shall we? Greg L 07:30, 8 June 2006 (UTC)

the same as above continued - october

Well, that was in June and now it's October. Over the months, the issue of whether or not molecules have an "internal temperature" has been reviewed by numerous Ph.D.s. Among them has been Dan Cole (who authored three published papers on absolute zero, one of which is Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, Third Series 42, Number 4, 15 August 1990, Pg. 1847–1862.) In simple terms, the response from all the experts could be characterized as "Well… Duhh!” The vast majority of the correspondence with the experts was usually on a topic of greater importance: absolute zero and the nuances of the phenomenon at that temperature. The harshest criticism from any Ph.D. was from someone who commented with something along the lines of "The internal temperature of molecules are always, on average, the same as the substance's temperature, so why make the distinction and risk confusing the issue?" So I re-wrote the paragraph to avoid any confusion.

In hindsight, this dispute should never have occurred: “temperature” is always the average kinetic energy of particle motion. If a molecule (as distinct from a monatomic gas) internally absorbs kinetic energy (heat), that kinetic energy is precisely associated with a particular internal temperature. The thermodynamic temperature of any plurality of fundamental particles of nature (atoms in a monatomic gas or 2+ atoms in a molecule) is always a proportional function of the kinetic energy of their movements. Molecular-based substances have greater specific heat than the monatomic gases precisely because the molecules absorb heat energy internally. Nothing can absorb heat energy and not attain a greater temperature. Nothing. Never. In a nutshell: If you heat up a sample of any molecular-based gas to, say, 1000 °C, and then release single molecules across a gap, the molecules will first emerge at 1000 °C and will immediately begin radiative cooling as they emit photons with a black-body spectrum of 1000 °C (on average). If it's monatomic atoms flying across the gap, they just fly and don't radiate; atoms of course, can't have an internal temperature.

I don't have any inclination to argue this point any further because it is so elementary. I did, however, feel compelled to make this "discussion" entry so others might not get thrown off track. If you still feel that molecules can't have an internal temperature, don't bother arguing about how you are right because you "understand thermodynamics" (like it's some sort of X-men power); go find an authoritative source (hopefully a reputable, published Ph.D. in thermodynamics) who supports your argument and cite the individual. And please save the “ARGH!!! MISCONCEPTION ALERT” stuff for some other forum. This behavior comes across as if you are such an awesome expert on a subject, that you just can't contain your shear frustration of how others can be such imbeciles. I just gave up on this "Temperature" article and went elsewhere to make contributions rather than put up with the frustration of all that. Greg L 21:48, 13 October 2006 (UTC)

I think a point that is being somewhat ignored is the fact that at equilibrium, at a given temperature, there is a distribution of individual particle energies. If we have a gas consisting of a large number of point particles (no internal degrees of freedom) at equilibrium, and at temperature T, then the average energy of each particle will be E=3kT/2. But there will be some particles with half that energy, some with twice that energy.

If the gas is isolated - not connected in any way to an outside system, then the total energy will be conserved, and the temperature will be exactly 2E/3k where E is the total energy divided by the number of particles - the average energy per particle. If we have just one particle, then ok, we could define its temperature to be 2E/3k where E is its (conserved) energy.

But this is only good for a single particle in isolation. If that particle is part of a larger system, then the whole idea of "its" temperature breaks down. Its energy will change radically with every collision, and so will its "temperature" defined by the above equation. At one instant it may have a "temperature" of 2T and a nanosecond later it may have a "temperature" of T/2. The formal definition of the "temperature" of a single particle has become useless. You might average its energy over time to get the time-averaged "temperature" of the single particle but this will be equal to the temperature of the whole gas, and so it wont be anything special.

If the particles have internal degrees of freedom, like vibrational modes, then each will have an additional energy of kT/2. (I'm assuming that temperature is high enough so that there are no quantum effects). With regard to the "internal temperature" of molecules, the same ideas mentioned above hold. The internal vibrational energy of an individual molecule will be jumping around with each collision just as drastically as its kinetic energy. The concept of the internal temperature of a single molecule only becomes useful if you average its internal energy over time, or average it over a large number of such molecules, both of which will give you the same answer, assuming equilibrium. PAR 03:10, 14 October 2006 (UTC)

subconversation 1

PAR: You are exactly right. It's nice to have support on the issue that molecules have an internal temperature. But no, the concept that individual molecules will have a distribution of energies and velocities hasn't been lost in the argument (at least mine). What you're describing is the Maxwell–Boltzmann distribution of speeds. That's why I wrote “…emit photons with a black-body spectrum of 1000 °C (on average).” Greg L 06:08, 14 October 2006 (UTC)

Well, my support is not total - There is the "no quantum effects" condition on the above discussion. That means the internal degrees of freedom will be strongly linked to the kinetic degrees of freedom so that the "internal temperature" will be the same as the "external" temperature (in equilibrium). But out of equilibrium, if the rate of energy flow between internal and kinetic degrees of freedom were different, the temperatures could be different. Also, I think it is a valid statement to say that a single particle has no temperature. It seems valid to say that each degree of freedom can have its own temperature, which is 2E/k where E is the average energy in that degree of freedom. Average over all particles, that is. An individual degree of freedom in an individual particle has no temperature. The statement that "temperature is not proportional to the average energy" means that its not proportional to the average kinetic energy, because different particles have different internal degrees of freedom availiable to carry more or less energy. PAR 14:12, 14 October 2006 (UTC)

PAR: All sorts of special conditions like "out of equilibrium" can be considered. The issue is strictly whether or not molecules have an internal temperature. One simply can't prevail with any argument predicated on the logic that “just one molecule can't have an internal temperature so none of them do.” Asserting that “[a]n individual degree of freedom in an individual particle [molecule] has no temperature” is like asserting that 50+ helium atoms can have a "temperature" (average kinetic energy) but two helium atoms can't have an average kinetic energy. Note that a single "degree of freedom" in a molecule requires at least two atoms (a plurality of fundamental particles). If I told you a single helium atom had a speed of 4780 meters per second, you could conclude that the bulk sample from which that atom originated had a most probable temperature of 5500 K. It's only a likelihood; not a guarantee. If ten such atoms were isolated within a container with a wall temperature of 5500 K (thus the system was in equilibrium), and if one waited for several million collisions (less than a second of observation time), one could properly draw a statistically valid conclusion about the temperature of the sample based on their average speed (and thus, their average kinetic energy). Such a sample obeys the Maxwell-Boltzman distribution as regards the likelihood of any particular atom having a particular velocity at any given instant. One might correctly argue that one can't have an average kinetic energy for a single helium atom which is in equilibrium with its environment (although I think even that statement isn't true), but it's certainly not true to say that two atoms (a plurality) can't have an average kinetic energy (temperature). You are correct when you state that “different particles [atoms] have different internal degrees of freedom [within a molecule]”. It's true that different degrees of freedom within molecules radiate black-body radiation, and when summed, this spectrum doesn't take the form of the classic black-body curve. It would be a mistake to conclude that this means that individual molecules can't have an internal temperature. Let's take the example of a molecule that has only one degree of internal freedom. Clearly, there is only one kinetic energy to measure so even by your argument, it would have an internal temperature. This concept doesn't break down just because there are two or three degrees of freedom. If one measured the effective black-body temperature of the spectra for each individual molecule that had 2+ degrees of freedom, one would find that their internal temperatures (average kinetic energy within a single molecule) were, averaged across many molecules, the exact same temperature as their translational temperatures. There is no magical minimum quantity of the fundamental particles of nature at which a temperature can no longer be assigned; one can always rely on the probabilities.

We're getting bogged down in minutia intended to show off how damn smart we are. The only two points I've been trying to make (and what previously got deleted ad nauseam) are these two statements: 1) Heat energy is stored in molecules’ internal motions which gives them an internal temperature. 2) The internal temperature of the molecules in any bulk quantity of a substance are, on average, equal to the temperature of their translational motions. This is well established and elementary. Greg L 23:40, 14 October 2006 (UTC)

subconversation 2

Greg L, I disagree with you again. For brevity, I shall point out only one of your errors - most of your others are repeats and you can find their refutations above somewhere. Error no 1: you said "Nothing can absorb heat energy and not attain a greater temperature. Nothing. Never." I say "Take a glass of water with some ice in it and let it absorb some heat energy. Observe whether it attains a greater temperature." If you concede this obvious point, then we can move onto some less elementary thermodynamics. LeBofSportif 14:16, 14 October 2006 (UTC)

Who do you think you're trying to kid? You're skirting the point and you know it. Yes, you correctly pointed out a hole in my written argument. I should have said "with the exception of phase changes and ionization etc. etc". This concept isn't lost on me and I doubt it's lost on most contributors who might try to make improvements to this article. You know full well what the point of this whole argument had been about: Whether or not molecules have an internal temperature or not. At first you fed me a bunch of your “ARGH” stuff, squatted on the Temperature article, and kept reverting anyone who added words to that effect. After reading some supporting documents I posted, you (sort of) conceded that *maybe* big complex molecules might have an internal temperature (as if something the laws of physics are different for 30 atoms and two atoms). I have zero interest in the no-doubt impossible effort of trying to get you to concede for the record that molecules have internal temperatures. The whole point of lowering myself into this muck was to get it into the talk page that it is a simple fact (I can't say “indisputable” fact because you will dispute it) that molecules have internal temperatures. Your argument (paragraph #7 from the top in this section) was “A single molecule does not have a temperature.” Unless the molecule is at T=0, this is simply flat wrong. All who come to this discussion page have a right to know this so this article and others on the Web can be improved without misinformation being propagated.

These two statements are true: 1) Heat energy is stored in molecules’ internal motions which gives them an internal temperature. 2) The internal temperature of the molecules in any bulk quantity of a substance are, on average, equal to the temperature of their translational motions.

It's a simple concept: Whether it's a gas sample of a molecule with 60 atoms or a simple diatomic gas like oxygen, if the sample has a temperature of, for instance, 1000 kelvin, the individual molecules have, on average, internal temperatures of 1000 kelvin. Also, as I stated above, releasing these molecules individually for inspection will reveal that they radiate black-body radiation (as shown in illustration b here). Averaging a statistically significant quantity will reveal that when first released from the 1000 kelvin sample, their black-body spectrum will be declining on a curve indicating that when they were first released from the sample, they had an internal temperature of 1000 K. This is an important concept and is at the heart of molecular interferometry (as written about in Physics World: Probing the limits of the quantum world Markus Arndt et al.). It's also an important underpinning in understanding where heat energy goes. Greg L 20:01, 14 October 2006 (UTC)

The simplest approach for me is to attack your two assertions. Since 2) depends on the existence of internal temperature (which I dispute), it depends on 1), so I shall only attack 1). My attack on 1) is thus:

Given an isolated hydrogen molecule which is in its rotational first-excited state and its vibrational groundstate, what is its internal temperature? And what is the general method whereby we determine the internal temperature of similar molecules? These both boil down to the question: what, precisely, is the definition of your 'internal temperature'? LeBofSportif 01:23, 15 October 2006 (UTC)

Regarding some of Greg's quotes made above, I think this would also give my answer to LeBofSportif's questions as well. In short, the internal temperature of molecules does exist, but only for large numbers of molecules, just as temperature may be assigned to the "external" degrees of freedom for a large number of molecules.

"There is no magical minimum quantity of the fundamental particles of nature at which a temperature can no longer be assigned; one can always rely on the probabilities."

But you have to somehow measure these probabilities. And you do this with a thermometer, which averages over a large number of particles. Even if you wish to assign a temperature to a single particle as the temperature of the population it came from, that temperature must be measured by averaging over the population. If you wish to assign a temperature to a single particle as the temperature of the population it came from, go ahead, but its never done in any literature I have ever seen. We agree its temperature cannot be related to its individual energy right? Because that would be jumping all over the place.

"Heat energy is stored in molecules’ internal motions which gives them an internal temperature."

Yes, as long as we average their internal energies over a large number of molecules which are in equilibrium, just like we do with the three translational degrees of freedom.

"The internal temperature of the molecules in any bulk quantity of a substance are, on average, equal to the temperature of their translational motions. This is well established and elementary."

Yes, at equilibrium. Otherwise maybe not.

Also, individual molecules do not emit black body radiation. They emit single photons with a specific single energy. If the emitting molecules are in thermal equilibrium and the photons are being constantly emitted and reabsorbed, then these photons will have a distribution of energies, just like the kinetic energy of the molecules have a distribution of energies. Like the molecules, this photon distribution will be an equilibrium distribution. An equilibrium distribution of photon energies is called black body radiation, while an equilibrium distribution of molecular kinetic energies is called a Maxwell-Boltzmann distribution. PAR 02:05, 15 October 2006 (UTC)

Par: You are wrong in both sentences where you state “Also, individual molecules do not emit black body radiation. They emit single photons with a specific single energy.” Read again Physics World: Probing the limits of the quantum world Markus Arndt et al.:

Again, this is paper deals with molecular interferometry where they fire individual, hot molecules through a slit. The individual molecules are emitting photons. Beyond a certain temperature, the wavelength of the photons becomes less than twice the distance between the separated atomic wavefronts and this carries sufficient "which path" information to destroy the interference pattern in the inteferometer. Anytime photons are emitted due to the collisions of atomic orbitals due to temperature-induced vibrational motion, it is called black-body radiation. The only exceptions I know of are ZPE-related photons (mostly a T=0 issue). True, any single photon will be at a single wavelength. However, a heated molecule doesn't cool all the way to T=0 with that one emission. If you capture the spectrum of the emmissions from an individual molecule, it takes the form of a cooling black-body. And even if you capture and observe only one black-body photon and can't establish a curve, that photon is still called a “black-body photon”. You should read the article. I found it very interesting. Greg L 02:34, 15 October 2006 (UTC)

Looking at that article, I searched on "black" and found "just as a little block of hot solid material glows, emits black-body radiation and cools through evaporation." I couldn't find anything that said an individual molecule emits black body radiation. In the example you gave, I could see how multiple emissions would approximate a black body spectrum, but the error would be roughly 1 over the square root of the number of emissions. I have never heard of a "black body photon", but I think we agree that if you specify the energy and spin of a photon, you have specified everything that can be known about that photon by measuring that photon alone. If I tell you the energy and spin of a photon, you cannot tell me if it is a black body photon. In order to be a black body photon, you must know that it came from a population of other photons in equilibrium. It's "black body" nature is not a piece of information that it carries with it. PAR 03:04, 15 October 2006 (UTC)

PAR: I think you're getting too hung up with quantum stuff. I think it's not so complicated. Everything that's hotter than absolute zero always emits black-body radiation. Even when the emitting object is not a perfect black body (as happens with anything that's not in equilibrium and even many things that are such as tungsten filaments), the radiation being emitted is still black-body radiation. Any given photon needn't be classified as a "black-body photon" by analyzing a particular property of a given photon; black-body photons can be classified as such simply by having knowledge of why they were emitted. Fluorescent emissions aren't black-body photons and neither are lasers. But pretty much anything a soldier every sees in a thermal imaging sight is black-body radiation. The cosmic background radiation is black-body radiation. Of course, if you receive unknown photons and a spectrum analysis shows the radiation has a black-body distribution, that tells you what you need to know about the source without directly confirming the fact. Black-body radiation is simply the product of collisions of atomic orbitals surrounding atoms as a result of thermal agitation. That's why the black-body spectrum and the Maxwell distribution appear so similar. I spent a lot of time corresponding with Ph.D. experts on black-body and ZPE photon subjects and still don't pretend to be an expert on the subject; particularly since most of my correspondence was in making sure what was going on at absolute zero was down pat. So maybe I'm about to learn something new. Why is the spin property of a photon a necessary bit of information to have when it comes to black-body radiation? No speculation now… quote real hard facts. Greg L 05:44, 15 October 2006 (UTC)

Sorry to interrupt...Greg, could you address my question above about the internal temperature of an isolated hydrogen atom? The way you answer this will likely explain your opinions on what counts as black body radiation and that sort of thing, so we may kill 2 birds with one stone, so to speak. Also, you say to PAR that "you're getting too hung up on quantum stuff". The world is a quantum world - a proper understanding of statistical mechanics and how it applies to the real world requires the "quantum stuff". Some of the points I make only make sense if you accept the "quantum stuff". Absolute zero, the quenching of heat capacities, the third law of thermodynamics - these have their proper context when viewed with the "quantum stuff". LeBofSportif 11:07, 15 October 2006 (UTC)

LeBofSportif : Quantum stuff is important. Yes. But there's no point arguing such details when one starts off with statements like “Temperature is not average kinetic energy. This is a misconception, and a dangerous one.” What I'm saying is that all atomic and molecular motion (whether internal degrees of freedom or translational motion), at temperatures greater than T=0, has a kinetic energy associated with it as fixed by the Boltzmann constant (K_b = 1.380 6505(24) × 10^–23 J/K). I'm also saying that for a system in equilibrium, the internal temperature of molecules (2+ atoms) are always—on average for a statistically significant quantity of molecules—equal to the temperature of their translational motions. This is the notion that you and I first collided on because you violently objected (“ARGH!!!”) to the notion that molecules can have an internal temperature. Or course they do! And this internal temperature is always the same, on average, as the substance's temperature. I'm also saying that for systems in equilibrium, all internal and external thermal motion of molecules and all external thermal motion of atoms, while this motion has a mean temperature (and a mean kinetic energy associated with it), actually occurs across a range of velocities as described by the Maxwell distribution. I'm also saying that all atom-based matter (monatomic atoms and molecular-based substances) radiate thermal photons whenever electron orbitals are perturbed by thermal agitation and the relationship of temperature to the peak emission wavelength of the resulting black-body radiation is given by Wien's displacement law constant b (2.897 7685(51) × 10^–3 m K). I'm also saying that individual molecules with temperatures greater than T=0 radiate thermal photons. Greg L 17:05, 16 October 2006 (UTC)

And for the record, I'm with PAR on this one. Call them thermal photons if you want, but not black-body photons, since black-body is a term which can only be meaningfully applied to describe a distribution of photons. Any one-photon can never be a black-body photon. It is like saying "I measured my classmates' heights and discovered that each person's height is normally distributed." When read carefully, what I just said in quotes is nonsense. If you want to express the "reason" it was emitted, call it a thermal photon. And since you are making claims about molecules, your claims should be valid for smaller molecules like hydrogren and chlorine, not just whatever beasts they were using in that experiment you keep referencing, so perhaps the examples you give could be framed in terms of these molecules. LeBofSportif 11:18, 15 October 2006 (UTC)

I don't have a problem with that. However, the experts I've been corresponding with have used "black body" more broadly than that. Of course, that was in the context of drawing a distinction to ZPE photons (which is a T=0 phenomenon). At temperatures greater than T=0, they've called them "black-body photons." Maybe they shouldn't and are just being a little loose when engaging in less rigorous e-mail correspondence. I'll read some of the papers I've received to see what terminology is used for individual photons. Greg L 17:05, 16 October 2006 (UTC)

I know this discussion is a bit old, but I can't help but respond to Greg L.'s continued appeal to his “experts”. I am a PhD Physical Chemist – my graduate work was with statistical thermodynamics. I'm intimately acquainted with this topic, and LeBofSportif is quite right that a single molecule (or a handful, for that matter) does not have “temperature”. Temperature is a description of an ensemble quantity. Calling excited states (rotational, translational, vibrational, whatever) temperature is akin to calling an individual's lifespan “life expectancy”. It may seem like a silly play in semantics, but folks in my line of work spend a great deal of time worrying about correctly reproducing ensemble averages, like temperature, from properties of individual atoms and molecules. The difference is profound - I really can't understand why your “experts” were so cavalier as to conflate the two. But, the energy of an isolated molecule is no more “temperature” than my birth-date is “a generation”, or my car is “traffic” - period.134.253.26.9 (talk) —Preceding comment was added at 22:27, 28 February 2008 (UTC)

The natural degrees of temperature

Maybe we should include a section (or at least mention) on the temperature scale based on natural units (the gravitational constant, planck distance, speed of light). Since this degree (absolute zero at one end, infinant temperature at the other, considered the original temperature of the big bang) is too large, bringing it down by a factor of 32, we get degrees roughly 3 degrees farenheit apart. Natural units are thought to be more universal, and less arbitrary than conventional units (ie, 100 units between the point at which the vapor pressure of H2O reaches 101.3 kPa, and where it condenses, again only at 101.3 kPa), as they are based on physical constants. With this system, the temperature of freezing water comes to around 193 degrees, and room temperature to 208, and the boiling point to 264. If we fix a parallel system to the freezing point as in Kelvin and Celsius, we get room temperature to be 15 degrees, and boiling to be 71. These units could be called centigrade (discarded by the metric system), or degrees Planck.

On another note; this may be misunderstanding on my part, but it seems to me that temperature is just energy/volume, as it is the average kinetic energy. This seems to make sense, but no where, on the internet or in chemistry, have I ever heard this even contemplated. GWC 10:50 EST 25 Oct 2004

It is the Heat that is an Job and hence an Energy. Changing the temperature of a mass (or of a volume) of a gas (or of an object) give a difference of the energy.

Note that what can be measure is only difference of energy not energy. This difference of energy is proportional to the mass (or volume) to the difference of temperatura. The proportional factor (that depends on the material) is called specific heat. That temperature and kinetic energy are related (and notably in an direct way) is the result of the [kinetic theory of gas]], but this is true only for a gas (indeed only for an ideal gas). Temperature and work (or energy) and the corresponding units of measure, kelvin and joule, are related by the Boltzmann constant.

Of course you can change the definition of the unit of measure to have the Boltzmann constant equal to one.

This is related to the above discussion on natural unit (Since the natural unit sistem is not easy for those who have not had theoretical physics studies, I suggest not to include this. It is an Encyclopedia, not a book of advanced physics.) The problem of the connection (and the problem of terminology) between temperature and energy is similar to the one between mass and energy.

If you do not understand the difference between temperature and heat (and heat is energy as shown by Joule's experiments) consider the diference between electrical voltage and electrical current (this parallelism is not easy to see, indeed). AnyFile 13:50, 12 Nov 2004 (UTC)

Explain Counterintuitiveness

In part of the dicussion this is said: "This average energy is independent of particle mass, which seems counterintuitive to many people. Although the temperature is related to the average kinetic energy of the particles in a gas, each particle has its own energy which may or may not correspond to the average." Perhaps an explanation of why this relationship exists would be useful? I'd be happy to write it, and so I'll do it here (in the discussion, so that if you like it you can just copy/paste). (I'm afraid I'm not too familiar with the Wiki Markup for math, so you'll probably have to clean that up a bit but otherwise it should be ok.) Right after the sentence about counter-intuitiveness, insert this:

However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that two systems when interacting with each other will reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an object (in this case a molecule) is:

$\ K_{E}={\frac {1}{2}}mv^{2}$

So a particle of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than a lighter counterpart, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this from Oklahoma State University makes the point more clear. Not all the particles in the container have the velocity, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. EagleFalconn 19:13, 30 Nov 2004 (UTC)

I cleaned up the formula, but I disapprove that "Temperature is a measure of the average kinetic energy of a system". Temperature is the increment of energy per unit of increment of entropy.

$\ T={\frac {dE}{dS}}$

If the entropy is proportionate to the number of particles in the system, then the temperature is proportionate to the average energy per particle, not the average energy of the system. Light molecules move fast, heavy molecules move less fast, and a cannon ball hanging in a wire from the ceiling moves too slowly for it to be noticed (when the transient oscillatory motion has faded away and the system is in a state of thermodynamic equilibrium), even if all these particles have the same average kinetic energy. Bo Jacoby 09:24, 14 September 2005 (UTC)

link requires subscription

The third link down in External Links requires a subscription to view the site.

Is there a policy against such links? SOP?

I don't know about any policy (but I've been away from WP for a while). Anyway I could not reach the site either and I got a spyware warning. So I'll delete it and keep it here just in case someone disagrees. The link was:Nanotubes may have no 'temperature'. Also, something with "no temperature" sounds weird...--Nabla 23:29, 2005 Apr 28 (UTC)

Here's a non-subscription mirror. (And it is weird...) [1] Rd232 17:13, 31 July 2005 (UTC)

Negative temperature

This section read to me as non-sensical, until I realized it was talking about spin and other quantum weirdness. If it's accurate, it needs references, or else it's likely to be removed as inaccurate. It could also be written to be clearer. What does it mean for something to have "hotter than infinite temperature"? Most people would assume that this means that it's very, very hot, as in hot to the touch, but in a non-sensical way. We think of temperature as being proportional to kinetic energy; does spin state really count toward kinetic energy? And if the total kinetic energy of a system is finite, it might be sensible to talk about a negative "spin temperature" but not a negative (or greater-than-infinite) overall temperature, right? -- Beland 09:17, 10 July 2005 (UTC)

About you question the answer is yes. Sometimes various degrees of freedom of a system have a different temperature, if their energy coupling is weak. So that here the heat would flow away from the spins, not only toward the outside of the system, but also towards other degrees of freedom of the system like the kinetic energies. And yes, negative temperature does exist. Here's a link with pretty clear explanations:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/neg_temperature.htmlThorinMuglindir 23:18, 4 November 2005 (UTC)

Oh, and I don't think we need to be that cautious with the question of neg temp and the definitions of temperature. The defintion of temperature from heat and entropy works, and the Maxwell Boltzman weights, too. The 0th law definition, I don't know, but anyway this one is just the one you use when you can't have statistical mechanics and for some reason you have to stick with just thermodynamics. Which means it's a bit outdated.ThorinMuglindir 23:28, 4 November 2005 (UTC)

The zeroth law isn't applicable; if a system initially at negative temperature is brought into thermal equilibrium with a gas, the resulting equilibrium temperature will always be positive. So you can't use a gas to measure negative temperatures. Melchoir 03:08, 11 February 2006 (UTC)

I run NMR (nuclear magnetic resonance) everyday. So, if I apply to the sample a 90 degree proton pulse which makes the populations of the two spin states equal, I have achieved a temperature of infinity? And if I apply a 180 degree pulse, I have achieved a negative absolute temperature? But when I look at the temperature reading, it still reads 25 oC, exactly what I have set. Furthermore, many people have taken MRI (magnetic resonance imaging) scans of their brain. And they still behave normal. I mean their brain is not fried. Both NMR and MRI are known as non-destructive analytical techniques, meaning samples are not destroyed by these analytical methods. This cannot be true if the samples have experienced a temperature of infinity. MRI is called MRI and not NMRI (nuclear magnetic resonance imaging) is because the perceived public fear of the word "nuclear" makes the word dropped. Perhaps, it's time to clarify the "negative temperature" because people start to question about MRI. 24.74.135.9 22:52, 18 April 2007 (UTC)

Correct usage

Anybody have a "definitive" on the correct usage of the ° sign? I notice that most WP pages have it as X °C but others are X° C. I'm looking at Enviroment Canada's manuals and it uses the second version in older manuals but both versions on different pages in some of the newer manuals.CambridgeBayWeather 19:46, 31 July 2005 (UTC)

It has been discussed some on Wikipedia talk:Manual of Style (dates and numbers). NIST Special Publication 811 calls for the space (there is no space, however, in 30° of arc). See the part of the talk page where NPL and IUPAC and BIPM and ISO are discussed, all supporting the space, with the degree sign butting up to the C. There may be some style guides still supporting omitting the space (the one you haven't mentioned, x°C). I doubt that any modern guide supports using the space but butting the degree sign to the number rather than to the letter identifying the temperature scale. Gene Nygaard 20:28:19, 2005-07-31 (UTC)

Thanks. I fixed the one page where I'd put it in the wrong way.CambridgeBayWeather 20:42, 31 July 2005 (UTC)

I, too prefer “x °C” to “x° C”, but I am not pedantic about it. My pet peeve in this regard is the need to distinguish “°C” from “C°”. That is, “10 °C” is a temperature, but “10 C°” is a temperature difference. Everyone knows this, but almost no one observes it. Georgeisomorphism (talk) 22:46, 17 February 2009 (UTC)

Personally, I tend use just "C" (and "K"): "°C" effectively amount to "degrees centigrade", which can only be justifed as a disambiguation from e.g. "degrees Fahrenheit", where "degree" is the original unit. The rational thing to do is to declare "C" a unit in its own right. Similarly, we do not use phrases like "scale-marks kilogram", but rather just "kilogram". 88.77.129.121 (talk) 04:41, 24 December 2009 (UTC)

vacuum

can a vacuum have an associated temperature? i had a friend who argued the space would feel "freezing", whereas i said that it would be both extremely cold (due to evapouration from bare skin to vaccum) and extremely hot (from ambiant radiation and solar currents - instant sunburn), and oddly neither at the same time, as there isnt enough matter for a temperature to be possible. was i close? mastodon 16:29, 13 December 2005 (UTC)

I'd say temperature is where an object reaches thermal equilibrium (which, in space, would be 2.7 Kelvins due to thermal radiation far away from the sun or in a shadow, or much higher while exposed to sunlight). Astronomers, however, might equate it to the average kinetic energy of the few random particles zipping about (which can be up to 10^7 Kelvins... though it wouldn't even be felt). Personally, I'd use the former; having temperature disassociated with "hot" and "cold" as it does for gasses in deep space seems counter-intuitive to me. Issues of evaporation and energy loss due to boiling are important, of course, but they can't really be considered part of the temperature itself. --Obsidian-fox 08:06, 11 February 2006 (UTC)

I think the section in the article on temperature of a vacuum is muddled, and inaccurate. I will change it unless anyone justifies what it says here. LeBofSportif 09:55, 13 May 2006 (UTC)

Why can't temperature be expressed in Hz?

Keep in mind that I'm only a grade 11 student, but it seems to me that if heat energy is caused by the vibration of particles, then it could theoeretically be measured in terms of cycles per second, yes?

I don't know...Maybe the frequency doesn't actually change as particles vibrate more, because even though they vibrate faster, the distance required to be travelled to make one full cycle also increases, and so the time would as well--in other words, it balances out, and the frequency always stays the same. I honestly have no idea. It's just a thought, I guess. Remember, I'm a grade 11 student, so please don't chastise me for these seemingly unintelligent thoughts.

First of all, heat is not about vibration of particles. It is about the kinetic energy of the particles. HOWEVER, in a solid, where particles are constrained to a lattice, the kinetic energy is mainly vibrational - hence your misconception. In a gas, where there is no such constraint, the particles don't vibrate, they can just move fast.

Secondly, you are correct that in most cases, vibrational frequency doesn't change as the energy changes. Think of a pendulum - the frequency is the same even when you vary the amplitude. LeBofSportif 15:40, 17 May 2006 (UTC)

In fact, temperature is often expressed in Hz, but not for the reasons suggested (vibrational frequency of particles). Temperature is rigorously defined using quantum mechanical theory, where microscopic objects (electrons, atoms, photons, etc.) are described as existing in discrete states of different energies. For an ensemble of these objects, temperature is a measure of how these objects are distributed over all their possible energy states. When the states are widely separated in energy, high temperatures are needed to "jostle" the objects from one quanta to another. In almost all cases, a transition from one state to another is accompanied by the emission (or absorption) of a photon (light particle) of energy. That's why things glow when they are hot, and the hotter something is, the higher the frequency of the emitted light. For example, blue flames are hotter than red flames, just as blue light (~6x10^14 Hz) is at a higher frequency than red light (~5x10^14 Hz). And even at room temperature, objects "glow" in the lower-frequency infrared spectrum (thus night-vision goggles). Even outer space glows, but it is so cold that that it only contains microwaves (1x10^10 Hz). This relationship between temperature and frequency can be quantified, and it turns out to be: T = hf/k, where h is Planck's constant, k is the Boltzmann constant, and f is frequency. But remember that this frequency is not how fast a particle physically vibrates; rather, it's the frequency of the light emitted when the particle makes a thermal transition between two quantized states.

Average Kinetic Energy

Temperature is not average kinetic energy. This is a misconception, and a dangerous one. It appears on the talk page in a number of places, and now someone has changed the article to read "temperature is a measure of the average kinetic energy..." If this was true, then all gases would have the same heat capacity. They don't, therefore it is not true. Temperature is related to the average kinetic energy, in that, for a given body, an increase in temperature will be proportional to the increase in energy. The proportionality is different for different bodies. When two things are brought into contact, equilibrium will be when they have the same temperature, not the same K.E.LeBofSportif 10:17, 4 June 2006 (UTC)

Hey, what d’ya know, you're right! Temperature isn't “average kinetic energy”; it's as written in the article: temperature is a function of the average kinetic energy of the particles’ translational motions. Please don't change it! In fact LeBofSportif, all the monatomic gases have the exact same molar heat capacity: 20.7862 J mol^-1 K^-1 (see table). Molecular-based gases always have greater specific heat capacities. And they typically vary from each other because they have differing abilities to absorb heat energy into their internal degrees of freedom. Also, hydrogen bonding (as with ethanol, water and ammonia) strongly influences molar heat capacity. At 25 °C, the mean kinetic energy of the translational motion of each molecule (it doesn't matter what kind) is 6.174 61 × 10^–21 Joule. Differences in molecular weight just make for different speeds; the kinetic energy of translational motion stays the same. For instance, at 4200 K, helium atoms will be moving at a mean speed (not vector-isolated velocity) of 5,176.55 m/s whereas uranium gas atoms will be moving much slower at a mean speed 671.2701 m/s, but both will have exactly the same kinetic energy bound in their translational speeds: 8.905 20 × 10^–20 J if they’re both at 4200 K. I just don't know how anyone who's made Wikipedia contributions to technical articles could utter a statement like “If this was true, then all gases would have the same heat capacity. They don't, therefore it is not true.” The only thing that's "dangerous" is confusing heat capacity with temperature and kinetic energy. Greg L 00:48, 15 October 2006 (UTC)

"Temperature is a function of the average kinetic energy" - fine, of course this is true. Except, from a pedagogical point of view it is problematic since you would need a different function for each substance you consider. On the 4th of june, when I wrote that comment, the article contained the line "temperature is a measure of the average kinetic energy". In my world, this implies that there exists some way of using temperature to work out average kinetic energy of a general substance. A 'measure' of height is pretty useless if we can't infer the height it measures, after all. Thus the statement that "Tmp is a measure of avg k.e" implies the existence of some unique function T(E), which takes energy and gives us temperature. Since specific heat is basically dT/dE, if there was a unique T(E), then all substances would have identical specific heat behaviour at any temperature. This is manifestly not the case, and hence the original supposition is false. Hence why I complained about the choice of wording "Tmp is a measure of avg k.e", since this leads, as I have just shown, to a contradiction. While not everyone necessarily will fail to realise that there are many different functions which describe the energy dependence of temperature, I felt it was necessary to make this explicit, since inferred misconception is as bad as implied when we consider the pedagogical context which many Wikipedia articles are viewed in. And for the record, I am not confusing heat capacity with temperature and kinetic energy. LeBofSportif 00:32, 15 October 2006 (UTC)

It is exceedingly bad form for you to keep on changing what you have written after I have replied to it. Can I suggest you decide what to write, then post it and then leave it alone. Any after thoughts beyond simple spelling/grammar corrections should really come under a separate post. LeBofSportif 00:56, 15 October 2006 (UTC)

Sorry, I agree. Edit conflict and I went ahead anyway. Shouldn't do it. My bad. Greg L 00:59, 15 October 2006 (UTC)

LeBofSportif: Getting back to your statement that “Temperature is not average kinetic energy. This is a misconception, and a dangerous one.” as well as “…from a pedagogical point of view it is problematic since you would need a different function for each substance you consider.”, neither argument is at all true. It's really, really simple LeBofSportif. The kinetic energy of the temperature-induced translational motion of particles relates to temperature via Boltzmann’s constant. Thus…

  $k=\$ 1.380 6505(24)×10⁻²³ joule/kelvin

If you’re still not convinced, see also Wikipedia’s Electronvolt article which relates electronvolts to joules as follows: 1 eV = 1.602 176 53 (14)×10⁻¹⁹ J and then see the subsection of that article, Electronvolts and temperature, which again relates energy to temperature by stating that one electronvolt is equal to 11,604.5 kelvins. Note that no term is necessary in either formula to account for different “substance[s]” as you alleged above. If you have a problem with the first-paragraph definition of the Temperature article, which—as of this writing—makes the following (very) simple statement:

“[Temperature] is a function of the average kinetic energy of a certain kind of vibrational motion of matter’s constituent particles called translational motions”

…then you need to go revise the Boltzmann constant and Electronvolt articles and all the physics books of the world on the same subjects. And again, your statement that “If this [Temperature / kinetic energy relationship] was true, then all gases would have the same heat capacity. They don't, therefore it is not true., well… that too is astonishingly incorrect. First, as I stated above, different molecular substances have varying molar heat capacities because they have varying abilities to absorb heat energy into their molecules’ internal degrees of freedom. Moreover, your statement is further incorrect because one actually can relate molar heat capacity (joules/mole) to absolute temperature for the monatomic gases such as helium, neon, and argon because they have no internal degrees of freedom; they have only translational motions into which they can absorb heat energy (see table).

By the way, one uses Boltzmann’s constant to relate temperature to the mean, or average energy of the translational motion of particles in a system (a statistically significant quantity of particles), as follows:

E_mean = 3/2K_bT

where…

E_mean = Joules

K_b = 1.380 6505 × 10^–23

T = temperature in kelvins

This well-recognized formula shouldn’t have to be defended against obfuscations such as “doesn’t apply for systems that aren’t in equilibrium” and similar circumstances, like “the system is being hit by a train.” It's the law. Again, I'm not necessarily trying to convince you about this; it's much more important that all others who are contributing to the Temperature article should have confidence in the fundamental underpinnings of what temperature is all about: temperature is a function of the kinetic energy of a particlular kind of particle motion. Extra specificity is still required in the Temperature article with regard to how temperature and the energy of translational motion are related. The Boltzmann constant and related articles on thermodynamics can be useful resources for contributors. Also different sections could flow together more fluidly (a common problem with collaborative writing)

I have no intention of making too many contributions to this article since, as is evidenced by these discussions, contributing to this article is time-consuming, unrewarding and is so not fun. Maybe others will find it easier to contribute here. Greg L 21:54, 15 October 2006 (UTC)

Temperature is a measure of the average kinetic energy per degree of freedom. At equilibrium, the average energy is kT/2 per degree of freedom. Translational motion in 3-dimensional space has three degrees of freedom, therefore an average energy of three times kT/2 or 3kT/2. Internal degrees of freedom will increase the total energy of a particle (atom or molecule). If there is one internal degree of freedom, then the total energy of the particle at equilibrium will be 2kT. If there are two internal degrees of freedom, then the total energy per particle will be 5kT/2. Different particles, different relationships between energy and temperature, therefore different heat capacities, but the same relationship between energy per degree of freedom and temperature. PAR 22:38, 15 October 2006 (UTC)

PAR: Whether it's “3kT/2” or “3/2K_bT”, it sounds good to me. Do you think there's anything you wrote that is at variance with what I wrote(?) or are you just expanding? Greg L 22:47, 15 October 2006 (UTC)

Well, going thru what you have said in this section, I would disagree that temperature is a function of the average energy of only translational motion. Temperature is not tied to the translational motion energy alone, it is tied to particular degrees of freedom. If all those degrees of freedom have the same temperature (i.e. they are in equilibrium with each other), then fine, but out of equilibrium, they may have different temperatures, or they may have such large statistical variations in their temperature that the argument that they have no temperature at all begins to rear its ugly head.

Also, in the classical case, at equilibrium, its not that molecules have varying abilities to absorb heat into their internal degrees of freedom, its simply that they have those degrees of freedom. The rate of absorption is only a factor for non equilibrium situations. The specific heat of a classical ideal gas is Dk/2 where D is the number of degrees of freedom per molecule (internal plus external). The variation of specific heat with temperature is a quantum effect. PAR 23:31, 15 October 2006 (UTC)

PAR: I think you are correctly quoting formulas but are drawing incorrect conclusions as regards their causes and effects. For instance, I think you are in error when you state “…its not that molecules have varying abilities to absorb heat into their internal degrees of freedom, its simply that they have those degrees of freedom.” In fact, different molecules have different molar heat capacities—even if they posses all three internal degrees of freedom—because different molecules have different constructions (that’s why they’re “different” molecules) and therefore exhibit different quantum properties. I’m excluding hydrogen bonding and crystal latice issues for the moment. The enormously complex ways that only three internal degrees of freedom can be expressed is perfectly well demonstrated by this animation. I do however, agree with your later statement that “[t]he variation of specific heat with temperature is a quantum effect.” I'm also puzzled at your quick tendency to cite out-of-equilibrium exceptions to various rules. In equilibrium, the temperature of the internal degrees of freedom of molecules are, on average, always equal to the temperature of their translational motions. That much is pretty much fixed by definition whenever one constrains the issue by specifying "in equilibrium” isn't it? Greg L 01:25, 16 October 2006 (UTC)

Greg L, you say that "The enormously complex ways that only three internal degrees of freedom can be expressed is perfectly well demonstrated by this animation". It is very clear to me that looking at the animation, you have misunderstood what a "degree of freedom" is in statistical mechanics. For the purposes of the equipartition theorem, a degree of freedom is any quadratic term in the expression for total energy. That animated molecule has many more than three degrees of freedom. When you say "In fact, different molecules have different molar heat capacities—even if they posses all three internal degrees of freedom—because different molecules have different constructions (that’s why they’re “different” molecules) and therefore exhibit different quantum properties." this also betrays your lack of understanding of what a degree of freedom really is. What you are trying to do, is define temperature backwards via the equipartition theorem, choosing only translational modes and using the 1/2 kT result. This is certainly problematic since not all systems which have temperature have translational modes, and moreover, the equipartition theorem as used in this context is only valid in the classical regime, and only valid for quadratic terms in the Energy. LeBofSportif 10:14, 16 October 2006 (UTC)

Yes, Greg, I was being too "classical". Classically, for an ideal gas, the "dimensionsless specific heat capacity at constant volume" is a fixed constant D/2 where D is the number of degrees of freedom per particle. (My error writing Dk/2 above). Deviations from this are quantum effects or non-ideality (i.e. long range forces between particles), but an argument can be made that long range forces introduce additional degrees of freedom. Anyway, If you have two different molecules with the same internal degrees of freedom, and they have different heat capacities, then that will be due to a quantum effect, as you stated.

Regarding the equality of translational and internal temperature, yes, they are equal at equilibrium. The reason I keep qualifying things with "in equilibrium" because it is the non-equilibrium situations which give a lot of insight into the dynamics of equilibrium. For example, you can have a plasma of neutral atoms, ions, and electrons in an electric field. The atoms and the ions will have one temperature, and the electrons will have a higher temperature because they pick up energy so much more quickly than do the ions from the electric field. The atoms then pick up their energy from collisions with the ions and electrons. All three particle types have a Maxwellian distribution because they collide enough to form one, but their temperatures are different, with the temperature of the atoms being practically the same as that of the ions. When you have non-equilibrium situations, then the average rates of energy transfer between degrees of freedom become important. At equilibrium, the average rates are equal and the average energies are the same.

This is all classical. The point I was trying to make is that I don't think that rates of energy transfer from translational to internal degrees of freedom is a factor in modifying the internal temperature of a bunch of molecules, which is what I took your statement about molecules having "differing abilities to absorb heat energy into their internal degrees of freedom". Maybe I misunderstood your meaning with that statement.

Also, yes, there are what look like hundreds of internal degrees of freedom in that animation you mentioned. A simple particle (i.e. an atom of a monatomic gas) has three degrees of freedom. That means you need 3 numbers to specify its configuration, and those three numbers are x, y, and z - its positional coordinates. The energy associated with these three degrees of freedom are its external, or translational energy. If you have a molecule composed of two such particles tied together, then you need to specify the distance between them to fully specify their configuration. (their orientation doesn't affect their energy, so that degree of freedom doesn't apply). For energy purposes, there are now four degrees of freedom, three external, one internal. The energy of the internal degree of freedom is carried by the vibration of the molecule in which the distance between them varies sinusoidally. If this can be viewed as a classical vibration, then the average energy of such a molecule will be four times kT/2 or 2kT. But if the vibration is quantized, and its first excited level is at an energy which is huge compared to kT, then that excited level will practically never be excited, and that internal degree of freedom is non-operational, or "frozen out" or whatever you want to call it, and the average energy of these molecules will be back down to 3kT/2. PAR 14:44, 16 October 2006 (UTC)

Geez guys. Take all this energy and make some good and correct contributions to this article; it needs a lot of improvements. I took the time to create graphics and animations for articles. Making one single graphic that displays nice and clear takes a boat-load of time. The “translational motion” animation I've placed in this article was a collaboration between me and a friend in New York. I've been working with a University on making a better one. I've taken the time to compress 6 MB animations that someone else made into an (actually useful) 280 kB version so all the articles that use it load in a reasonable time. And I've cited my work where necessary. I encourage you to do the same. Greg L 17:20, 16 October 2006 (UTC)

Ok, I will do. LeBofSportif 19:17, 16 October 2006 (UTC)

Minor correction, PAR. The degrees of freedom only contribute if they appear in the energy, and contribute kT/2 only when they appear quadratically. Thus, x, y, and z are not the degrees of freedom - vx, vy, and vz are. More commonly it is written using px, py, and pz, the three components of momenta. For instance, if all of the particles were hooked to springs so that the Hamiltonian was: H = p^2/2/m + m*omega^2 * x^2/2 then the contribution would be 6 kT/2 per particle.

Internal and External Temperature

There is no such distinction I am aware of, except the idea that weakly coupled subsystems may be at different temperatures, eg, spin temperature and lattice temperature might be different, but this is not what the article is talking about. " "internal energy" or "internal temperature" ". ARGH!!! MISCONCEPTION ALERT LeBofSportif 19:58, 5 June 2006 (UTC)

“Spontaneously give up energy” and other errors

The first sentence of the definition, where it says: In thermodynamics, temperature is a measure of the tendency of an object or system to spontaneously give up energy. seems to be omitting critical wording such that it is misleading to the point of being incorrect. To take out its first-order error, it ought to say "…to spontaneously give up thermal energy.” Without this addition, the potential energy of holding an object off the ground would qualify as “temperature” since potential energy is very arguably the “tendency of an object to spontaneously give up energy.” Secondly, even with this correction, the tendency to give up (thermal) energy is really and actually the product of two characteristics: 1) a substance's temperature, and 2) a substances thermal conductivity. Even if they are at the same temperature, silver has a fabulous tendency to give up thermal energy whereas carpeting, fiberglass, and air, have poor capability.

I suggest that someone should dig through an authoritative text book and quote a classic definition. It seems inescapable that any definition should address the laymans’ needs by saying something along the lines of “temperature underlies the common notions of hot and cold.” It should also quickly follow up with the broad, but technically correct definition of temperature. All I can propose is as follows: “temperature is a function of the average kinetic energy of a certain kind of vibrational motion of matter’s constituent particles called translational motions.” Any contributing author should note that in the case of thermodynamic temperature (either Rankine or Kelvin), absolute temperature is a proportional function of this kinetic energy; for any non-absolute scale, temperature is a slope-intercept (y = mx+b) function of the kinetic energy. Greg L 21:11, 9 October 2006 (UTC)

OK, I gave my attempt at fixing the first two paragraphs of the article. The first paragraph of the Overview section sure seems to be in need of work though. For example, it is incorrect where it says [Temperature arrises from degrees of freedom. And with] “an ideal gas, the relevant degrees of freedom are translational, rotational, and vibrational motion of the individual molecules.” The best analog for an ideal gas is the smallest of the monatomic atoms: helium. An ideal gas doesn't have any rotational and [internal] vibrational (as distinct from “translational”) movements; that's precisely why it's called “ideal” in this context. Secondly, even for complex molecules (not monatomic atoms), rotational and vibrational motions store heat energy but are not motions that contribute to temperature. It was seemingly written by someone who was confusing heat-related phenomena with "temperature." This paragraph is wrong on so many levels, it’s FUBAR. An expert needs to step up to the plate and rewrite this article. Greg L 00:09, 10 October 2006 (UTC)

OK, so I had to do that too. That FUBAR paragraph was best fixed by wholesale deletion. The rest of the section stands well enough on its own. I also added the animation I created for the thermodynamic temperature article. Greg L 16:44, 10 October 2006 (UTC)

Temperature and translational motion

The statement in the Overview that "The translational motion of the fundamental particles of nature gives substances their temperature" is incorrect. For example, translational motion of atoms or electrons has nothing to do with the well-known thermal properties of magnets (try a google search or see http://www.coolmagnetman.com/magstren.htm). Rather, it is the electron spin states in a magnet that change their equilibrium polarization as the temperature changes. Electron spin is a quantum phenomenon, with nothing to do with translational motion, and is best described as a "degree of freedom."

I'll probably wait until the current contributors "cool off" before attempting any changes to the article.

I couldn't agree more. Don't let anything stop you. LeBofSportif 13:08, 17 October 2006 (UTC)

Looks like PAR did a good job for that fix. Thanks, PAR. 137.78.59.167PhysicsPhD

The anonymously contributed comment above (someone in the Los Angeles CA area) is completely wrong. He or she confuses heat with temperature. The magnetocaloric effect has to do with how randomizing the electron spins of a plurality of atoms absorbs heat energy. Magnetic materials heat up upon application of a magnetic field and cool when the field is removed. When the substance is cooling, the heat energy stored in vibrational motion (the translational motion of atoms and molecules) is absorbed by the randomizing electron spins as the magnetic field is removed. The magnetocaloric effect is one of several mechanisms that comprise heat energy. Another is the creation of molecular bonds during phase changes. These all have to do with entropy. The statement “The translational motion of the fundamental particles of nature gives substances their temperature” is 100% true and 100% complete. Don't confuse heat with temperature. Heat arises from several phenomenon; temperature is the result of just one.

This relationship between temperature and the kinetic energy of the translational motion of a given particle is perfectly established by the Boltzmann constant. The Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy of the translational motions of its constituent particles as follows:

E_mean = 3/2K_bT

where…

E_mean = joules (symbol: J)

K_b = 1.380 6505(24) × 10⁻²³ J/K

T = thermodynamic temperature in kelvins

If someone's got a problem with the statement “The translational motion of the fundamental particles of nature gives substances their temperature,” go take it up with Ludwig Boltzmann and all the physicists of the world who rely on his constant. Greg L 02:11, 15 December 2006 (UTC)

No. The most basic relationship involving temperature is:

$T=\left({\frac {\partial U}{\partial S}}\right)_{X}$

where U is internal energy, S is entropy, and X are all the other extensive variables. The internal energy (U) is not composed of just the translational energies (or translational degrees of freedom) of the particles, it involves their internal energies (degrees of freedom) as well. For example, a complex molecule can have all sorts of internal vibrational motions going on.

I could just as well say:

"The relationship between temperature and the kinetic energy per degree of freedom of a given particle is perfectly established by the Boltzmann constant. The Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy per degree of freedom of its constituent particles as follows:

$E_{mean}={\frac {n_{dof}}{2}}\,\,K_{b}T$

where $n_{dof}\,$ is the number of degrees of freedom of the particle."

For a point particle, there will be only three translational degrees of freedom, giving the original equation, but for a diatomic molecule with translational vibration only, there will be four, and so on. PAR 04:59, 15 December 2006 (UTC)

• PAR: Your too are confusing heat issues with temperature. Perhaps you didn't thoroughly read what the issue is about. Again, the issue is: What phenomenon underlies temperature? The answer is the thermodynamic temperature of any bulk quantity of a substance (a statistically significant quantity of particles) is directly proportional to the average—or “mean”—kinetic energy of translational motion. Period. Full stop. In your supporting arguments above, you consistently and properly kept on using the term "energy" and described how heat energy is stored in the internal degrees of freedom of molecules. Good. That much is correct. But somehow, you seem to think that undermines what I said temperature is.

Remember, the heat energy stored in all such mechanisms as 1) group nuclear spin moment (a magnetic effect), 2) group electron spin (magnetism), 3) molecular bonds that haven't formed yet (phase changes of cooling), and 4) the internal degrees of freedom in molecules do not contribute to the temperature of a substance. Really really. These simply are all places heat energy is stored.

Still don't believe me? Consider this: Imagine a box filled with steam (water gas) at 120 °C. Steam molecules have three internal degrees of freedom and these degrees of freedom can store just as much heat energy as do the three degrees of freedom that comprise translational motion. Now get this. This is why steam has twice the specific heat capacity as do the monatomic gases such as helium. Focus on this important point: the heat energy absorbed into the internal degrees of freedom of the steam molecules is contributing neither to the translational motion of the steam molecules nor to the temperature of the steam. That's precisely why steam absorbs more heat energy for a given amount of temperature rise. Remember the Ideal gas law? That equation doesn't have a term for molar heat capacity (heat energy or joules), it is a simple formula describing the relationship of temperature, pressure, and volume of gases. All three of these gas attributes are the result of one phenomenon: the translational motion of the molecules or atoms comprising the gas.

One final time for the record now. Focus. Here's the statement I was rebutting from the anonymous reader: The statement in the Overview that "The translational motion of the fundamental particles of nature gives substances their temperature" is incorrect. And I say the quoted text is perfectly and wholly correct. I further said that [The] relationship between temperature and the kinetic energy of the translational motion of a given particle is perfectly established by the Boltzmann constant. The Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy of the translational motions of its constituent particles as follows: E_mean = 3/2K_bT

Temperature arises from the translational motion of the fundamental particles of nature. Period. All the other mechanisms you cited are places heat energy is stored into without increasing translational motion (the temperature of the substance). Do you get it now? Greg L 17:37, 15 December 2006 (UTC)

It is a shame, Greg L, that during your time away from this page you have become even more convinced by the fallacies about temperature that you promote. There is nothing unique about translational motion when we talk about temperature. I think I can suggest your misconception: when we measure the temperature of something with a normal thermometer, it is the translational motions of the system which most strongly couple to the thermometer - in this situation you are conflating thermometry with temperature - a grave error. In fact, some systems have temperature which do not have translational motions, eg the spin system in a magnetised solid. It is imperative from a pedagogical point of view that this page does not give a muddled account of what temperature is. Have you read any good physics books recently? LeBofSportif 21:17, 15 December 2006 (UTC)

Effects such as nuclear spin temperatures are well beyond the bounds of this article. "Temperature" as the term is used in thermodynamics for its fundamental physical underpinnings such as the Ideal gas law (pV = nRT), applies only to translational motion. The heat energy stored in all such mechanisms as 1) group nuclear spin moment (a magnetic effect), 2) group electron spin (magnetism), 3) molecular bonds that haven't formed yet (phase changes of cooling), and 4) the internal degrees of freedom in molecules, do not contribute to the thermodynamic temperature of a substance. These are all simply places heat energy is stored. Translational motion is what gives us all the common thermodynamic effects (pressure, the vast majority of gas volume, and temperature). If you take one mole of a molecular gas such as nitrogen and heat it up one degree Celsius, 20.7862 joules of heat energy will be absorbed into the translational motions and 8.33 joules (@ 25 °C) will be absorbed into the molecules' internal degrees of freedom. The heat absorbed internally does not contribute to the thermodynamic temperature of the gas. But as a consequence of absorbing heat internally into its molecules, the molecules then have an internal temperature that is, on average while in equilibrium, equal to the thermodynamic temperature of their translational motions. As of today, this poor article says Temperature is a measure of the average energy of the particles (atoms or molecules) of a substance, or a measure of how hot or cold something is. This energy occurs as the translational motion of a particle or as internal energy of a particle, such as a molecular vibration or the excitation of an electron energy level. These two sentences completely fly in the face of the entire concept of specific heat capacity (how different substances absorb different amounts of heat energy as they are heated up the same amount to the same temperature). Those two sentences are saying that nitrogen (29.12 J mol⁻¹ K⁻¹) must be hotter than helium (20.7862 J mol⁻¹ K⁻¹) because it has more total energy. This article has suffered from common misconceptions and, unfortunately, it shows. I certainly have no intention to change it. It's clear any further discussions with you are a colossal waste of my time. I've accomplished my objective of getting the facts here-memorialized for other, contributing authors to consider. Fini Greg L 22:56, 16 December 2006 (UTC)

Ok, now I am starting to understand. Maybe. If we have an ideal diatomic gas, then we could define temperature as PV/nR. We just measure pressure, volume, moles, and that would be our thermometer. The pressure only comes from the translational motion of the gas, so the temperature reading is only the result of the coupling of the translational motion of the gas to the pressure sensor. {Diatomic, monatomic, doesn't matter. And it's the result of coupling to the temperature sensor, not pressure sensor. Other than that, you've got the concept! — Greg L 00:11, 17 December 2006 (UTC)}

If we can find a situation in which temperature is measured by some means other than a device which couples to the translational degrees of freedom of the particles of the object being measured, would you then be convinced that temperature does not arise from translational motion alone? PAR 22:46, 15 December 2006 (UTC)

Greg L - please answer the above question before you leave. PAR 23:07, 16 December 2006 (UTC)

PAR: See the early part of my above response to you-know-who above. As for your second paragraph, of course; all the other places into which heat energy is absorbed (except for the potential energy of phase changes as materials transition from a less ordered state to a more ordered state), have temperatures that are, on average, equal to that of their translational motions. These temperatures can be measured and I even referenced such concepts when I had the misfortune of having a go at it with you-know-who above on the discussion topic regarding internal temperatures of molecules. Further, a quantum phenomenon such as nuclear spin temperature can be isolated and reduced in magnitude. For instance, the Helsinki University of Technology's Low Temperature Lab achieved a nuclear spin temperature of 100 pK in 2000. But unless someone is using specialized lab magnets to accomplish tricks like this, all these temperatures are equal and simultaneously diminish as a substance is cooled. You know as well as I do that details such as these are entirely beyond the scope of this article—at least in its current, unfortunate state where it has huge errors such as asserting that temperature is the measure of all the various energies of molecules (“translational motion of a particle or as internal energy of a particle”). What a mess! This article sorely needs to get heat issues separated from temperature issues.

Now, I'll directly address your final question (sentence): “…would you then be convinced that temperature does not arise from translational motion alone?” In a word, no. But the answer must be qualified. By "temperature” I'm talking about the common notion that underpins thermodynamics and its laws such as the Ideal gas law (pV = nRT). Do these other mechanisms that store heat energy (such as the internal degrees of freedom of molecules) have temperatures of their own? Yes. The important point to remember is that when you measure the "temperature" of a substance using a thermometer (mercury bulb, alcohol bulb, SPRTs, thermocouples, thermisters, etc.) you are measuring only the effect of the translational motions ("coupling" as you put it). Translational motions are the only motions that create pressure and give gases their volume. All the other motions and phenomena are places where heat energy is absorbed into. This is precisely why some substances have higher molar heat capacity than others; that is, absorb more heat energy for a given amount of "temperature rise" than other substances. Anyone who asserts that the temperature of a substance is caused by anything other than translational motion, is also asserting that the concept of molar heat capacity is incorrect.

And remember, the "ideal" gas law isn't dependent on whether a gas is monatomic, diatomic, or triatomic. The extra degrees of freedom with non-monatomic gases only absorb more heat energy for a given temperature rise. The "ideal" part of the name only pertains to treating the particle as a point-like entity. As can be seen in the animation I made (and which is now included in this article), at a pressure of 136 atmospheres, even the diameter of helium atoms take up a relatively significant portion of the volume. Greg L 00:11, 17 December 2006 (UTC)

Hi - Ok, one more question that I forgot to ask which would help me immensely in understanding your point - can you think of an actual experiment in which you would give a correct answer to the outcome, while someone who disagreed with you on this subject would give an incorrect answer? You know what I mean, not like an answer to a question on an exam, which tests whether two people agree on the answer, but an experimental outcome, which tests who has the better ability to predict the future outcome of an experiment. PAR 02:21, 17 December 2006 (UTC)

PAR: Let's try. I can prove my point based on math. Anyone who thinks I am wrong must show how the below math and/or logic is incorrect.

Let's calculate the particles’ mean kinetic energy using two different techniques.

The Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy of the translational motions of its constituent particles as follows:

E_mean = 3/2K_bT

where…

E_mean = joules (symbol: J)

K_b = 1.380 6505(24) × 10⁻²³ J/K

T = thermodynamic temperature in kelvins

Now let's calculate the mean energy another way. Let's start by calculating the speed of particles. The rate of translational motion of atoms and molecules is calculated based on thermodynamic temperature as follows:

${\tilde {v}}={\sqrt {\frac {{K_{b} \over 2}\cdot T}{m \over 2}}}$

where…

${\tilde {v}}$ = vector-isolated mean velocity of translational particle motion in m/s

K_b (Boltzmann constant) = 1.380 6505(24) × 10⁻²³ J/K

T = thermodynamic temperature in kelvins

m = molecular mass of substance in kg/particle

Note that the above formula again uses the Boltzmann constant (a fundamental underpinning of thermodynamics). Now…

The mean speed (not vector-isolated velocity) of an atom or molecule along any arbitrary path is calculated as follows:

${\tilde {s}}={\tilde {v}}\cdot {\sqrt {3}}$

where…

${\tilde {s}}$ = mean speed of translational particle motion in m/s

Note that the mean energy of the translational motions of a substance’s constituent particles correlates to their mean speed, not velocity.

Now let's calculate the kinetic energy of translational motion using an entirely different method. Substituting ${\tilde {s}}$ for v in the classic formula for kinetic energy, E_k = ¹/₂m • v ² produces precisely the same value as does E_mean = 3/2K_bT.

The above are well-accepted formulas in physics. Both techniques convert thermodynamic temperature into kinetic energy. Ah… but what comprises this kinetic energy(?): translational motion as well as other kinds of motions? Have I proven that the kinetic energy arises only from translational motion? So here's the test: If you plug the values for nitrogen (a diatomic gas) at 25 °C into the above, and then repeat it for helium (a monatomic gas), I say you will end up with precisely the same value of kinetic energy per particle. Repeat again at 26 °C. You will obtain a slightly greater kinetic energy value than at 25 °C but… the nitrogen and helium values will again be identical. Yet raising the temperature of a mole of nitrogen by one kelvin requires 40% more heat energy (see table) than does helium. Therefore, the thermodynamic temperature of a substance is a function of kinetic energy associated only with translational motion; it is independent of how much heat energy is absorbed into all internal degrees of freedom of molecules. Greg L 03:31, 17 December 2006 (UTC)

But that's an "exam" type question. It consists of writing down equations, paper, pencils, so forth. I'm looking for an actual experiment. Something where you take an actual thermodynamic system and measure something and get a number. I mean, suppose we have one person who says the acceleration due to gravity is 32 feet/sec/sec, and another says its 100 feet/sec/sec, then we ask them how long will it take for a ball dropped from 100 feet to hit the ground. They will give different answers. Thats the kind of experiment I am looking for. A real one. Can you think of an actual experiment in which you would give a correct answer to the outcome, while someone who disagreed with you on this subject would give an incorrect answer? This is not like some kind of challenge. I am trying to think of such an experiment too, because it would help me to understand the problem. PAR 04:34, 17 December 2006 (UTC)

Not really. Perhaps the best answer to your question is to turn it around and ask you a question: Why must one put more heat energy into molecular-based gases vs. the monatomic gases in order to cause the same quantity (by volume or moles) to increase by the same increment of temperature? Please explain why the diatomic gases such as N₂, O₂, and H₂ (see this table) require roughly 28.5 joules of energy to increase the temperature of one mole of them by one degree C, whereas all of the noble gases require only 20.7862 J. Seriously. Would you please write the proper explanation below? Greg L 05:34, 17 December 2006 (UTC)

P.S. If you want to do some reading before answering, read this. Greg L 05:40, 17 December 2006 (UTC)

The explanation I would start with is that the N2 and O2 gases have internal degrees of freedom and the monatomic gases do not. In fact they have four internal degrees of freedom (two rotational, two vibrational). If they were triatomic molecules, they would have 9 internal degrees of freedom (If I remember correctly). The second part of the explanation is the equipartition of energy. In equilibrium, each degree of freedom acquires an energy of kT/2 unless there are quantum effects which "freeze out" or uncouple certain internal degrees of freedom from the three translational degrees of freedom. So, if you add energy to the gas, that energy must be distributed to more internal degrees of freedom, and so the temperature will rise less per amount of heat added. Assuming no internal degrees of freedom are frozen out, for a diatomic gas, there will be a total of 7 degrees of freedom (3 translational, 4 internal) and so the specific heat will be dU/dT = 7k/2 per molecule.

Note that in the above, there is no need to distinguish between internal temperature and translational temperature, since equilibrium is assumed, and therefore they are identical. (Please let me call it "translational temperature" so there is no confusion over the word "temperature".) If we are going to come up with an experiment which we disagree on, it has to be one in which the internal and translational temperatures are different. Suppose we have a case of a multi-atomic gas where the internal and external degrees of freedom require a time of ΔT to equilibrate, and we manage somehow to drop the translational temperature in a time that is small compared to ΔT. Then, for a short time, we could have a gas in which its translational temperature was different from its internal temperature. We might be able to monitor the radiation from such a gas, and see that its spectrum reflected this fact. I'm not sure what the spectrum would look like, maybe two superimposed black body curves, reflecting the two different temperatures.

Does this all sound like a scenario you agree could happen? PAR 14:57, 17 December 2006 (UTC)

PAR: Yes, as far the distinction of internal energy & temperature of molecules vs. the mean kinetic energy of their translational motions and thermodynamic temperature. No, in reality as regards the experiment. It appears you have a good command of the principals underlying heat energy, molar heat capacity, and temperature. But…

I would expect that when one quickly chills a gas, the cold plate — upon which the gas is impinging— will instantly chill both a molecule's translational and internal temperatures. This is because heat exchange mechanism that excites the internal degrees of freedom is instantaneously quick and efficient. All it takes is a single collision with something cold for the kinetic energy of both translational motion and internal motion to be transfered into the molecules comprising the cold plate. So a brief exposure to something cold just partially chills some of the gas sample's molecules — both internal and translational. In this case, all you have is a gas sample that momentarily is not in equilibrium. When that's the case, you can't take a valid temperature measurement because the sample will momentarily not obey the Maxwell–Boltzmann distribution of translational velocities. In other words, the ∆T-effect isn't selective beteween internal motion and translational motion.

As regards nitrogen's “four” internal degrees of freedom, you should know that two different conventions are used in science when counting degrees of freedom. The one I use (because it's quite common in science and physics) counts each dimension or mode of movement as a single degree of freedom. The other convention counts each of these as two degrees (back and forth, up and down, etc.). Thus, translational motion has three degrees of freedom according to the convention I've been using, but six degrees according to the convention you used above. To test for yourself which one would be best for you, Google on the water molecules' degrees of freedom. Some will say six, others will say twelve.

You might be interested in Probing the limits of the quantum world at PhysicsWeb. It's about physicists who experimented with the interference patterns created by shooting whole molecules (not photons) through interferometers. There's a point where they were shooting individual, hot C₆₀ molecules through their interferometer. They also write about how thermal photons were being emitted by these individual molecules as they shot through the interferometer. It's very interesting reading.

Now, since you clearly have a grasp of why different gases have different molar heat capacities, it begs the question: Why does this article talk about how temperature is the measure of both the translational and internal energies? Greg L 17:20, 17 December 2006 (UTC)

P.S.: As regards your request: “Can you think of an actual experiment in which you would give a correct answer to the outcome, while someone who disagreed with you on this subject would give an incorrect answer?,” I guess I can. I predict that if you inject 20.7862 J of heat energy into one mole of helium (a monatomic gas), it will increase in thermodynamic temperature by exactly one kelvin. I also predict that if you inject the same amount, 20.7862 J, into oxygen (a diatomic molecule), its temperature will only increase by 707 millikelvins. The thermodynamic “temperature” as it applies to the laws of thermodynamics, won't increase as much for oxygen because 6.08 J of heat energy was absorbed internally into the oxygen molecule and is unavailable to contribute to its temperature (translational motion). Accordingly, any statement along the lines of "the thermodynamic temperature of a substance is the measure of its total kinetic energy — both its translational and internal energies such as a molecular vibration and the excitation of an electron energy level” is incorrect. It is a big goof and flies in the face of the entire concept of molar heat capacity. The above-described experiment (measuring molar heat capacity) is routinely performed in the scientific world and will prove my point. If one doesn't have the necessary equipment, they can look here to see the results of molar heat capacity experiments others have performed.

And to memorialize for the record (for the benefit of those who came late to this debate and don't want to wade through its whole history), the heat energy stored in all such mechanisms as 1) group nuclear spin moment (a magnetic effect), 2) group electron spin (the magnetocaloric effect), 3) the internal degrees of freedom of molecules, and 4) the potential energy of molecular bonds that haven't yet formed (the phase transitions of cooling), do not contribute to the thermodynamic temperature of a substance. These are all simply places where thermal energy is stored. Also, the first three items in this list have temperatures of their own, and under normal circumstances, these temperatures are equal to the thermodynamic temperature of the substance. Further, effects such as nuclear spin temperatures are well beyond the bounds of this article. The temperature of a substance, as the term is used in thermodynamics for its fundamental underpinnings such as the Ideal gas law (pV = nRT), is the result only of translational motion. This relationship between the kinetic energy of translation motion vs. the thermodynamic temperature of a substance is fully described by the Boltzmann constant. More specifically, the Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy of the translational motions of its constituent particles as follows:

E_mean = 3/2K_bT

where…

E_mean = joules (symbol: J)

K_b = 1.380 6505(24) × 10⁻²³ J/K

T = thermodynamic temperature in kelvins

Accordingly, the proper statement as to the nature of temperature is as follows: “The temperature of a substance arises from a certain kind of vibrational motion of its constituent particles called translational motions. More specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the mean kinetic energy of these translational motions.” Greg L 19:11, 17 December 2006 (UTC)

With regard the experiment you mentioned - you are saying that the error someone would make would be that they would assign the same temperature increase to both cases because they thought that temperature was proportional to the energy added. Is that right? {Yes, that's what I'm saying. Greg L 21:46, 17 December 2006 (UTC)}

In that case, I agree with you to this extent - the temperature of a substance CANNOT be used to predict the average total energy per particle until you know how many internal degrees of freedom there are and to what extent they are being excited at that particular temperature. The temperature of a substance CAN be used to predict the average translational energy per particle of that substance without any additional knowledge (except the number of particles). PAR 20:58, 17 December 2006 (UTC)

So what do you think of the first two sentences of the Overview section(?), which currently states as follows:

Temperature is a measure of the average energy of the particles (atoms or molecules) of a substance, or a measure of how hot or cold something is. This energy occurs as the translational motion of a particle or as internal energy of a particle, such as a molecular vibration or the excitation of an electron energy level. (my emphasis).

Can we agree that it ought to read as follows(?):

“The temperature of a substance arises from a certain kind of vibrational motion of its constituent particles called translational motions. More specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the mean kinetic energy of these translational motions.”

Greg L 21:46, 17 December 2006 (UTC)

Well thats where I start to have trouble. I agree the sentence is not optimum, because it might give the idea that temperature and internal energy are simply related in the same way for all substances. I agree it should be changed somehow.

We both agree that there are two concepts, which I call internal temperature and translational temperature, and that they are equal (in equilibrium).

What I hear you saying is that the term "thermodynamic temperature" should refer to what I am calling the "translational temperature". Is that correct? PAR 22:22, 17 December 2006 (UTC)

Temperature concepts such as nuclear spin temperatures are far beyond the bounds of this article. The term "temperature" in this article, unless it is very explicitly stated otherwise, has got to address the term as it applies to thermodynamics: such concepts as the conjugate variables of thermodynamics and its various formulas such as the ideal gas constant. What good is the Boltzmann constant (which relates “temperature” to kinetic energy), if this article has the effect of broadening the very notion of what “temperature” is? What feels hot, and what thermometers measure, and what makes all gases expand in volume is only translational motion. If one wants to address other phenomenon such as how molecules’ internal degrees of freedom also have a temperature (which, on average, happen to be identical to that of translational motion), then by all means, say so. But do it somewhere else in the article and be clear! As it is currently written, the first two sentences of the overview are simply and completely false because they totally undermine the concept of molar heat capacity by stating that “temperature” is a measure of total kinetic energy (both translational and internal). You and I know this isn't true.

And no, the term “thermodynamic temperature” does not necessarily have the connotation of “the temperature associated with translational motion.” It merely has its null point at absolute zero. As such, it is an absolute scale (so it works well in formulas involving other absolute measures such as energy and pressure). Any "thermodynamic temperature" in kelvins can readily be converted to the Celsius scale by simply subtracting 273.15 from it. Regardless of what scale is used, temperature is temperature. If you are talking about “the temperature of a substance,” it has only one meaning and must be kept completely separate from the notion of thermal energy and its various other forms.

Over 5200 words have been written on this discussion topic. I don't know what more I can offer. Greg L 00:05, 18 December 2006 (UTC)

P.S.: I'm not positive, but I think I can define what the key distinction is that you're wrestling with: what is having its temperature measured. Thermodynamics deals with the temperatures of substances. If you want to talk about nuclear spin temperatures, that's another issue. If you want to talk about the internal temperature of molecules, that's another issue. But if one asks "What gives a substance its temperature?”, the answer is, “The temperature of a substance arises from a certain kind of vibrational motion of its constituent particles called translational motions. More specifically, the thermodynamic temperature of any bulk quantity of matter is the measure of the mean kinetic energy of these translational motions.” If you want to talk about how thermal energy is absorbed into the internal degrees of freedom of molecules, great. We can just look at the molar heat capacity and calculate exactly what portion of the heat energy is borne by translational motion and how much is borne by the internal degrees of freedom of the molecule. And the answer as to what the internal temperature of the molecule is, well, that's simple; for a bulk quantity in equilibrium, it's equal to the temperature of the substance (its translational motion temperature).

All of these issues seem to be beyond the proper scope of this article. I suggest you simply state what phenomenon gives substances their temperature. Then you can state that heat energy is absorbed only into translational motion for monatomic gases. You can also state that for molecular substances, additional heat energy is absorbed into internal degrees of freedom and you can refer them to specific heat capacity to learn more. It's quite simple. Discussing it is what's complex. Greg L 00:45, 18 December 2006 (UTC)

Ok - Two questions

• We agree that most temperature measurements are responding to what I call the translational temperature of the object measured. I don't understand if this is the basis of your argument, though. If I were to find a temperature measurement that measured the internal temperature of a gas of complex molecules, would that change your mind?

• Given that you know more or less how I am thinking about things, in terms of internal and translational temperature, is there now any real-life experiment that you can think of on whose outcome we would disagree? (Remember how I suddenly understood what you were saying when you came up with that last experiment.)

PAR 02:58, 18 December 2006 (UTC)

{PAR and Greg L have spent several days corresponding directly with each other off-line to discuss and debate this issue.} (Greg L 00:05, 20 December 2006 (UTC))

PAR: Here's a straw-man paragraph for you and others to consider for starting the Overview section:

Temperature arises from the random submicroscopic vibrations of the particle constituents of matter. More specifically, the thermodynamic (absolute) temperature of any bulk quantity of a substance (a statistically significant quantity of particles) in equilibrium is directly proportional to the average—or “mean”—kinetic energy of a specific kind of particle motion known as translational motion. Translational motions are ordinary, whole-body movements in 3D space whereby particles move about and exchange energy in collisions. Fig. 1 above illustrates translational motion in gases. The Boltzmann constant relates the thermodynamic temperature of a bulk quantity of a substance to the mean energy of the translational motions of its constituent particles as follows: E_mean = 3/2K_bT. Translational motion is also what gives gases their pressure and the vast majority of their volume, as established by the ideal gas law. The kinetic energy of translational motion is a major contributor of contributes to the total heat energy contained in a substance. For monatomic substances such as the noble gas helium, this kinetic energy arises only from translational motion. Molecules however, are complex objects; they are a population of atoms that can move about within a molecule in different ways (known as a molecule’s internal degrees of freedom). Heat energy is stored in these internal motions. Accordingly, the total heat energy of molecular substances includes not only the kinetic energy of translational motion, but also the kinetic energy bound in a molecule’s internal degrees of freedom. The heat energy stored internally in molecules does not contribute to the temperature of a substance (nor to the pressure or volume of gases). This is because any kinetic energy that is, at a given instant, bound in internal motions is not at that same instant contributing to the molecules’ translational motions. Differences in the number of internal degrees of freedom is one of the reasons why different substances have different molar heat capacities.

Greg L 21:35, 23 December 2006 (UTC)

Hi Greg - As we discussed in our conversation, I prefer to think in terms of a temperature associated with each degree of freedom. Classically, each degree of freedom gets an average of (1/2)kT of energy. So that means we can talk about a translational temperature for the three translational degrees of freedom, and an internal temperature for the rotational and vibrational degrees of freedom. At equilibrium they are all equal.

You point out that:

• Pressure is the result of translational motion. In fact, if T_t is the translational temperature, then the ideal gas law is actually PV=NkT_t.
• Heat transfer between bodies is basically mediated by the translational motions of the particles.
• It follows that most temperature measurements are measuring the translational temperature.
• It also follows that the sensation of heat is caused by translational temperature difference.
• For the translational degrees of freedom, the average energy is always proportional to temperature via E=(3/2)kT except for extremely low temperatures. The internal (i.e. non-translational) energy on the other hand, cannot be said to be proportional to temperature due to quantum effects. Thus, assuming a proportionality between translational temperature and energy is almost always correct, while assuming a proportionality between internal temperature and energy is almost never correct. Temperature is therefore not proportional to the energy of a molecule, only to its translational energy.

If I understand your argument, this is the basis for your saying that the term "temperature" actually refers only to what I am calling the "translational temperature". In particular you make the statement:

The heat energy stored internally in molecules does not contribute to the temperature of a substance (nor to the pressure or volume of gases)

This is a statement I disagree with, simply because it conflicts with my understanding of temperature. If the words "translational temperature" were substituted for "temperature", then I would agree with it. In your above paragraph, I agree with just about everything else.

Importantly, I think that we agree that there is no objective way to resolve this disagreement. In other words, there is no experimental outcome for which we would give different answers as the result of our disagreement. I believe the difference is semantic, or one of terminology. In other words we disagree on how to use words to describe a situation we both have the same understanding of. In this case, we have to conform to the usage of the community at large. I think that your terminology is not "standard" in this sense.

PAR 07:29, 27 December 2006 (UTC)

I agree, Greg's terminology is totally non standard. An example where his concept of temperature becomes totally inadequate is a long-chain polymer liquid. Internal and translational "degrees of freedom" get totally mixed up. LeBofSportif 22:02, 27 December 2006 (UTC)

How so? PAR 22:44, 27 December 2006 (UTC)

If someone is swinging a double ended chain around their head and it thwacks you in the face you will feel it. Do you get my point now? LeBofSportif 23:26, 28 December 2006 (UTC)

PAR: I appreciate your thoughts. I'm searching for a way to demonstrate that internal degrees of freedom (and their associated contribution to increased molar heat capacity) is truly very really distinct from external degrees of freedom and its association with temperature. I thought I had made a good case with the intimate association between external degrees of freedom and both the pressure and volume of gases (pV = nRT). Perhaps, it is just an issue of semantics. Greg L 03:27, 29 December 2006 (UTC)

Diurnal Temperature Variation

I have been searching Wikipedia on diurnal temperature variation and have found nothing on the subject so far. I think this is a very important field to be covered when it comes to air temperature. For example, the fact that deserts tend to have very big diurnal temperature variation or that the diurnal temperature variaton decreases when moving pole ward. —The preceding unsigned comment was added by 217.209.60.200 (talk) 18:13, 18 January 2007 (UTC).

Overcomplication

I removed the following from where it had been used to write the introduction. In my view this is way too advanced for the introductory paragraphs. However, I leave it here in the hope that an expert might recycle it into the more detailed parts.

The absolute temperature of a system is defined as the energy of microscopic motions in the system per particle per degree of freedom (with half of the Boltzmann constant to be the proportionality factor between unit of energy and unit of temperature). For a solid, these microscopic motions are principally the vibrations of the constituent atoms about their sites in the solid. For an ideal monatomic gas, the microscopic motions are the translational motions of the constituent gas particles.

Notinasnaid 16:19, 15 March 2007 (UTC)

Congratulation! Now - when you removed my definition of T (which is actually not my but simply the accepted definition of T in science) everyone can see that now this article has NO consistent definition of temperature at all. We all can safely and loudly laugh at the "definition" dT = dQ/S which you (or someone else) put in the article without understanding that entropy in thermodynamics is in turn defined via temperature - as dS = dQ/T (dS=dQ/T can be derived from the statistical definition of entropy S=wkln(w) but again PROVIDED that temperature T is predefined first). The circle (or better to say, the circus) is complete and perfect. Good entertainment. Enormousdude 21:17, 27 June 2007 (UTC)

[Copied from user talk page]:

Please do not revert definitions - clear definitions are important as everything follows from them. Some definitions are not elementary. Temperature is a statistical parameter of large ensemble of identical particles. Its definition can not be understood without proper background (at least statistical mechanics or statistical physics must be taken, well understood, and passed with good grade prior to contributing to the matter of this subject).

What is seen as "fantastic overcomplication" to you is actually starting chapter in any standard statistical mechanics text.

Sincerely, Enormousdude 16:40, 15 March 2007 (UTC)

Mathematical definition

This section I removed is just plain inaccurate. As a working understanding of temperature in people's everyday experience it is fine, but what was quoted is the result of the classical equipartition theorem. It fails when dealing with non quadratic contributions to the energy, like you get for relativistic particles (eg a very hot plasma or photons), and in quantum mechanical limits. Bottom line, there are two accurate definitions of temperature: the zeroth law definition that appeals to equilibrium and lets us set a standard and the statistical mechanical one where it is defined in terms of entropy and energy. So, if you're going to appeal to the microscopic properties of the system, go the second route, if you're not stick with the zeroth law definition. BlackGriffen 20:56, 13 June 2007 (UTC)

Hold on, there no temperature for relativistic or QM system anyway (and if in some cases it is possible to define it, then T is defined as I said - average energy of particle per degree of freedom: T = 2<E>/k.

And you also are incorrect about entropy definition of temperature. Fundamental definition of entropy is statistical one: S=-kwlnw from which then t/dynamical definition dQ/T follows as a corollary PROVIDED that temperature T is already defined (so, t/d definition of entropy REQUIRES T to be pre-defined BEFORE t/d entropy can be defined). Thus t/d entropy CAN NOT be used to define temperature.

Zeroth law is obviosely NOT a definition of T - it can not even give units of T (not to say about other properties of T).

So, your revert is incorrect.

Sincerely, Enormousdude 20:46, 22 June 2007 (UTC)

---

My apologies for not knowing how to sign in.

I tried to use the statement in "overview" that scientists achieved a temperature of 700nK (nanoKelvin) by getting Cesium atoms to move at 7 mm per second. By my math, 100 degrees Kelvin would then be achieved if Cesium atoms were moving at 1000 km/second. I know that this extrapolation would fail completely if atoms were traveling faster than the speed of light. So, how would you explain the translational motion of atoms versus temperature? What happened?

I got 83.7 m/sec for 100 K, which is rather consistent with the average kinetic energy of Cs atoms at that temperature. Remember that kinetic energy is proportional to SQUARE of speed.

Sincerely, 161.28.196.101 21:16, 26 June 2007 (UTC)

Yet One More Scale.....

When I studied math in Junior High School we were taught the principles of different numbering systems. That is, numbering systems other than the decimal or "base ten" system.

Many criticized such "new math" priorities as idle and not practical. This was a generation before the cyber-students. Soon even amateur programmers were using four systems: Base Two or binary, base eight or octal-decimal (8 bit processors of the 1980's), base 16 or hexadecimal and the conventional base 10.

My curiosity was raised when I read of the "duodecimal" or base 12 concept that apparently the Babylonians may have used. It made much more sense to use the prime numbers (1), 2 and 3 instead of (1), 2 and 5, especially for subdividing. But I digress....

During College we were trained in a bilingual nomenclature system, converting constantly from the SI/metric units to the much maligned SAE or "Imperial" system. The ability to work in two systems was as probably the greater benefit of the exercise.

For example, the "old" system would express units for Refrigeration equipment as: (1)tons of refrigeration (heat transfer at the evapourator) (2) Btuh for heat transfer at the condenser (3) bhp - brake horse power for the compressor shaft power and (4) Kw for the "electrical" power into the compressor motor. The new system uses Kw to describe all four rates of energy transfer!

So it only seemed reasonable to propose, when possible, new more logical systems of measurement, since the status quo, at times, appeared so tangled anyway - especially to non-technical people. What about temperature measurement?

I thought about a scale that would have 0 (zero) degrees as the freezing point of water and approximate human body temperature as 100 degrees -98 2/3(98.6667) degrees F. That is 66.67 degrees F from 0 to 100 or units exactly 1.5 time degrees F.

The zero degrees for freezing water had an environmental (weather) and physical sciences application. The upper 100 degrees would have a physiological life sciences application. Moderate room temperature would be therefore 54 degrees exactly.

The only question remained what to name this scale. The "Earth" scale (degrees E) the Science Scale (degrees S)..... I don't know.... maybe the Wiki scale (degrees W)??

Peter 142.163.53.194 (talk) 15:24, 25 March 2008 (UTC)

---Rebuttle---

Peter,

Seriously? This scale has less applicable use than any other scale I've ever seen, IMHO. While I am a fan of having a greater degree of precision in the temp readings we take, the average human body temperature is itself in a state of flux and it's value is in debate.

You should never make one end of your scale a moving value, because this only leads to confusion about what a referenced tempature was in the past,present,or future. What happens if the average human body termperature raises or drops by 10 degrees in the next 100 years? The only truely fixed points you can create are abs(0) and a phase-chaneg of a set compound in set circumstances.

The boiling point of water and freezing point of water (usually salt water) have been used over the years because of the relationship between the availability of salt water and consistancy of phase change, however I do agree it to be relatively arbitrary as it is not a homogenous substance and therefore far more variable than basing it on say abs(0)=0 and the melting point of Pure Nickle at sea-level = 1000.

However two problem befall my example, it is hard if not impossible to gather an ounce of a pure element, and 1000 may not be a value which lends to understanding the temperature on your day to day, there may need to be many decimal places in order to see the small temp changes humans percieve, making the scale somewhat cumbersome, much the way that the imperial scale F generally needs a single decimal place after it to really account for the subtle temperature changes humans can feel, there may need to be 3 or 4 decimal places on my arbitrary scale.

So it's nothing against you personally, but I hope you see why the arbitrary choices made in temp scale in the past have been with what most consider good reason. I personally would prefer a scale where Abs(0) = 0 and Fresh Water Freezing at sea level = 1000, this would have about double the preciscion of the Rahnkienscale, and in my oppinion would be much easier to understand relative temperatures once adopted. But, that is neigther here nore there, good luck in tweaking your scale to make more sence.

~Q —Preceding unsigned comment added by 69.74.205.178 (talk) 16:17, 29 August 2008 (UTC)

The zero point has significance in the physical and meteorological sciences, the upper scale ("100") is fixed (98 2/3 deg. F) thus it has a more of a nominal than any arbitrary significance in the physiological sciences.

Fahrenheit originally considered the (approximate)human body temperature to be 96 degrees even, making it divisible by prime numbers 2 and 3. "...His third point, the 96th degree, was the level of the liquid in the thermometer when held in the mouth or under the armpit.....". Thus, as you point out, even his scale fell into the pitfalls of using an imprecise, albeit significant, boundary. [2]

Not to be vain, but mine is at least a clever proposal and is at least intriguing to even amateur scientists. Daring of you to rebut, though.....thanks.

Peter 72.139.113.118 ([[User talk:72.139.113.118|talk]]) 19:28, 31 August 2008 (UTC)

P.S.: The "100 degrees" need not be a fixed point, the calibration point would be 270 W(Or E, or S or whatever) - the boiling point of water. 100 W need only be a reference point which may or may not have a useful medical application.

Peter 142.163.53.194 (talk) 21:45, 2 September 2008 (UTC)

Peter, It's been a while, I was just thinking of this scale you had thought up again the other day, let me first say 'thanks' for the complement. Now down to Business. The reason a non fixed scale is bad is because if 98.6 were the 'average' human temp, which it's not, it's lower, and you have people that range from 95 degrees to 101 degrees F lets say, then your 'end-point' would never read right on almost anymore, nearly every human would read something other than 100 (You would have people who range from 94.5 to 103.5, so I’m not really seeing the advantage to the average being 100 there.)

--Also as an aside fevers would be anywhere from 102 to 111, I don’t consider this either an improvement or a disadvantage to the system over Fahrenheit or Celsius, just for reference really.--

Now 54 degrees may be 68 degrees which you consider a comfortable room temperature (this is highly debatable especially considering he time of year and the person involved lol, but besides the point), it doesn’t in any way mean that 54 degrees is about 54 times as hot as 0 and ½ as hot as 100, which I somehow have a feeling your expecting from creating a new scale.. But perhaps I’m reading into things too much. For reference your Absolute zero will be -737.505 Degrees.

So now consider you have 100 years go by ,and in that 100 years the average human body temperature drops by 10 degrees Fahrenheit, how does that affect your temp scale? Are you going to re-center yoru scale so 88.6 = 100? Now what about all the work ever done in the scale before? Now it no longer makes sense because you’ve changed the conversion rate into another scale, you can now never be certain whether someone recorded a temperature in the old or new scale, and how do you compare the changes from the past?

Well maybe you’re thinking well no I’ll just leave 100 be the max = 98.6, who cares that it’s now completely arbitrary to a person’s daily life? Well okay so what happens in 1000 years if the average body temperature of a human changes to be + 100 degrees more, so now it’s 188.6 (yeah I know that’s a bit farfetched as humans would be on the verge of boiling) So now in this world where humans all have faster metabolisms, you’re going to find all temperatures they are interested in for their bodies, and appropriate ‘comfortable’ temperatures all fall above 100 degrees, so now your scale isn’t used because it’s not really applicable in the way it was intended

These are again the problems with a scale that will use a moving point as an end, either the scale constantly changes, and you can never correlate data, or the scale can run out of usefulness because the value at one end has changed so far from he fixed point originally meant to represent it.

Also your scale is not 1.5 F, as you stated-- Instead, your scale converts as: P = (F-32)*(3/2) And to convert back obviously you are needing to use: F = 32+(P*2/3)

~Q —Preceding unsigned comment added by 71.169.9.246 (talk) 04:57, 27 November 2009 (UTC)

Very good of you to contemplate this concept and take the time to reply.

Methinks you must have a medical background, since the criticisms focus largely on clinical applications.

It would, could, be an ambiguous situation when some students might assume that something other than 100 deg, (exactly) would be abnormal. However for lay persons observing any significant deviation from (about) 100 deg would be cause for concern and they would then check with their doctor. They would not have to try to remember if normal temp is 96.8 or 98.6. Celsius increments are too large - you have to focus on 1/10 degree changes to detect a developing complication such as an infection. [BTW the mean typical core temperature, for this scale, would be 98 2/3 F = 100 deg EXACTLY - more a numeric necessity than a medical one.]

You make a good point though, body temperature is the business of doctors and biologists - what if this changes? Then the scale serves as at least an historical reference. Then again, if you have ever travelled to higher altitudes, the coffee is cooler. Water does not boil at 100C everywhere. The scale is still relevant, in fact it now reflects the change in barometric pressure. However, boiling water cannot be used to calibrate a tranducer or an instrument.

With the proposed scale, the scientist only has to place the probe in melting snow for the zero point and under his tongue for the 100 deg point to calibrate the equipment approximately.

Then there is the application for environmental applications, specifically comfort temperatures. 54 deg would equal 68 exactly (numeric requirement).[BTW 54 X 0=0]. However the physiology of human and animal comfort is a science in itself. Actually "comfort" is a misnomer except at resorts, HVAC is more a matter of worker productivity in factories and offices.

Referencing body core temperature to skin surface temperature to air temperature is a significant concept. However heat transfer and humidity complicates the equation.... think wind chill factors and humidex.

The conversion factor of 1.5 X F is accurate (exactly) for Change in Temperature, i,e, "delta T", not the scale temperatures. However your conversion algorithm is correct - flattered by the use of the "P" symbol... thanks!

This exchange of criticisms displays the other feature of the scale...... that of an academic teaching device. Asking the students to propose their own scale, or other system to measure paremeters is clever exercise in itself for the serious science students.

Thnks,

Peter

(aka) Pete318 (talk) 20:18, 6 January 2010 (UTC)

maximum limit of temperature?

Is there any theoretical maximum limit of temperature? Say due to relativistic limit on speed of particles? manya (talk) 05:28, 1 September 2008 (UTC)

No, temperature is proportional to energy per particle and there is no limit on the energy a particle can have. Dragons flight (talk) 06:15, 1 September 2008 (UTC)

That's a good question, and, AFAICT, the article doesn't really answer it. There is a brief mention of "infinite temperature" in the summary section on Temperature#Negative temperature that cites Kittel & Kroemer, but that section is buried in the middle of the article. ISTM, the lead could say something about the limits of temperature. BTW, Zemansky's Temperatures Very Low and Very High has a chapter called Beyond Infinity to Negative Temperatures. --Jtir (talk) 20:19, 3 September 2008 (UTC)

• Yes, there is a theoretical maximum limit of temperature. It is the Planck temperature, which is 1.41679(11)×10³² K. Greg L (talk) 22:06, 4 September 2008 (UTC)
  • No, that's a temperature at which existing physics ceases to make sense. Like Planck length, Planck time, etc. it is not at all clear if those measures are fundemental limits or merely limits beyond which our existing physical understanding is inadequate to probe. In each case a theory of quantum gravity is necessary to describe phenomena under those conditions. Dragons flight (talk) 22:11, 4 September 2008 (UTC)

• Your argument splits hairs a bit too finely and is almost one of those “classic and theoretical physics isn’t good enough for me”-answers. The Planck temperature is the closest known thing there is to a “theoretical maximum limit of temperature” and is considered to be the temperature of the Universe during the first instant (the first unit of Planck time) of the Big Bang. If that isn’t the maximum possible temperature, I don’t know what is. If you don’t think the Plank temperature is a theoretical maximum limit on temperature, tell us, what is? Greg L (talk) 02:21, 5 September 2008 (UTC)

Thank-you both for your informative comments. It sounds like you agree that the Planck temperature is a theoretical limit, which is what the original question asked for. Could either of you cite a reliable source on this limit? Planck temperature cites a web site; it would be better to cite a physics book. --Jtir (talk) 19:58, 5 September 2008 (UTC)

definition of temperature scale

The article states that the triple point of water is 273.16 degrees Kelvin. This is an obvious clerical error. I have a newly established account on wikipedia and have not yet learned how to fix such things. I hope someone more knowledgeable than I will do it. Georgeisomorphism (talk) 00:58, 10 January 2009 (UTC)

Um, I believe 273.16 K is correct. Dragons flight (talk) 01:19, 10 January 2009 (UTC)

Yes, thank you, 273.16 K is correct. I am a double idiot. Firstly, I misread the article which does correctly state "273.16" K. Secondly, when I typed my comments, I typed 273.16 rather than what I thought I had seen. Pleae forgive me. If I ever summon the courage to make another comment on a wikipedia article, I will try to be more careful.Georgeisomorphism (talk) 01:25, 7 February 2009 (UTC)

Rankine Scale does not have a degree sign

The Rankine scale does not need a degree sign before R as it is listed in this section as °R This is because it is an absolute temperature scale like the Kelvin scale. This error is replicated in all the temperature scale pages in the temperature converstion graph

Temperature temperature conversion formulae

	from Temperature	to Temperature
Celsius	x K ≘ (x − 273.15) °C	x °C ≘ (x + 273.15) K
Fahrenheit	x K ≘ (x × ⁠9/5⁠ − 459.67) °F	x °F ≘ (x + 459.67) × ⁠5/9⁠ K
Rankine	x K ≘ x × ⁠9/5⁠ °R	x °R ≘ x × ⁠5/9⁠ K
For temperature intervals rather than specific temperatures, 1 K = 1 °C = ⁠9/5⁠ °F = ⁠9/5⁠ °R Conversion between temperature scales

Would someone please correct this. I do not have the ability to edit this article with my account.

Mrjoebob (talk) 01:36, 9 March 2009 (UTC)

I'd like to see a reference for this one way or the other. The discussion at Talk:Rankine scale seems to suggest that even though it is an absolute scale, that nonetheless the degree sign is used more often than not. If there is a "right" and "wrong" way to write this, I would like to know "according to whom" and whether or not there is a reliable convention here? Dragons flight (talk) 01:45, 9 March 2009 (UTC)

Confusing Carnot Equation

In the section "Phenomenological definition based on second law of thermodynamics," the article states

"Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T1 and T3 must have the same efficiency as one consisting of two cycles, one between T1 and T2, and the second between T2 and T3. This can only be the case if:"

   q_{13} = \frac{q_1}{o_7}

The equation q13 = q1 / o7 seems confusing to me because I don't think that the variable o has been defined in this article (I could have just overlooked it, of course.) It seems that this equation may have a typo, or at the least requires additional explanation. Also, I'm not an expert in thermodynamics by any means, but I have never heard of a variable "o" being used in a thermo equation. WilliamJenkins09 (talk) 13:24, 29 November 2009 (UTC)

Rigorous definition of temperature

This section was introduced without any links [3] and it claims "The definition of temperature in modern physics is the other way around". Given the completely weird definition of heat in Wikipedia I think a link to the variety of modern physics the editor has in mind is vitally important to avoid confusion in this section. --Damorbel (talk) 21:08, 29 November 2009 (UTC)

What I wrote can be found in e.g. the book Fundamentals of Statistical and Thermal Physics by F. Reif, i.m.o., the best book on this subject. The point is that entropy can be defined in terms of the fundamental properties oif the system. If you have some gas in a container, then the fndamental laws of physics fix the states the system can be in. Entropy is proportional to the logartihm of this number of states. Temperature is then the derivative of the entropy w.r.t. the internal energy taken at constant volume (and whatever other external parameters the system has).

Work is by definition any transfer of energy from one system to another system as a result of a change in external parameters. Heat is by definition transfer of energy that happens in any other way.

You have to consider that such definitions have to be applicable to completely arbitrary systems or to familiar systems for which you consider doing something completely unusual. E.g. the volume of a system does not need to be the only external parameter. In principle you can consider a system that has trillions of independent external degrees of freedoms. In that case any change in internal energy as a result of changing any of these parameters counts as work. But if you cannot control any of these parameters, then these external parameters will be subject to thermal fluctuations. Energy transfer that happens via these parameters would then be heat transfer. Count Iblis (talk) 22:22, 29 November 2009 (UTC)

I've renamed the section to the "Definition of temperature in Statistical mechanics". --Dc987 (talk) 23:04, 1 December 2009 (UTC)

Introduction

The opening statement "In physics, temperature is the average energy in each degree of freedom of the particles in a thermodynamic system" is complete nonsense, if it were true temperature would be measured in Joules, not K.--Damorbel (talk) 15:25, 7 January 2010 (UTC)

Absolutely right. I have changed the introduction to not only reflect this, but also to state that the scientific definition of temperature is in the realm of thermodynamics, not statistical physics. It was defined by Lord Kelvin, before the advent of statistical physics. Statistical physics provides an explanation and a deeper understanding of temperature rather than a definition. I'm just worried that the introduction now sounds too technical in the beginning. PAR (talk) 16:45, 7 January 2010 (UTC)

Thanks for your rapid response. I now have second thoughts about the nonsense bit and I am looking at your revision with a great deal of interest. --Damorbel (talk) 20:17, 7 January 2010 (UTC)

Mean temperature

Some climate denialists are oposed to the very notion of mean temperature.

The idea was advanced by Christopher Essex, Ross McKitrick, and Bjarne Andresen in February 2007 issue of the Journal of Non-Equilibrium Thermodynamics: http://www.uoguelph.ca/%7Ermckitri/research/globaltemp/GlobTemp.JNET.pdf

It appears the paper ( and the idea) don't have any merit:

http://www.realclimate.org/index.php/archives/2007/03/does-a-global-temperature-exist/

http://rabett.blogspot.com/2007/03/once-more-dear-prof.html

http://scienceblogs.com/deltoid/2004/05/mckitrick3.php —Preceding unsigned comment added by Mihaiam (talk • contribs) 18:04, 10 May 2010 (UTC)

"Some climate denialists are oposed to the very notion of mean temperature." Mihaiam, you are in the wrong place. Read what it says at the beginning of the article -->

This article is about the thermodynamic property. For other uses, see Temperature (disambiguation). Temperature is an intensive thermodynamic property, meaning it is localised i.e cannot be averaged, (see Intensive and extensive properties). Please refrain from using terms like denialist which may be considered abusive. --Damorbel (talk) 18:40, 10 May 2010 (UTC)

I wasn't trying to be abusive, just framing the context generating the humorous idea that a mean temperature cannot be defined or even useful. On the contrary, intensive thermodynamic properties are often averaged, at least for practical purposes, the above paper notwithstanding. —Preceding unsigned comment added by Mihaiam (talk • contribs) 20:10, 10 May 2010 (UTC)

"intensive thermodynamic properties are often averaged" Before making remarks like that you should read the link I gave you. You clearly do not understand what is involved. You can see examples of intensive properties in the article here [4] If you try to make an 'average' temperature you have to put it in another, perhaps climate related, place.

In thermodynamics e.g. this article, if there is a need for something like 'an average temperature' it means that there is disequilibrium of some sort i.e. the temperature is not uniform, the entropy is not at a maximum and there will be energy flow of some sort. As I have pointed out before, the 'Greenhouse Effect' requires heat transfer from a cold troposphere to an Earth's surface that is already many degrees warmer. This is a massive breach of the 2nd law of thermodynamics which says that heat always flows from a hot place (the Eath's surface) to a cold place (the troposphere). Claims for heat to go against a thermal gradent are the 'business' of perpetual motion inventors.

What do you mean by 'practical purposes?', This article should be about the well established science of thermodynamics. I have the strong impression you are not familiar with this branch of science, a rather difficult but extremely practical one.

Referring to other contributors as denialists means quite plainly you define their contribution as worthless, as you do here, this is clearly abuse. Please avoid these personal attacks. --Damorbel (talk) 21:09, 10 May 2010 (UTC)

Oh good grief, enough with the long words, try reading the article: Since thermodynamics deals entirely with macroscopic measurements, the thermodynamic definition of temperature, first stated by Lord Kelvin, is stated entirely in empirical, measurable variables - any *measurement* of temperature is inevitably an average, even if over a very short time and small region William M. Connolley (talk) 21:44, 10 May 2010 (UTC)

William, you are clearly right out of your depth. To grasp these matter properly you need to get a grip of kinetic theory and (preferably) statistical mechanics. Kinetic theory is the fundamental mechanism of heat in atoms and molecules, from there you will get a basic understanding of heat transport at atomic level. Without this you are totally lost when dealing with matters seemingly so simple as temperature. Sorry you find the words a problem, the concepts are far from obvious but quite essential for a competent analysis. You take a very strong line on climate matters, how this is possible when you appear to have only a passing aquaintance with thermal physics I do simply do not know.--Damorbel (talk) 11:40, 11 May 2010 (UTC)

I'll ignore the falacious appeals to expertise William M. Connolley (talk) 11:49, 11 May 2010 (UTC)

Then I'll explain. A mean temperature only exists in an ensemble of molecules when the average momentum of the molecules is the same, there is a characteristic Maxwell–Boltzmann distribution of velocities (or momenta for inhomogeneous ensembles). If an ensemble has a non-uniform average i.e. there is a (macroscopic) difference in averages between the various parts (aka a temperature difference) then the concept of an average temperature is inapplicable. For a start the condition is unstable because heat will transfer from the warmer part to the cooler. The effect on the temperatures of this transfer cannot be predicted without detail knowledge of the thermal properties of the various parts so, in this case, any figure given as 'an average temperature' is meaningless. The misunderstanding that commonly arises comes with thermometry, for practical reasons molecular temperatures are not measurable so thermometers measure a 'bulk' temperature which averages and cannot readily detect small temperature differences; that does not mean that the concept of temperature does not extend to the microscopic level. It is similar with infrared thermometers, a mottled infrared image will always create some kind of 'temperature' reading that may be satisfactory for some purposes but scientifically it is probably worthless. --Damorbel (talk) 13:12, 11 May 2010 (UTC)

Damorbel is right in the sense that a system that is not in thermal equilibrium but which consists of parts that are (to a good approximation) in thermal equilibrium at different temperatures, is not equivalent to a system in thermal equilibrium at some average temperature. But this (well known) issue has been abused by some people to argue against Global Warming. If we want to mention something about this, I propose we stick to the relevant physics. E.g. one can mention that temperature gradients give rise to transport phenomena (heat conduction etc.). You can then delve deeper and explain that this means that a gas that is in dynamical equilibrium where you maintain a temperature gradient cannot be described by a velocity distribution function obtained by inserting the local position dependent "temperature" in the Maxwell distribution. It is in fact the deviation from this that gives rise to the heat transport. So, in a sense this can be taken to mean that even the concept of a local thermal equilibrium breaks down.

Now, we actually all use this fact when solving heat conduction problems. We don't have to bother about the fact that the local speed distribution is not precisely Maxwellian; you only need to consider that if you also want to compute the heat conduction coefficient from first principles. But you can just as well take the heat conduction coefficient as a given and then the local state at some point is specified by a local temperature, albeit that the distribution is not Maxwellian at the local temperature. But the point is that whatever it is, is now implicitely fixed.

This fact makes it possible to do thermodymnamics in practice where things are not in thermal equilibrium. You can make models of the Earth's atmosphere and describe the time evolution using differential equations. Those equations contain transport coefficients like the viscosity, heat conduction coeffienct etc. etc. Such a description arises precisely from a perturbation away from exact global thermal equilibrium and is valid if you are close to global thermal equilibrium. But here "close" means that the deviations from the Maxwell distribution is not large. This will only break down in extremely violent processes, certainly not when you model the Earth's atmoposhere. Count Iblis (talk) 14:56, 11 May 2010 (UTC)

A recent edit by User:89.43.152.15 restored the global temperature map with the remark that the consensus in this thread is "clear enough". I see no statement here that says "okay, let's put in the temperature map". I thank Count Iblis for his/her insightful remarks, but I don't see how they address the issue of whether to have the map.

My opinion is this: Temperature is a very fundamental property. To explain it, we should stick to simple, tangible examples. The planet Earth is arguably as far from this ideal as we could get. It would be like discussing childhood obesity in the mass article; it's an important topic, but it doesn't belong. The map does not add to the article. The text makes no reference to it. It is clutter that can be removed with no negative impact. Spiel496 (talk) 18:58, 12 May 2010 (UTC)

I disagree with your argument, but at least it is plausible. The original argument (this article can't talk about average temepratures) clearly wasn't plausible William M. Connolley (talk) 19:09, 12 May 2010 (UTC)

I disagree too. If we want to stick to a narrow and simple treatment we should remove the vacuum and negative temperature paragraphs, too, as they are neither fundamental or tangible. The map is illustrative about temperature use in other sciences, the scope of the respective paragraph.

The very reason given for the initial removal of the map (the alleged inappropriate use of the term in most natural sciences) is an example of its importance in this article, as it is universally used nevertheless (with credible scientific motivation IMHO).

I don't see a vote here for the removing of the map, either, user:79.113.7.217 removed it without even initiating a discussion, with a contentious reason. —Preceding unsigned comment added by Mihaiam (talk • contribs) 05:55, 14 May 2010 (UTC)

So, to paraphrase, I said "the Earth is too complex a system" and you said "then so is the vacuum". Earth---Vacuum; Everything---Nothing. They're practically opposites. I want to hear from a different editor on this matter, because I don't follow Mihaiam's logic. Spiel496 (talk) 19:27, 15 May 2010 (UTC)

There is no logic from mihaim. He has something with 'denialists', and his weapons are a web page and a couple of blogs against a published paper, ad hominem attacks (denialists, contentious reason = he's a telepath?) and apparently he didn't understand several clear replies abut averaging the temperature, which were given to him. As for me, I decided that I have no business with this page anymore. If the editors want to mislead people with that map, keep it here. You should also add maps on averaging intensive quantities on all pages describing them, to keep things consistent. —Preceding unsigned comment added by 79.113.2.40 (talk) 12:08, 20 May 2010 (UTC)

Mean temperature is a useful enough concept to appear in many published papers to this very day, as a quick search may reveal:

http://arxiv.org/find/all/1/all:+EXACT+mean_temperature/0/1/0/all/0/1 —Preceding unsigned comment added by Mihaiam (talk • contribs) 06:18, 21 May 2010 (UTC)

Thank you for proving once again my point. For your information, 'useful' in not a valid logical argument. Just because some statistical figure which isn't a thermodynamical value is used in a lot of papers, doesn't mean that it should be pushed into thermodynamics.

The presence of a map showing locations with different temperatures is only justified if it illustrates the confusion that can arise in a faulty thermodynamic analysis. The property "temperature" is quite independent of size. By assigning a temperature to a particular (macroscopic and larger) object, by definition all the parts of it must have the same temperature. In the case of a gas Maxwell and Boltzmann recognised that the heat transmission process described by kinetic theory meant that the particles comprising a mass of gas (i.e. at the macrosopic level) meant that the various particles of gas (microscopic level) had different (translational) kinetic energies, even at the "degree of freedom" level. What they did was to show that, when there was thermal equilibrium (no heat transport taking place at the macroscopic level) the distribution of the microscopic energies i.e. the energies of the individual particles, followed a statistical distribution now called the Maxwell-Boltzmann distribution; it is these statistics that connect the definition of temperature at the atomic level with the bulk temperature measured by a themometer.

But this is as far as you can go when assigning a temperature to a multiplicity of locations. When assigning an average temperature to a large object (it doesn't have to be as big as a planet!), not in thermal equilibrium i.e. has parts definitely at different temperatures with heat transport taking place between them according to the 2nd Law, any figure produced will be meaningless. What actually happens when defining an "average temperature" this way is that the temperatures of the different parts are added together in an undefined way, perhaps to give a publishable figure. It is fairly easy to understand why this is unreliable; should the measure be made using infrared radiation then two locations with the same temperature but differing emissivities will appear to have quite different temperatures. A good example is data for the Sun, its temperature is often given to four figures by measuring its radiance. But as seen from the Earth its surface is far from uniformly bright (because of limb darkening) and its spectrum is only vaguely black body, all of which makes nonsense of four figure accuracy for the actual temperature. --Damorbel (talk) 09:47, 21 May 2010 (UTC)

Somewhat imprecise don't mean useless. In many cases it's useful to define a baseline (however imprecise) in order to study the evolution of a system. —Preceding unsigned comment added by Mihaiam (talk • contribs) 11:38, 21 May 2010 (UTC)

Overview section overhaul

I've looked at this page for the first time today and the Overview section is in need of a major overhaul. The first sentence wasn't even complete. When I looked through the history to see what was deleted I noticed that much of the information in there is incoherent and/or incorrect. I will change a few things today to fix the incomplete sentences and I will hopefully revisit this page to give it some help. What do other people think? What should be in the Overview section anyway? The stuff that is currently in there isn't really an overview of anything? Should it just be deleted? Sirsparksalot (talk) 00:39, 13 May 2010 (UTC)

Contradiction

The following is a quotation from Temperature of vacuum "If a thermometer orbiting the Earth is exposed to sunlight, then it equilibrates at the temperature at which power received by the thermometer from the Sun is exactly equal to the power radiated away by thermal radiation of the thermometer. For a black body this equilibrium temperature is about 281 K (+8 °C)." This is correct but the "black body" reservation is misleading because the equilibrium temperature is in fact independent of the optical properties of the body.

The contribution goes on to say "Since Earth has an albedo of 30%, average temperature as seen from space is lower than for a black body, 254 K, while the surface temperature is considerably higher due to the greenhouse effect." Introducing temperature as a function of the reflected radiation (the albedo) is a contradiction since the first quoted statement makes no reference to the reflectivity of the thermometer. The first quotation remains correct because, in these conditions (no other sources or sinks of thermal energy) the absorption and emission of radiation equilibrate at the same temperature for all materials, independent of their reflectivity and transparency.--Damorbel (talk) 08:20, 21 May 2010 (UTC)

I'm afraid the equilibrium temperature actually depends on the optical properties of the body, being lower for bodies with high reflectivity (or transparency for that matter). —Preceding unsigned comment added by Mihaiam (talk • contribs) 09:50, 21 May 2010 (UTC)

"I'm afraid the equilibrium temperature actually depends on the optical properties" Care to justify this? It's a popular fallacy stated many many times but that doesn't make it true. I take it you mean the temperature in a thermal radiation field.

Tell me what would be the temperature of a 1m spinning ball plated so that it reflected 99% of the incident radiation, same orbit as Earth but far away?--Damorbel (talk) 10:49, 21 May 2010 (UTC)

Giving some simplifying assumptions, I'll say about 89K —Preceding unsigned comment added by Mihaiam (talk • contribs) 11:19, 21 May 2010 (UTC)

89K? Ok. Now if you changed one half to carbon black (emissivity 0.99) the black side would, I imagine, be about 190K warmer, giving you a nice thermal gradient which could be used for generating electricity, maybe 500W/m²? Which, when scaled up a bit and sent to Earth, could save the planet from AGW. Cheers! (You can patent it too!)

PS Nearly as good as cold fusion! --Damorbel (talk) 12:06, 21 May 2010 (UTC)

And your point is .... ?--Mihaiam (talk) 18:41, 21 May 2010 (UTC)

Haven't you noticed my point? If your idea that the equilibrium temperature is dependent on reflectivity etc. was true you could be getting energy from nothing, you would have a perpetual motion scheme (or scam). The sad truth is, equilibrium temperature of any object in a uniform radiation field is independent of its reflectivity, its colour or its transparency. History is full of such perpetual motion schemes to "get energy from nothing". Pons and Fleischman's cold fusion scam is ever so slightly different in that they just had no way to get the energy output to exceed the input. --Damorbel (talk) 19:33, 21 May 2010 (UTC)

The reflectivity simply don't play a role in all this. It just reduce the amount of incident radiation to be absorbed by the body. You do have a cold sink as the body will radiate according to Stefan–Boltzmann law. —Preceding unsigned comment added by Mihaiam (talk • contribs) 19:56, 21 May 2010 (UTC)

You have to make your mind up. A while ago you wrote about body with an albedo (reflectivity) of 99% having an equilibrium temperature of 89K, that is the role I am talking about. You refer to the Stefan-Boltzmann law, fair enough, but a body that reflects 99% of the incident radiation has an emissivity of 1%, what emissivity did you use in your calculation? --Damorbel (talk) 20:09, 21 May 2010 (UTC)

You are right if the emissivity of the object is the same at all wavelengths (gray body). One of the assumption I've made is that the object have a reflectivity of 99% for the solar spectrum (UV, visible and near infrared), but 0% in far infrared. Although not really warranted from your premises, this assumption does not contradict them since you only specified the reflection for incident solar radiation (albedo). As it happens, most materials exhibit low infrared reflectivity:

http://minerals.gps.caltech.edu/FILES/Infrared_Reflectance/index.htm FWIW, albedo is a more specific form of reflectivity, over the incident light wavelengths —Preceding unsigned comment added by Mihaiam (talk • contribs) 23:26, 21 May 2010 (UTC)

Equilibrium temperature in a way does have to do with reflectivity and in a much more meaningful way does not. As described I gather that while Equilibrium temperature can appear to be AFFECTED by reflectivity of various energies, it is however not a FUNCTION of reflectivity. In improper testing of material which does not take into account reflectivity properties of the material used in the experiment the equilibrium temperature of the material would appear higher than in actuality.

IE, Equilibrium temperature is the POINT at which the energy absorbed by the material is exactly equal to the energy released by he material. However a material may reflect a certain percentage of energy, never absorbing it in the first place, thereby artificially inflating the equilibrium temperature in improper observations.

However the equilibrium temperature is actually the point at which the energy ABSORBED it the same as the energy RELEASED by the substance, so you can subtract the amount of radiation REFLECTED as irrelevant to the equation.

That is NOT to say that a material which is reflective will not have to have more energy expended to reach the equilibrium temperature, or to say that an object cannot be higher or lower than it's equilibrium temperature.