Talk:Temperature/Archive 4

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What's wrong in the opening section.

1/ Opening paragraph - replace 'warm' with 'warmer' & 'hot' with 'hotter' (temperature is relative (2nd Law))

2/ 2nd paragraph has nothing to do with temperature per se and everything to do with a thermometer, i.e. how to measure it. To clarify, temperature as a measure of the concentration of thermal energy, temperature exists independently of however many systems are defined by the observer!

3/ 3rd (see 2/ above) should indicate very clearly that scales of temperature are there purely for the convenience of the observer and can be defined in any convenient way.

4/ 4th paragraph has no place in an introduction. Cleaned up, it might have a place under a section called 'History' which is yet to be written!

5/ 5th para. is completely confused, e.g. the first phrase "Microscopically, temperature determines the statistical distribution and the mean value of energy of motion" - not remotely true, check Maxwell-Boltzmann statistics or Maxwell-Boltzmann distribution (why on earth are there two articles for this in Wikipedia?) Microsopicaly means 'at the smallest possible subdivision', which is a 'degree of freedom' in this instance.

6/ 6th para. Much the same as the 5th. It refers to Thermal energy which redirects to Internal energy which opens with "internal energy is the total energy contained by a thermodynamic system" together with a reference to an article on chemical energy [1] which says (usefully) "the fundamental equation for the internal energy may involve terms for chemical work, gravitational work, work of electric transport, elongation work, surface work, work of electric and magnetic polarization, and other kinds of work. (p2, 1st para)

Intuitively thermal energy should be related to temperature and not internal energy, so it should it include the internal energy contained in the vibrations and rotations of complex molecules? These 'internal energy stores' only serve to increase the energy needed to raise the molecules temperature. Much the same can be said of latent heat which is (mostly) the potential energy due to intermolecular forces. Since 'latent heat' is a form of potential energy, temperature is not a function of the energy decribed by the term 'latent heat'. The 6th paragraph should infact be completely revised since when refering to liquids and solids it doesn't do anything to explain the relationship between the energy contained in particle momentum of a gas and that in the resonating harmonic structures in liquids and solids.

7/ The 7th is quite mistaken, it should say "differences in temperature are the driving force for energy transfer" (NB not 'thermal energy' because that would needlessly imply a temperature change), that is what the 2nd Law is all about, since temperature is the measure of thermal energy density i.e. Joules per degree of freedom. Of course thermal energy does not include latent heat, chemical bond energy etc. etc. --Damorbel (talk) 11:28, 3 November 2010 (UTC)

Differences in temperature are the driving force for entropy transfer. Each pair in the fundamental equation dU=TdS-PdV+μdN consists of a driving force which is intensive (P, T, μ) and the extensive variable being driven (V, S, and N, respectively). In other words, pressure differences drive volume changes, temperature differences drive entropy changes, chemical potential differences drives the change in the number of particles. Each pair contributes to the change in internal energy U. I suppose you could say that the intensive variable drives the energy change for the energy term in which it is involved. You might be able to say that pressure differences drive the work energy change, temperature differences drive the heat (or thermal) energy change and chemical potential differences drive the energy change due to the change in the number of particles. PAR (talk) 20:44, 3 November 2010 (UTC)

Yes, entropy transfer also. But entropy is a macroscopic concept which may be introduced later if thought necessary, as Spiel496 points out below, the article should be as simple as reasonable. Entropy is far from simple, it is not normally considered in absolute terms, generally it is dS, the change in entropy that is of concern to avoid the difficulty of handling absolute entropy. Change in entropy corresponds very well with energy transfer from hot to cold, entropy is best left to another article, don't you think? --Damorbel (talk) 21:48, 3 November 2010 (UTC)

Yes. I don't think there should be a big problem with saying that temperature difference drives the transfer of heat energy. Saying that it is the driving force for energy transfer is not good, though. The idea that each pair of terms in the fundamental equation corresponds to a "force" and a "displacement" is taken from mechanics where dE=F dx, dE being energy increment, F being force, dx being displacement. That neat correspondence will be lost. PAR (talk) 03:04, 4 November 2010 (UTC)

Yes, 'force' is not the appropriate term, the term is used in para. 7, I should not have used it. What about 'parameter'? Para. 7 also refers to 'heat flow', I've mentioned 'heat flow' before. The concept of 'heat flow' has its origins in phlogiston and caloric, 'heat flow' lost out to the conservation of energy in the first half of the 19th C. 'Flowing' in thermodynamics is still valid for fluids e.g. convection etc. I make no claim to have discovered all the inconsistencies in this article, nor to perfection in my own contributions! --Damorbel (talk) 09:30, 4 November 2010 (UTC)

The statement is very correct both scientifically and in common language. Temperature is one of the intensive generalized forces of thermodynamics, like voltage in E&M. Multiplied by its extensive conjugate yields energy change in form of heat, by which entropy is maximized towards equilibrium. Kbrose (talk) 02:35, 5 November 2010 (UTC)

Why in 5th paragraph "determines the distribution ... is not remotely true"?. It is not written "temperature alone determines", and may well be intended as "determines together with other system-dependent parameters" (degrees of freedom, density of states, in this case, but this is a lead, not an in-depth treatment). "Microscopically" does not mean "per degree of freedom", means "from the point of view of what are doing the molecules of a hot or cold object", and is contrapposed to "macroscopic", that is measuring a macroscopic system with a thermometer and making thermodinamic experiments. --GianniG46 (talk) 14:14, 3 November 2010 (UTC)

The distribution is calculated on the basis that it is random or more precisely, a normal distribution. The microscopic properties are the properties of the individual particles, when considering a number of freely interacting particles, because it is thought they are colliding randomly. The momentum (or velocity) of the various particles when there is a mass of them in the same volume (called an ensemble) take on different values, slow ones can get a kick that speeds them up, others slow down. The Maxwell-Boltzmann distribution assigns a probability density to the occurrence of particles with a particular velocity or momentum. The average energy of all the particles in the ensemble is equal to the total energy of all its particles, the total energy is proportional to the temperature. Note that this is the explanation for a gas where the distance between energy exchanging collisions is large. For liquids and solids the energy exchange takes place via intermolecular forces that hold them (more or less) in place. --Damorbel (talk) 15:50, 3 November 2010 (UTC)

Regarding the 5th paragraph, the phrase "temperature determines the statistical distribution and the mean value of energy of motion" doesn't belong in the Lead regardless of whether it's true. It doesn't help me understand what temperature is. I can't imagine it means anything to a novice. Spiel496 (talk) 16:31, 3 November 2010 (UTC)

Couldn't agree with you more. I didn't want to say every thing should be thrown out, perhaps I should! With careful wording and a careful structure for the rest of the article it should be possible to let those that need to arrive at the deep end. Thermodynamics is not easy but simplifying the explanation to the point of being incorrect just doesn't help anybody.--Damorbel (talk) 17:49, 3 November 2010 (UTC)

Over Editing

Does anyone else feel that this article is being over edited? While it is absolutely, positively apparent that this article needs an extensive amount of work, continuously editing the article WITHOUT thorough discussion is leading the article into a downward spiral. Why are so many edits being made without having at least some sort of consensus among active editors? Can we please do something about this? Sirsparksalot (talk) 23:01, 3 November 2010 (UTC)

I agree that parts have gotten unreadable, but look at the bright side: the thousands of words on this Talk page reflect a lot of self-restraint by editors who could otherwise be hammering away at the article. I think our priority should be to build some consensus on a shorter, simplified Lead section. Once done, editors can just revert edits that complicate the Lead and try to keep the ultra-precise language down in the main body where it's appropriate. Spiel496 (talk) 13:27, 4 November 2010 (UTC)

Good - Lets pick one thing to fix, get consensus, and fix it. Then go to the next. I think the first thing to fix is the intro. I think the paragraph about the zeroth law is too technical and should be moved to a more theoretical section. Any other fixes? PAR (talk) 06:31, 9 November 2010 (UTC)

No, it is not too technical, it is a quite general presentation without much technical detail and it covers, as an overview, aspects of temperature in all the thermodynamic laws which many people are familiar with if only by name. The lead should reflect the state of science and not just trivialize the presentation. That overview discussion logically sets the stage of everything else. The reason for you to want to remove it is your misconceived point of view of the role of the 0th law. The lead should not be trivial, but useful also to readers that desire more and it should challenge a reader and not just confirm what they likely already know. Otherwise you might want to visit the simple English WP. The main body of the article now needs to start to address these relationship more usefully. Kbrose (talk) 18:16, 9 November 2010 (UTC)

A second fix in the lead should be to explain that thermal energy means movement of molecules, otherwise temperature and thermal energy remain formal things: intensive, can be transferred, but which phenomena they describe, apart from hot and cold? --GianniG46 (talk) 16:58, 9 November 2010 (UTC)

Agreed. The lead needs to consist of tangible concepts like this one. Please, no one remove the temperature<-->movement connection without providing a really convincing argument that it is incorrect or misleading. Spiel496 (talk) 17:11, 9 November 2010 (UTC)

While the relation to kinetic energy paints a simple and pretty picture, and it certainly is the correct one for gases of trivial composition, even for particle ensembles like the ideal electron gas, in condensed matter and extreme temperature regimes the view becomes quickly very murky using classical pictures. Modern statistical thermodynamics looks at almost everything as ensembles of appropriate microstates with bound or unbound discrete energies, of harmonic and anharmonic oscillators, all formulated through the partition function and the density of states, where that classical picture of motion is not so intuitive anymore. The picture however is good for simple treatments. I used the discussion on the basis of thermal energy first because it is more general, as thermal energy description is primarily based on the general equivalence of energy and temperature, E=T/2, partitioned into any kind of quadratic degree of freedom accessible in a system. But in retrospect, mentioning kinetic energy in the lead is good, because it's what people may come to expect. Kbrose (talk) 18:16, 9 November 2010 (UTC)

OK for "particles" instead of molecules. But I believe that, at least in the lead, one cannot discuss the properties of thermal energy without first explaining what is it. Also, I do not understand why you say that kinetic energy "is good for simple treatments". The relation temperature-kinetic energy is essential, not limited to simple cases. Oscillations, rotations, translations, all are kinetic energy, and, also in the quantum case, for any available energy level the factor exp(-E/kT) holds (even for a fermion or boson assembly). In simple cases (e.g. for translational motion, which in sizable volumes has no quantization) we have a direct proportionality temperature - average energy per degree of freedom; in other cases we have a more complex dependence deriving from a sum of exp(-E/kT) over some density of states, but it is always true that the temperature governs the distribution of kinetic energy. --GianniG46 (talk) 23:28, 9 November 2010 (UTC)

Certainly you are right about kinetic energy. I was not specific enough and should have used the phrase 'the mechanical model of kinetic energy' as that is usually the simple picture used in introductory texts. Kbrose (talk) 05:33, 10 November 2010 (UTC)

To get some simplicity, address the relationship between temperature and kinetic energy of the gas molecules and liquid molecules of water in a pressure cooker on a stove top at 212 degrees F. The temperature is the same while the kinetic energy of the gas molecules is much more. Isn't temperature the intensity of the energy and not the amount of energy? Geweber (talk) 04:42, 25 January 2011 (UTC)

I don't think that the 'intensity' of energy can be defined. Intensity implies a flux of some sorts. Since temperature is only defined at equilibrium, the net flux of energy into and out of different parts of the system should be zero. As for the comment about it being the amount of energy, you raise a valid point as the temperature is inherently related not only to the amount but also the distribution of energy (entropy). Since this relationship is well addressed in the article I don't think it needs further refining. As for the pressure cooker analogy, I think that it would end up being a bit too complicated for this article. It would be riddled with semantic issues like to those that editors have struggled to eliminate from this page in the past. Sirsparksalot (talk) 17:45, 27 January 2011 (UTC)

"Since temperature is only defined at equilibrium". Not so, temperature is an intensive quantity which is the reason 'intensity' is appropriate noun for temperature. There is absolutely nothing wrong with a system having any number of temperatures; if it can be described as being in equilibrium it means that, thermodynamically speaking, nothing is happening, the temperature is uniform; it is - "The End"! Energy is an 'extensive' property meaning the quantity of energy is proportional to the volume of material present. Think of the 2nd Law, a system in disequilibrium means that there is a temperature difference betwen at least two places. It is better not to use 'flux' in thermodynamics, it harks back to the days when heat was seen as a fluid!

Incidently, the concept of an 'average temperature' is also dangerous since it implies that different temperatures exist in different parts of the system that might otherwise be thought to be in equilibrium; so there can be no knowing just how far from equilibrium the system is. --Damorbel (talk) 19:08, 27 January 2011 (UTC)

I think what is meant by equilibrium is "local thermodynamic equilibrium" (LTE). In other words, you must first be able to define a volume element which contains enough particles so that the statistical fluctuations in temperature practically negligible compared to the temperature itself, and secondly, the temperature must be practically constant inside that volume element. In this sense, temperature is only defined at LTE. Other volume elements can have other temperatures if they too are at LTE, and the whole system can be out of global equilibrium.

Total energy is extensive, energy density is intensive. If anything defines energy intensity it is the energy density. The relationship between energy density and temperature is given by the specific heat, and specific heat is not constant, so, no, temperature is not a measure of the intensity of energy. PAR (talk) 20:14, 27 January 2011 (UTC)

It is not possible to define temperature without reference to the Boltzmann constant. The Boltzmann constant does not need a volume element in that it is the energy in a vibrational mode, as it says in the wiki article "The Boltzmann constant (k or k_B) is the physical constant relating energy at the individual particle level" I think that is plain enough, I also think it also fits the definition at the microscopic i.e. atomic level which why it is an intensive property. Because the practical world does not easily interface with the microscopic world of atomic oscillators it is necessary to have a definition of temperature that works at the macroscopic i.e. measurable-by-a-thermometer bulk or volume level; so temperature is also defined for an ensemble of particles having a Maxwell–Boltzmann velocity distribution. Such a velocity distribution gives the particles an average energy equal to the temperature of one particle having the average temperature; so it is the M-B distribution that makes the link between the Boltzmann constant and the average temperature of bulk (ensemble) particles. In the Boltzmann constant article you will find that the Boltzmann constant is further defined at the bulk level of one mole since, on the third line it gives the Boltzmann constant k_B = R/N_A where N_A is Avogadro's number, the number of particles in a mole. --Damorbel (talk) 21:21, 27 January 2011 (UTC)

This is not correct. Temperature is defined in classical thermodynamics, which was developed before Boltzmann, and therefore contains no reference to the Boltzmann constant. Temperature is explained, but not defined in statistical mechanics. Classical thermodynamics is a macroscopic theory therefore temperature is a macroscopic concept. Classical thermodynamics relates the temperature to the internal energy via the heat capacity, another macroscopic concept. What Boltzmann did (among other things) was to relate macroscopic temperature to the microscopic energy, thereby giving insight into the statistical basis of temperature, internal energy, and the heat capacity. This is where the Boltzmann constant enters into the picture. It makes no sense to talk about the temperature of a single particle in a gas because it is colliding with other particles billions of times per second. The fluctuations in its "temperature" are huge and rapid, much larger than the thermodynamic temperature of the gas as a whole, and much more rapid than any macroscopic (i.e. thermodynamic) process which is going on at the time. Statistical mechanics is not about individual microscopic processes, it is about the statistics of many such processes and how they produce the macroscopic results of classical thermodynamics. PAR (talk) 22:44, 27 January 2011 (UTC)

I really do not find from your contribution how you can say "This is not correct". Up until the end of the 19th C the atomic theory of matter was not generally accepted, actually it was vigorously contested by a number of prominent scientists. Why does it 'make no sense to talk about the temperature of a single particle'? As for thermodynamics I pointed out that the gas constant R is the heat capacity of a mole of ideal gas. Since a mole comprises N_A particles (N_A is Avogadro's number), why is it a problem for the average energy of the particles to be k_B x T? If you accept this then each particle will have an energy (and thus a temperature defined by k_B) even though in any given volume, as you say, the particles will all have different energies (and thus temperatures) given by the Maxwell–Boltzmann velocity distribution, the effect of of this on a thermometer will be to give the average energy and thus an average temperature.

But, as I pointed out above (on 27 January 2011) the average can be dangerous concept. It is, or should be, a well known feature of quantum physics that it is the energy (temperature?) of the individual particles that has to reach a clearly defined threshold before a quantum effect takes place, this was Einstein's conclusion when he noted that electrons were only ejected from the surface of metals by light below a particular wavelength. A practical example of this is the troposphere which is heated by the absorption by O₂ of UV at 200nm and below, the Sun's output is (roughly) thermal at 5780K but it is only the UV that interacts with the O₂, thus it is clear that not all (perhaps very few) reactions are dependent on average particle energy (temperature) but on the actual energy of the individual particles. --Damorbel (talk) 06:59, 28 January 2011 (UTC)

The temperature is not just proportional to the average particle energy, it is proportional to the average particle energy of a volume in which there is equilibrium. If you define temperature as simply proportional to the average particle energy, then your thermodynamic equations will fail if the average is taken over a volume which is not equilibrated. To quote from the Wikipedia Thermodynamic equilibrium article:

If the description of the system requires variations in the intensive parameters that are too large, the very assumptions upon which the definitions of these intensive parameters are based will break down, and the system will be in neither global nor local equilibrium. For example, it takes a certain number of collisions for a particle to equilibrate to its surroundings. If the average distance it has moved during these collisions removes it from the neighborhood it is equilibrating to, it will never equilibrate, and there will be no LTE. Temperature is, by definition, proportional to the average internal energy of an equilibrated neighborhood. Since there is no equilibrated neighborhood, the concept of temperature breaks down, and the temperature becomes undefined.

As far as the mole is concerned, it is a classical thermodynamic concept, defined before the atomic theory of matter was decided. It added weight to the atomic theory, and further investigation revealed that it was in fact related to the number of particles in the system by Avogadro's number. Sure, I would never think of the mole as anything but Avogadro's number of particles, but I would not make the mistake of assuming that it requires the atomic theory for its definition. PAR (talk) 15:38, 28 January 2011 (UTC)

PAR, by putting your spaces all over the place you have reduced this discussion to incoherence. You appear to be convinced that concept of temperature is only applicable to a particular volume of material which you do not define, it would help if you could explain why. Other intensive properties such as density and pressure are not restricted this way, why should temperature?

Before you make more remarks on the Avogadro constant I suggest you read this: Avogadro constant history. You will see that the current value of this constant was not established until 1926, by which time the (modern) atomic theory was quite well established; it earned the finder a Nobel prize. --Damorbel (talk) 16:27, 28 January 2011 (UTC)

When a bullet is fired from a gun, it has a high kinetic energy. However, that kinetic energy has nothing to due with its temperature. Temperature is a measure of the average *random* kinetic energy, not a measure of the net kinetic energy. This is why it makes no sense to speak of the temperature of a single atom. If the atom travels through space and never hits another atom, then its kinetic energy is not temperature. However, if lots of atoms are hitting each other, then temperature is a measure of the average randomly directed kinetic energy.

Also, UV is absorbed in the stratosphere, not the troposphere. Q Science (talk) 16:49, 28 January 2011 (UTC)

"UV is absorbed in the troposphere" - Typo! Sorry.

Yes, and you have to be careful about bullets too. When a gun is fired the chemical energy is turned into heat in the combustion products, these expand and the bullet begins to move, taking random kinetic energy and converting it to linear momentum, giving the bullet linear, none-heat linear kinetic energy. A good example of this is the armour piercing discarding sabot projectile were a large proportion of the chemical energy in the propellant is transferred to a high density bolt which can penetrate armour efficiently. With such a projectile, if it hits well, its kinetic energy is converted back into heat by friction and the tank may be set on fire. The lesson of this tale is that energy can be converted from one form to another and back again. None of this detracts from the truth that, even when the molecules, atoms etc. are moving randomly they can be assigned a temperature; this is fully in agreement with the concept of a thermodynamic system where the system temperature in equilibrium is the average of a large number of temperatures (or energies) with a [[2]]Maxwell-Boltzmann distribution distribution of energies. If you insist on a statistical approach the probabilities of all possible distributions of energy are the same in a Maxwell-Boltzmann distribution, including the one where all particles have the average temperature; this condition may not last long but then neither will any other distribution. The temperature of a single particle is just as valid as the energy of a single particle, that is the whole meaning of the Boltzmann constant. --Damorbel (talk) 20:40, 28 January 2011 (UTC)

The volume I refer to is any volume element in which the concept of equilibrium can be defined. If you have a bunch of particles in a small volume they will have an average energy and there will be a statistical fluctuation in that average, from their interaction with other volume elements. If that statistical fluctuation is on the order of the average itself, or larger, you cannot have equilibrium. Generally, if you have an intensive parameter (including pressure and density) then you will have statistical fluctuations, and yes, even for pressure and density, if the statistical fluctuations are large compared to their average, then there will be no equilibrium: The pressure and density as used in thermodynamics, will not be well defined. Yes, you can define pressure as the time average of the force per unit area due to molecular collisions with some area element inside the volume, but if the volume is too small, there is no time interval that you can choose which will make the equations of thermodynamics work. Thats what I mean when I say pressure (or density, or temperature) are undefined.

To repeat, temperature is not just a measure of the average energy of the particles in some given volume, it is a measure of the average energy in an EQUILIBRATED volume. If you insist on defining the temperature in an unequilibrated volume to be a measure of the average energy, that temperature will not work in your thermodynamic equations. That's what I and everyone else means when we say that the temperature in this case is undefined.

Yes, Avogadro's number was established after the development of classical thermodynamics. That was my point - Classical thermodynamics defines the mole without reference to Avogadro's number, Avogadro's number is the result of the introduction of atomic theory to the understanding of thermodynamics. The fact that it was finally defined in 1926 and not in 1726 proves my point.

PS - I have fixed the indentation on the quote, hopefully restoring coherence. I will try to be more careful in the future. PAR (talk) 22:11, 28 January 2011 (UTC)

"If that statistical fluctuation is on the order of the average itself, or larger, you cannot have equilibrium", simply not true! That argument would reqquire some distributions to be excluded. I think what you have in mind is Brownian noise which is the noise made in an ensemble of gas particles at a given temperature.

None of this nullifies the need to accept that at the microscopic level a particle has a temperature because 'temperature' is energy density, right down to the microscopic level as well as the ensemble average which is what you refer to as an "EQUILIBRATED volume". Quantum interactions depend on this, you will have a lot of work to overcome the argument that quantum interactions are dependent on the particle energy not on the average energy which is what you are saying here: "temperature is not just a measure of the average energy of the particles in some given volume, it is a measure of the average energy in an EQUILIBRATED volume". This is not so because not all particles in a volume with distributed energies will have sufficient energy to produce a change at ANY energy level; you do not appear to take into account the Photoelectric effect which illustrates exactly why the individual particle must have sufficient energy (i.e. high enough temperature) if it is to make a quantum change. --Damorbel (talk) 07:16, 29 January 2011 (UTC)

"... some distributions to be excluded" - Yes, some will be excluded. A volume containing a 10^9 particles with zero energy and one particle with energy k*10^11 will not thermodynamically anywhere near the same as a volume element with a billion and one equilibrated particles at a temperature of 10^11/10^9=100 degrees. "because not all particles in a volume with distributed energies will have sufficient energy to produce a change at ANY energy level" - yes but those changes will not be described by thermodynamic equations involving temperature. "you do not appear to take into account the Photoelectric effect" - Please describe the photoelectric effect in terms of thermodynamic equations involving temperature. PAR (talk) 22:44, 29 January 2011 (UTC)

" A volume containing a 10^9 particles with zero energy and one.... will not thermodynamically anywhere near... one equilibrated particles at a temperature of 10^11/10^9=100 degrees" Of course not but the first volume is irrelevant for two reasons; 1/ it is not in equilibrium and 2/ it has much lower average energy than the 2nd vol. "Please describe the photoelectric effect... " In choosing coloured light to test the emission of electrons the photons do not have the thermal distribution of energies characteristic of black body radiation but a narrow selected energy range, Eistein concluded that because red coloured light, however bright, did not cause any electrons to be emitted; whereas quite dim green light cause the emission of electrons that it was the colour not the brightness that decided if electrons were emitted or not. Further, when illuminated with blue light the emitted electrons had more energy than those emitted by green light. --Damorbel (talk) 13:22, 30 January 2011 (UTC)

A "particle" may only have a temperature if it is made of more than one particle which themselves occupy an equilibrated volume. However, it is obviously not clear that particles which apparently are fundamental would contain particles within them which are equilibrated. (And good luck trying to propose new hidden particles!)Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 04:22, 30 January 2011 (UTC)

"If the atom travels through space and never hits another atom, then its kinetic energy is not temperature." I'm pretty certain that this is more than true. Fundamentally, temperature is a phenomenon related to forces between particles (again, plurality of particles is a requirement for temperature to exist!), which implies that acceleration has much to do with the origin of temperature. This can be seen in the Larmor formula for example. The power emitted by a charged particle varies with the square of the acceleration. All heat is produced in exactly the same way heat is produced in sources of light—deflection, scattering, absorption, and ejection of charged particles at the atomic scale. The forces that drive the production of conductive and radiative heat are of the same fundamental nature—electromagnetism. The only difference is whether matter is transparent to such heat (as is the case for radiation) or opaque to it (as is the case for conduction). Convection is an intermediate case where the matter, at some scale, is translucent to heat.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 02:17, 30 January 2011 (UTC)

Damorbel - ok, I made a mistake by a factor of maybe 3/2. Assume a monatomic ideal gas. The average energy of 10^9 particles with zero energy and one with energy k_B*10^11 will have an average energy of k_B*10^11/(1+10^9)=100k_B. (close enough). A volume element with 10^9 particles with a Maxwell distribution at 66.66 degrees will have average energy (3/2) 66.66 k_B = 100k_B: it's the same. Classical thermodynamics will only give correct results for the second case. Thermodynamic temperature, as defined by thermodynamics, always works in thermodynamic equations, therefore the temperature as you define it for the first case, will not, therefore your definition is not consistent with the definition of thermodynamic temperature. PAR (talk) 15:45, 30 January 2011 (UTC)

I think I misunderstood. However when you speak of (A volume element with) "The average energy of 10^9 particles with zero energy and one with energy k_B*10^11" and "A volume element with 10^9 particles with a Maxwell distribution at 66.66 degrees will have average energy (3/2) 66.66 k_B = 100k_B: it's the same." Yes, the average energy is the same but the first one is not in equilibrium and Maxwell-Boltzmann distribution doesn't apply, it has one particle at 10¹¹K and the rest ar 0K; this situation will not last long! When the energy is shared out with the Maxwell-Boltzmann distribution equilibrium has come about and the volume now has an equilibrium temperature; your case with one very hot particle is also very, very far from equilibrium. The "k_B*10^11" will be shared with the other particles in a fairly short time if it doesn't fuse with another first, it probably has enough energy to do this! (BTW you can do indexes (indices?) using the 3rd of the special'Advanced' character buttons above - A^{^} like 10¹¹)--Damorbel (talk) 17:43, 30 January 2011 (UTC)

And that is my point - Before the volume equilibrates, it's temperature will be undefined. After it equilibrates, its temperature will be defined. There are other cases in which a volume element never equilibrates. For a plasma in an electric field, it may be that the volume element large enough to contain enough particles to yield an equilibrium distribution will have a steep gradient in the average energy of the particles, rendering an equilibrium distribution (and therefore equilibrium itself) impossible. If you shrink the volume enough to have a more or less constant average energy, there won't be enough particles to establish an equilibrium distribution. In this case, temperature is not defined and will remain undefined.

"Before the volume equilibrates, it's temperature will be undefined" But you said that 10⁹ particles had zero energy i.e. 0K and 10⁰ particles (1) had 10¹¹k_B i.e.10¹¹K, thus there were two parts of your system, one at 0K and the other at 10¹¹K. You could easily change the 10¹¹k in one particle to 10⁴ x 10⁷k if you have 10⁴ particles instead of one, the initial energy is 10^-4 lower; if the 10⁴ particles have a Maxwell-Boltzmann distribution of energies theen it would be appropriate to assign a temperature to them; if they are not in equilibrium then it is not possible to assign a temperature to them, it is not possible to assign a temperature to a volume of particles until they are in equilibrium i.e. with a Maxwell-Boltzmann distribution of energy. One could go further let us think of 10¹¹k in one particles divided between two particles, it doesn't have to be 2x 5x10¹⁰; there is no law that says the energy is to be split equally, the total energy remains the same.--Damorbel (talk) 20:32, 30 January 2011 (UTC)

You are not addressing the problem. Assigning a temperature to a volume with 10^9 particles at zero energy, one at 10^11K as the average energy over k will not yield proper results when used in thermodynamic equations. PAR (talk) 21:03, 30 January 2011 (UTC)

"Assigning a temperature to a volume with 10^9 particles at zero energy, one at 10^11K as the average energy over k will not yield proper results when used in thermodynamic equations." Is it at all possible to get proper results with this? It seems to me that "your problem" assumes that the two sets of particles are mixed together in the same volume. Damorbel seems to not even care about "your problem". He thinks that such a system can be given a physical treatment. One would just have to define the borders around such particles to determine the thermodynamics. However, if they occupy pretty much the same space such that the borders cannot be formulated, then obviously he couldn't define separate areas of temperature, now could he?Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 21:33, 31 January 2011 (UTC)

Assigning a temperature... will not yield proper results." Sorry I do not understand your problem since, in the case of a volume, a temparature can only be assigned if the volume is in thermal equilibrium i.e. particle energies have a Maxwell-Boltzmann distribution. With a hypothetical system of 10⁹ + 1 particles with 10⁹ at 0k (i.e. zero energy) and one particle with 10¹¹k is very, very far from equilibrium, of course you cannot assign a temperature to it. Divide your system in two, put the 10⁹ zero energy particles in one system, its temperature is 0K, no problem; the other has one particle vibrating in three axes with 10¹¹k which, if I haven't made a mistake, is the same as 10¹¹K. Let us say that the high energy particle is inserted in the 0K system; ther will be an enormous disturbance be cause of the discrepancy of temperatures; let us say that the energy of the hot particles is redistributed thermally between the 10⁹ + 1 particles without any fusion reactions or the like; the result will be a Maxwell-Boltzmann distribution of energy among the 10⁹ + 1 particles so now it is perfectly valid to assign a temperature to the volume. --Damorbel (talk) 08:54, 31 January 2011 (UTC)

Obviously the before and after conditions are not even the same. The summary of the above is that you cannot assign a temperature to the whole when it is very far from equilibrium (just different temperatures for each imaginatively-separated equilibrated region), while you can assign a temperature to the whole after equilibrium is achieved. Why you people continue to argue despite agreeing is beyond me.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 21:45, 31 January 2011 (UTC)

You two seem to be both arguing that something does not work. So who is claiming that something works?Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 21:22, 31 January 2011 (UTC)

Right, we agree that a volume element must be in equilibrium for the concept of temperature to have meaning. I'm not sure we agree that a single particle or a few particles cannot have a temperature, because the fluctuations or deviations from Maxwell are large, of the order of the average energy or more. PAR (talk) 05:33, 1 February 2011 (UTC)

Could someone provide the mathematical relationship between 700nK temperature of cesium atoms and their velocity of 7mm per second in the NIST test in 1994 to reach a low temperature? My theory is that if temperature is a physical property like velocity is then temperature is related to the frequency of the vibration of the atoms/molecules. The velocity and frequency of the vibration of molecules as a gas in a confined container have a direct correlation. However, with liquid and gas of H2O in the same container the average velocity of the gas molecules is much greater than the average velocity of the molecules in the liquid yet they have the same temperature. Since the distance between molecules in the gas is much greater the frequency of the vibration of the molecules in the liquid and gas could be the same since the temperature is the same. Until you guys can explain why the temperature of the gas and liquid in the same container is equal while the energy is much different you are not explaining temperature where the lay person can understand it. This description of temperature in Wikipedia does nothing to help me.Geweber (talk) 18:13, 5 February 2011 (UTC)

Temperature is ultimately dependent on fundamental forces. If you have two substances touching each other, one at 100K, and another at 200K, it means that forces are directed from the substance of 200K to the one at 100K, moreso than the reverse. Here we are not talking about the physical flow of particles - just their vibration. It turns out that these vibrations will tend to dissipate energy over more mass than the originating source of that vibration. This reduces the frequency of those vibrations — per $E_{em}=N*h*f$. What force are we dealing with specifically? Of course, it is the electromagnetic force. We know it is not enough for particles to travel in a straight line to be "hot". They must continually run into things. Obviously, the more frequently this is done, then the hotter it gets. To prove that, just rub your hands together at different speeds to see how the results vary, and then compare that to waving your hands in the air. If atoms are constrained to a predefined volume element, then the velocity varies proportionally to frequency. Forces tend to increase with the square of the velocity at impact. However, this is true only up to a point. As you approach the speed of sound in a medium, then those forces will ramp up much faster than the square of the velocity. Then it would seem that even in a constrained volume, the relationship between the kinetic energy of particles and the forces between is no longer direct, provided that the temperature rise above a certain point.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 03:40, 6 February 2011 (UTC)

Kmarinas86, your description above makes no sense to me. I don't believe it would help the lay person to understand temperature. I doubt you have a reliable source for this material; it does not belong in the article. Spiel496 (talk) 15:58, 6 February 2011 (UTC)

I'm not suggesting that it be added to the article. You're right about there not being a reliable source for this information. Thermodynamics is usually taught without giving great emphasis to the fact that forces are responsible for the transfer of heat. Although it takes no Einstein to recognize that fact, the fact is usually never taught to students. In most cases, thermodynamics can be applied just fine without understanding how fundamental forces come into play. Instead we have PV-work, which seems to do the trick for most people. However, such an empirical treatment is devoid of any connection to fundamental forces, including electromagnetism.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 00:06, 7 February 2011 (UTC)

You make some interesting points. However, if you're not proposing content for this article, then it would probably be better to take the discussion to Geweber's talk page. Spiel496 (talk) 22:13, 7 February 2011 (UTC)

Does your two substances have to be touching. Doesn't this electromagnetic force travels through space? What creates this electromagnetic force and what determines the frequency? Will two objects placed in close proximity of each other with different atom/molecule frequency of vibration end in a steady state at the same atom/molecule frequency of vibration?Geweber (talk) 15:15, 6 February 2011 (UTC)

1) Range may vary, 2) Yes, 3) It's not "created", 4) Its frequency is the result of changing electric fields (the cause and effect of magnetic induction), 5) It may approach it, but it will never attain it exactly.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 00:06, 7 February 2011 (UTC)

You might find this interesting: Ising model.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 00:41, 7 February 2011 (UTC)

In response to Geweber's original question about the speed of Cs atoms, I feel the relationship between temperature and average velocity is handled pretty well in Temperature#Zeroth_law_of_thermodynamics:

$\displaystyle {\frac {1}{2}}mv_{rms}^{2}={\frac {3}{2}}kT.$

Perhaps this is buried too deep? Or it's too mathematical? And I don't know how many people know what rms means. Anyway, if I solve for v_rms with T = 700nK and (for Cs) m = 133g/mol *mol/6x10²³ I get about 11 mm/sec. (Not sure why the article says 7 mm/sec. Maybe it's just the rms of v_x.) Anyway, that's all there is to it for a monotonic ideal gas. The situation in liquids and solids is more complicated, but the above relationship remains roughly true between temperature and the average kinetic energy of the constituent particles. That's the layman's description the article should be giving. The article rightly says nothing about a relationship between temperature and vibrational frequencies. Spiel496 (talk) 18:01, 6 February 2011 (UTC)

Spiel496, thanks for the equation. I am surprised by your last sentence. The Overview section of the article is all about the relationship between temperature and vibration. I don’t know how you can say it is related to the vibration and not be related to the frequency of the vibration. Are you saying if you increase the molecular vibration you are not changing the frequency of the vibration? The graphic diagram of the vibrating protein alpha helix has the caption that the amplitude of the vibrations increases with temperature. Would this be true for a monatomic gas in a container? Since the average space between the atoms would not change with a temperature change would the distance of travel of the vibration change? Instead would not the frequency of vibration increase as the temperature increased?Geweber (talk) 13:51, 13 February 2011 (UTC)

Geweber, yes I am saying vibration frequency does not change with amplitude (or energy). This is really an issue of terminology. "Vibration" refers to the (periodic) oscillation exhibited by a mass on a spring or by a pendulum or by the atoms within a molecule, in which the restoring force is proportional to the displacement. By contrast, an atom of a gas experiences no force except when it occasionally bounces off another atom or the wall. Yes, the bounces happen more "frequently" as the temperature increases, but this type of motion is simply not referred to as "vibration"; it is "translation" with occasional collisions. And the frequency of the collisions would depend not only on temperature, but also on the number of atoms in the container. I'm too immersed in the standard terminology to make a judgement as to whether a change of wording is necessary to avoid this confusion. If you or others feel strongly, I suggest starting a new section on this page specifically for this issue. Hope this helped. Spiel496 (talk) 19:29, 13 February 2011 (UTC)

"the above relationship remains roughly true between temperature and the average kinetic energy of the constituent particles" Some people would prefer to have an undisputed general equation from which they would derive these said "rough" relationships. To not disclose this leaves a void for those who want a more fundamental look at what temperature is. Teaching "rough" relationships as fact, only to be relearned as applicable only for a majority of cases (assuming that's what "rough" means), is extremely dissatisfying to me.Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 00:06, 7 February 2011 (UTC)

Kmarinas86, what do you feel the article fails to disclose? In addition to the relationship between T and KE, it has the equation $T\equiv \left({\frac {\partial S}{\partial E}}\right)^{-1}$, which is true generally. Spiel496 (talk) 00:00, 8 February 2011 (UTC)

So basically that would mean that temperature is proportional to energy density and inversely proportional to the logarithm of the density of states. I wonder why it would be the logarithm....siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 04:08, 8 February 2011 (UTC)

Doesn’t this then mean that the temperature number is an empirical number and not a physical property? This first sentence of the Temperature article states it is a physical property. See where the confusion is. I am a mechanical engineer and have had to use many thermodynamic formulas so I can go along with temperature being an empirical number, but it feels like a physical property.Geweber (talk) 14:12, 7 February 2011 (UTC)

Theoretical foundations - first paragraph

Thermodynamics is a discipline separate from statistical mechanics and/or kinetic theory. To quote "Thermodynamics" by Enrico Fermi:

But the approach in pure thermodynamics is different. Here the fundamental laws are assumed as postulates based on experimental evidence and conclusions are drawn from them without entering into the kinetic mechanism of the pheonomena. This procedure has the advantage of being independent, to a great extent, of the simplifying assumptions that are often made in sttistical mechanical considerations.

To quote "Thermodynamics and and Introduction to Thermostatistics" by Callen:

...the amalgamation of thermodynamics and statistical mechanics runs counter to the "principle of theoretical economy".... Models, endemic to statistical mechanics, should be eschewed whenever the general method of macroscopic thermodynamics are sufficient.

Unless you can give references which state that statistical mechanics and/or the kinetic theory of gases is a sub-discipline of thermodynamics, please do not revert.

As for the Boltzmann constant, to state that it has meaning only in the SDI system of units is clearly wrong. It is a physical constant, much like the speed of light. The speed of light is not a numerical constant, the real number used to represent it changes depending on your system of units. The same is true of the Boltzmann constant. Unless you can give references which state that the Boltzmann constant has no meaning outside of the metric system of units, please do not revert. PAR (talk) 19:30, 9 November 2010 (UTC)

None of these statements exclude these descriptions from thermodynamics, different approaches do not make different fields. They simply are different descriptions of the same physics. You are simply overemphasizing unintended separation. The first quote of an outdated book by Fermi even distinguishes 'pure thermodynamics' since he acknowledges it as a part. The second reference talks of the 'amalgamation of TD and SM, acknowledging the same, only to point out that not always are the advanced description of SM necessary or desirable. The quotes do not support your claim. They all describe the same thing. To postulate differently is preposterous and against the practice in teaching and researching the field where it is used, whatever method is necessary to explain something without worrying about artificial boundaries of disciplines. The same is true for all the physical sciences where the traditional distinction between the fields of study are all floating or blurring. The only practical benefit from separating these fields is that each require different theoretical tool sets to learn. At today's level of understanding the science, it is impossible to separate QM or SM descriptions from understanding of thermodynamical systems. Today thermodynamics is the sum of all models, and the earliest description is now explicitly singled out as classical thermodynamics. Kbrose (talk) 20:42, 9 November 2010 (UTC)

As for the Boltzmann constant, it is only needed in the practical use of systems of measurement as historically developed. In pure physics, it is not needed, if you want to keep it, it's dimensionless unity, if it weren't for the need to convert to historical metric systems, it might not have been proposed for use and it probably would be called something else. It's not as fundamental or limiting as the speed of light, physics works the same without it, when all natural units are used. It always is used in the product with the thermodynamic temperature, t = kT, which is the measurement of temperature in energy units. That's its only use. If someone talks about the Boltzmann constant, it is implicitly assumed to be related to our practical system of measurement, not to natural physics, because it's not necessary there. If you want to learn more about that read M. I. Kalinin, S. A. Kononogov (2005). "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility". Measurement Techniques. 48 (7): 632–636. doi:10.1007/s11018-005-0195-9.. But yes, of course it's needed for any other (non-natural) system of units, but that can be learned from another article. Kbrose (talk) 20:57, 9 November 2010 (UTC)

Ok, please provide references, quotations preferably, that back your statements up. Otherwise, please do not revert. PAR (talk) 22:32, 9 November 2010 (UTC)

Books such a the one by F. Reif "Fundamentals of statistical and thermal physics" treat the subject in the way described by Kbrose. This is also my preference. Specifically about temperature, you'll read that Reif introduces temperature using the Omega function and k is introduced a scale factor without any physical meaning just to be able to scale the tempurature in some convenient way. Reif actually covers a lot of ground discussing statistics, the fundamental postulate, the omega function, the ideal gas, heat and work before introducing temperature; Temperature is only defined on page 99. What Reif does is to chose k to have the dimensions of energy, so that temperature is dimensionless. Count Iblis (talk) 23:10, 9 November 2010 (UTC)

Ok, Reif is on my list. I will be interested in learning the development of temperature there. Regarding the sentence under consideration, however, here is a quote from "Thermodynamics" by Lewis and Randall, to go along with the other two:

Statistical mechanics constitutes in large part a parallel science to thermodynamics"

How many references do I need to quote before I see just one quote that says that statistical mechanics is a branch of thermodynamics? Recent edit said "references are required for non-standard descriptions". I agree, and yet I have provided (in the talk page) three references for the standard description. I have yet to see one reference of an opposing point of view. PAR (talk) 02:45, 10 November 2010 (UTC)

Perhaps you don't read well. Nowhere was the statement made that SM is a branch of thermodynamics, although many may well hold the view that a large part of SM is just that. Another name for statistical mechanics is statistical thermodynamics, which makes the relationship quite clear. In any case, the text was composed carefully to state that thermodynamics includes a description based on SM, which cannot be argued away. The science of heat, temperature, pressure, volume, etc. is always thermodynamics, no matter what tools one uses to describe it. Furthermore you don't read your references well either since they do not support your claim that a description of thermodynamics based on SM is not part of thermodynamics, and no credible source will state such a thing. But this isn't clear to you, for obvious reasons. Lewis and Randall is another one of the old texts (80 years? SM wasn't even fully developed), that you like to use, in which thermodynamics surely referred to the classical thermodynamics, wrt which SM is surely a parallel field. 04:27, 10 November 2010 (UTC)

And still, no quotes, no references, only pronouncements. Can you even produce one quote from one book? Lewis and Randall was copyright 1961. (50 years). Does Reif support your POV? Reif is 1984 (37 years). Why not quote Reif if it is so up to date? Still, you have no problem referencing Catheodory (100 years at least). Callen is 1985, so I guess it trumps Reif, but no, the clear quote from Callen is, by your pronouncement, not clear. I can reproduce the entire paragraph, which makes it abundantly clear, if you wish. It seems that books only become out of date when they disagree with your POV. So now we have "Thermodynamics" and "Classical Thermodynamics". Please produce a reference and quote which makes this distinction. Seriously, I'm willing to learn here, but please stop issuing pronouncements and produce.

You say that "The science of heat, temperature, pressure, volume, etc. is always thermodynamics, no matter what tools one uses to describe it". But statistical mechanics is not descriptive, it is explanatory. When it deals with thermodynamic problems, it describes NOTHING that has not already been or could be described by what you call "classical" thermodynamics. It explains and predicts the descriptive results of thermodynamics. Heat, temperature, pressure, volume, etc. and are defined prior to and without reference to statistical mechanics and the description of their relationships are fully expressed by the laws of thermodynamics and subsequent macroscopic measurements. PAR (talk) 18:34, 10 November 2010 (UTC)

Is Entropy strongly correlated with degrees of freedom?

Given that:

Generally:

T = dE / dS

and...

In a classical ideal gas:

dE / degree of freedom = (1/2) * k * T

It would follow that, in a classical ideal gas:

T = dE / (degree of freedom * k/2)

dS = degrees of freedom * k/2

Because k is constant, this would imply that in a classical ideal gas that entropy is proportional to degrees of freedom. In other words, two ideal gases having the same number of degrees of freedom will have the same entropy regardless of their temperature. Does classical thermodynamics really assume this? Does it contradict classical thermodynamics? Or did physicists just overlook this?siNkarma86—Expert Sectioneer of Wikipedia
^{86 = 19+9+14 + karma = 19+9+14 + talk} 03:38, 15 March 2011 (UTC)

Maximum temperature

In an Spiegel online quiz I learned that there is (theoretically) a maximum temperature in the universe. However they could not appropriately explain that. I am wondering if the Planck temperature in the table (shortly after the big bang) would be this maximum. The argument would be that for higher temperatures the region would isolate itself from this universe (via an event horizon, i.e. forming a black hole).

Unfortunately I cannot give any reference for that. If someone knows a reference maybe he could add a corresponding note to the entry about the Planck temperature.

Thanks MelchiorG (talk) 10:58, 7 April 2011 (UTC)

Really stupid question...

I know wikipedia science articles can't afford to try to explain everything about any topic. However is it possible that the article could at least explain why temperature is expressed as $T\equiv \left({\frac {\partial S}{\partial E}}\right)^{-1}$ instead of as $T\equiv {\frac {\partial E}{\partial S}}$ which seems to be simpler?Zebulin (talk) 16:19, 18 May 2011 (UTC)

I think you know that this has to be the case because you want to define temperature such that heat flows from high to low temperature. So, we would then need to find a way to explain why at higher internal enegies, adding the same amount of energy leads to a smaller entropy increase than adding that same amount of energy at lower internal energies. The number of available states increases as a function of energy as a power of the energy, the entropy is the logarithm of that and that is thus proportonal to Log(E), the derivative of this is a decreasing function.

The problem then that because this article does not give any theoretical background to temperature, this does not really explain a lot. So, perhaps a rewrite is in order where we give the treatment of temperature like most books on statistical mechanics do. Count Iblis (talk) 17:04, 18 May 2011 (UTC)

The present statement $T\equiv \left({\frac {\partial S}{\partial E}}\right)^{-1}$ assumes a thermodynamic context of chosen dependent and independent variables, but does not say what that context is, or why it was chosen. A different choice of context of thermodynamic dependent and independent variables could have been made and led to a different statement. In other words, this formula as stated here in the present article is produced like a rabbit out of hat. Perhaps, for this reason, lacking the thermodynamic context at this point, the sentence at this point should simply be deleted. At a later point in the article it is at least stated that one is considering a system defined with internal energy as an independent variable and entropy as a dependent variable. This is followed by a statement that there is a "modern" definition provided by statistical thermodynamics, as if statistical thermodynamics has some kind of superior or prior status. Many empirical facts of thermodynamics are likely to wait a long time for an explanation by statistical thermodynamics. Empirical temperature is well defined by macroscopic calorimetry without recourse to thermodynamics.Chjoaygame (talk) 03:25, 19 May 2011 (UTC)

First of all, as Chjoaygame said, the equation as written by Zebulin is not what is in the article, and is furthermore incorrect without specifying what other parameters are held constant. The correct equation in terms of partial derivatives is:

$T=\left({\frac {\partial E}{\partial S}}\right)_{V,\{N_{i}\}}$

or, equivalently,

$T^{-1}=\left({\frac {\partial S}{\partial E}}\right)_{V,\{N_{i}\}}$

where volume V and particle numbers N_i are held constant. In the article, it states that if S is a function of E only, then:

$T^{-1}={\frac {dE}{dS}}$

or, equivalently,

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

which is correct, since "is a function of E" specifies that all other variables besides E, whatever they may be, are held constant.

To get to Zebulin's question, then, I guess I don't know why it is expressed as T^-1, other than Count Iblis' explanation. PAR (talk) 10:42, 19 May 2011 (UTC)

clarity exists in geometric topology

I don't want to argue the accuracy, but does the article really benefit from the phrase "hotness exists on a one-dimensional manifold"? I suppose it will set straight any mathematicians out there laboring under the misconception that temperature is a Möbius strip. But for most readers... really? Spiel496 (talk) 18:22, 9 June 2011 (UTC)

Thank you Spiel496. Fair comment. Yes, sad to say, there are many textbooks that, intending to improve the logic of the exposition of thermodynamics, follow Carathéodory (1909) who postpones acknowledgement of the fact that temperature can be expressed on a numerical scale until after the full exposition of the second law of thermodynamics; in that view, the notion that temperature expresses hotness, and that hotness has a direct physical meaning, are not accepted as basic or primary. The point here is that temperature has good status as a basic primary notion of physics, understood by the ordinary person, and does not need to rely on such sophisticated arguments about entropy, and I think this point needs to be made in this article. The usual statements of the so-called "zeroth law of thermodynamics" do not by themselves provide that temperature is essentially on a numerical scale. Your comment rightly calls for an improvement in the wording, which I have now tried to make.Chjoaygame (talk) 21:29, 9 June 2011 (UTC)

temperature of cosmic microwave background radiation

I originally went to this page hoping to get some insight into the nature of the temperature of the CMB radiation. I had a vague assumption that maybe the temperature of the CMB was the temperature that matter would reach when in thermal equilibrium with the CMB. But while the article does a pretty good job describing the nature of temperature of matter in relation to the kinetic energy of the particles in an object it's very difficult for uninformed fools such as myself to relate that concept to something other than matter like the CMB. Is it possible that something could be done in the intro to help the general public better understand temperature in the way it is used for the CMB in the same way that the article describes temperatures of matter? Thanks for any insight in improving this portion of the article!Zebulin (talk) 14:06, 10 June 2011 (UTC)

suggest removing section on heat capacity

The present section on heat capacity is nonsense, and something should be done about it. I agree with the idea of editor 121.58.217.83 to remove its present content, but I would go further and remove the whole section. It is not so relevant to an article on temperature that it cannot be dealt with just by a "see also".Chjoaygame (talk) 04:01, 28 June 2011 (UTC)

Please discuss what you think the problem is. I am currently against simply removing the section. Q Science (talk) 18:27, 28 June 2011 (UTC)

I repeat: The present section on heat capacity is nonsense, and something should be done about it. The use of the term "kinetic energy" is muddled. The writer of it apparently meant to refer to the kinetic energy of individual particles such as molecules, and perhaps to thermal vibrations of crystals, but this is not properly expressed by what he wrote. Kinetic energy has two, more or less different, meanings in thermodynamics, and the writer did not deal with that. One meaning refers to the motion of individual particles and this belongs to statistical thermodynamics and should not be presumed, as the writer presumes, in an article on a macroscopic quantity such as temperature, to be the primary meaning of the term. The other meaning of 'kinetic energy' that is relevant, and is perhaps the obvious meaning in such an article, is kinetic energy of bulk flow or even bulk movement, which is not thermal, though it can be developed from thermal energy, for example in convection. It is not good enough for a Wikipedia article section to work on the 'guess what I'm thinking' plan.

The subject of heat capacity does not belong to an article on temperature. The present section is merely tokenistic and any section as short as this would be likewise. A section on heat capacity merely clutters the article. Just a couple of "see also" pointers would be better, as intended by editor 121.58.217.83 .

The editor 121.58.217.83 would have done better to offer some reasons on this talk page and perhaps he will very kindly do so now.

Why does Q Science think the article on temperature needs a section on heat capacity? I think he should offer reasons.Chjoaygame (talk) 21:12, 28 June 2011 (UTC)

Maybe "kinetic energy" should be appended to read "kinetic energy of the random motions of the microscopic particles" or some such thing. That would cover lattice vibrations, as well as molecular vibrations, rotations and translations. Chjoaygame is right to point out that we should make a distinction from center-of-mass motion.

Aside from that point, the section doesn't seem muddled to me. And it was introduced not by 121.58.217.83, but by Kbrose about 9 months ago in this edit. Perhaps you should take it up with him. Kbrose is a patient individual who never resorts to insults when discussing article content. As to whether the section belongs, I would vote yes. Elsewhere, the article teaches that heat flows from higher temperatures to lower temperatures; that there is a metric -- heat capacity -- which says how much heat flows, is a pretty fundamental truth. Spiel496 (talk) 00:11, 29 June 2011 (UTC)

It was not that 121.58.217.83 introduced the section; it was that he proposed the removal of its text. One does not deny the fundamental truths that heat flows from higher to lower temperatures and that heat capacity is part of the apparatus for measuring heat. But here one is talking about cluttering an article. The section here tries to summarize a lot of theory in a few words; not an easy thing with precision and concision. It does not make clear that heat capacity has two aspects, specific heat at constant volume and latent heat with respect to volume. This distinction is needed to give precise thermodynamic meaning to what the section is trying to summarize. I agree with 121.58.217.83 that the section should go. If not, I think it needs thorough remedy, but not conversion into a new long section.Chjoaygame (talk) 22:31, 29 June 2011 (UTC)

Any discussion of temperature should include something about specific heat - the heat capacity per unit mass of a material. As for "kinetic energy", the concept is clarified in the linked article. If only a link is provided, then readers will have no idea why they might want to click on it. The current text at least provides a hint. Q Science (talk) 22:42, 29 June 2011 (UTC)

A "hint" is not good enough for an encyclopaedia. It is not good enough to defend a faulty section on the grounds that its faults are remedied elsewhere. If the section is to be retained, it needs to be remedied.Chjoaygame (talk) 23:24, 29 June 2011 (UTC)

Q Science here repeats his assertion that the section should be included, but does not offer reasons why.Chjoaygame (talk) 23:29, 29 June 2011 (UTC)

Kelvin was not a Scot

Kelvin was not a Scot as mentioned. He was born in Belfast. He studied in Scotland also in many other places, returning to Scotland to lecture and spend most of his life. — Preceding unsigned comment added by 86.144.179.215 (talk) 17:51, 29 June 2011 (UTC)

Overview? Temperature? Difference?

Surely the overview Overview is mistaken when it states "temperature tells of the tendency of matter to transfer heat from hotter to cooler bodies"? This is about the difference of temperature. How can you define a property by the effect of its differential? Temperature is the measure of thermal energy density, Joules per DOF (degree of freedom) a relationship defined by k_B, the Boltzmann constant

Further in the section Theoretical foundation it says "temperature may be measured directly in units of energy" which, if it were true, would enable you to tell the doctor your temperature was 10Joules, which is quite absurd, temperature in measured in Kelvins, ^oFahrenheit, ^oCelcius etc., etc.

Further in the same section it says " microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy" which is not correct, partly because it doesn't say which kinetic energy it's referring to so we are left hanging in the air. What it should say is the energy in a DOF (degree of freedom), this allows for the acurate definition of temperature for molecules such as O₂, He and CO₂, all of which have different numbers of DOF and thus different kinetic energies at the same temperature. --Damorbel (talk) 13:59, 16 July 2011 (UTC)

Welcome, Damorbel.

The overview is an overview, not an attempt at definition.

And even for a definition in the body of the article, following the lead, temperature is above all a macroscopic notion. For some statistical mechanical models, one can define a temperature, but that is more along the lines of microscopic explanation of macroscopic phenomena than of fundamental definition.

The sentence you criticize reads: "In the fundamental physical description, using natural units, temperature may be measured directly in units of energy." The clause you criticize is modified by an adverbial phrase that you seem to have ignored.

You object to the clause: "microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy." This clause is part of a sentence, again modified by a compound adverbial phrase that you seem to have ignored.

I am not suggesting that the article will not benefit from improvement.Chjoaygame (talk) 07:52, 17 July 2011 (UTC)

"The overview is an overview". But an overview of what? It says "transfer heat from hotter to cooler bodies" which is between two temperatures, it is not about temperature but about the 2nd law of thermodynamics.

"Temperature is above all a macroscopic notion". I don't agree, temperature is "energy per particle" as defined by the Boltzmann constant. When you have a collection of particles, as in a volume of gas, exchanging energy through collisions the the particles do not all have the same energy but energy distributed according to the Maxwell–Boltzmann distribution which means that the average energy per particle, i.e. the temperature, corresponds to the the energy of a single particle with the same temperature. This should be obvious since the size of the 'collection' of particles is not defined, it can be reduced to one particle without introducing any error. --Damorbel (talk) 09:43, 18 July 2011 (UTC)

Ideal gas animation does not show an ideal gas

The animation that claims to show an ideal monatomic gas does not, in fact, do so. One of the assumptions about an ideal gas is that the particles do not interact, but the particles in the animation clearly collide and bounce off one another. Adam Lein (talk) 19:49, 6 September 2011 (UTC)

Surely the "no collisions" hypothesis requires the particles of an ideal gas to have zero size? I suggest the less stringent definition of an ideal gas, a definition that has practical application, is one where the only interaction of the particles is elastic collision. Monatomic gases approach this very well and the effect of different atomic masses is also easy to understand.

Further, if the particles of an ideal gas do not collide with each other, what will they collide with? The whole of kinetic theory falls to bits if you insert this 'no collision hypothesis', so what useful purpose does it serve? --Damorbel (talk) 20:29, 6 September 2011 (UTC)

Its not that they have zero size. The particles must be of negligible size compared to the interparticle distance. Your suggestion would also include a Van der Waals gas, which is not an ideal gas. An ideal gas is a limiting case. Its not that they do not collide. The duration of the collision must be very small compared to the mean time between collisions. Again, its a limiting case. The time it takes for the particles to "thermalize" (i.e. acquire their equilibrium distribution) will then be much longer than the mean time between collisions. The animation is not too bad in this respect. PAR (talk) 20:52, 6 September 2011 (UTC)

'Negligible size compared with... ', then the relevance of the size would be a function of pressure. This really is not so important. What is important is that the particles should exchange energy by collision, if this doesn't happen then there exists only a number of unrelated particles in a volume. This becomes interesting at an altitude of about 85km sometimes called the 'top of the atmosphere' where the atmosphere loses it 'gassy' character and begins to take on the nature of an interplanetary medium. Up to that height the atmosphere is 'thoroughly mixed', it has a uniform composition (apart from water vapour); also its temperature becomes dependent on the Sun's activity; this is at the top of the Mesosphere. --Damorbel (talk) 06:57, 7 September 2011 (UTC)

edits by editor Red787

Editor Red787 made a well-intentioned but mistaken edit, from hot and cold to exothermic and endothermic. The latter two terms refer to heat production not to hotness and coldness as such. I reverted his edits.Chjoaygame (talk) 03:27, 24 September 2011 (UTC)

I agree. PAR (talk) 01:02, 25 September 2011 (UTC)

Agreed, it is correct as "hot" and "cold". VQuakr (talk) 05:11, 25 September 2011 (UTC)

new edit by La goutte de pluie

I do not like the new edit by La goutte de pluie and will probably delete it when I have examined it more carefully; I am busy elsewhere right now. La goutte de pluie may feel that the layman will benefit from his edit, but I am not so sure.Chjoaygame (talk) 04:35, 14 October 2011 (UTC)

Correction to temp value

Absolute Zero is shown as -459.68 degrees Fahrenheit, when conversion scales in the article (and references in linked Rankine scale) indicate absolute zero would be -459.67 degrees Fahrenheit. CWallwork (talk) 21:25, 23 October 2011 (UTC)C. Wallwork 10/23/11

some or most of the world

Editor 219.89.117.203 changed "Some of the world" to "Most of the world', but did not offer a reliable source for change. I have therefore reverted the change.

For all I know, the change by editor 219.89.117.203 may have been for the better. But Wikipedia policy is that such a change should be supported by a reliable source, for the better or not.

Dear editor 219.89.117.203, you are of course free to make the change again, but if you do, you should supply a reliable source for it. A reliable source is not just any source that agrees with you, but one that can be reasonably verified as giving reliable information on the point. If you do not provide a clearly reliable source for a change, I will oppose the change.Chjoaygame (talk) 02:11, 4 January 2012 (UTC)

the large majority of people in the world

The problem here is not as to the truth or otherwise of the edit, but is as to its conformity with the Wikipedia requirement for reliable sourcing. This is the same as for the previous edit commented on just above. If you want to make an edit like this, you need to provide a reliable source for it. It is no easy thing to provide reliable sourcing, because it calls for careful assessment of source reliability.Chjoaygame (talk) 02:50, 8 January 2012 (UTC)

microscopic particles?

"average speed of the microscopic particles that it contains" 

suggests particles that can be seen with a microscope. That is, particles which are bigger than nano-paricles, but smaller than milli-metres.

Perhaps that should read: "average speed of the atomic particles that it contains" 203.206.162.148 (talk) 01:32, 25 January 2012 (UTC)

I have removed the word "microscopic" - By the equipartition theorem, a thermalized particle of any size will have a kinetic energy of 3kT/2.PAR (talk) 04:12, 25 January 2012 (UTC)

You're incorrect. Microscopic does not mean "visible by optical microscope". In fact, there are several microscope technologies that allow to see single atoms or even single orbitals. Field ion microscopes, scanning tunnelling microscopes, and atomic force microscopes resolve single atoms. Additionally, the emission from a single atom has been imaged using an optical microscope. "Microscopic" means "smaller than can be seen by eye", essentially. --vuo (talk) 17:26, 20 July 2012 (UTC)

PAR is right! Correctness doesn't really come into it; the good old English language has long thrived by using any word that sounds right to have a desired meaning, it doesn't need an etymological justification. Vuo, all the effects and observations you list make no difference, if they did it might imply that all old texts would either need revision or lose their meaning, both of these options would be plain silly, better leave well alone.

As an example I have been struggling with refrangible, in the 19^th C rays (of light) were frequently described as being more (or less) refrangible. It seems to be something to do with refraction but I don't have a good definition. --Damorbel (talk) 09:44, 21 July 2012 (UTC)

Heat 'flows'?

The 2nd line of the article has "Heat spontaneously flows from bodies of a higher temperature to bodies of lower temperature". this is the rather outdated caloric theory. It should be "Energy is transferred from bodies with a higher temperature to those with a lower temperature". Heat in measured by temperature and thus is is not a substance that can 'flow'. There are many ways a body can change its temperature, none of them involve 'flowing'! It has been said that Wikipedia is not for scientists, this reads like 'keeping the ignorant in their place' to me. --Damorbel (talk) 12:12, 25 January 2012 (UTC)

As long as you keep in mind that the temperature is a function of the velocity squared then you can see it as an averaging out process with the faster particles giving up energy (velocity squared) to the slower particles, and the resulting average being a square root of the sum of squares value. So it's an energy redistribution process.WFPM (talk) 16:09, 5 April 2012 (UTC)

And heat 'flows' like this in solids? Heat 'flowing' is a concept belonging to the Caloric theory. Surely it is time that encyclopedias admit this 'theory' does not fit the evidence and abandon it? I do not understand why so many people want to teach this theory, could it be that they do not understand why it is outdated? --Damorbel (talk) 12:24, 7 May 2012 (UTC)

The term "heat flow" is still in use, and thus probably does not belong exclusively to the caloric theory, except etymologically. A similar problem can be found with the word "weight," which in law and commerce has always meant that property measured by a balance scale in conjunction with a standard reference mass, and thus still refers (in law and commerce) to "mass" as physicists define the term. In thermodynamics one would probably not use the term heat flow but heat transfer. However, since "heat flow" is a generally accepted term in many disciplines, including engineering, it might be a good idea to at least mention this issue in the article. For example, at the first occurrence of the term heat flow, some sort of explanation could be provided, if only in a footnote or parenthetic statement. Zyxwv99 (talk) 13:11, 7 May 2012 (UTC)

Damorbel: Generally speaking, when objecting to a statement, you can save a lot of time by introducing a tangible consequence that contradicts observation. For example, you could have said "To assert that heat 'flows' would imply that ________________, from which it would follow that ____(nonphysical result)_____". Otherwise we just go in circles. I have no problem with the statement that heat "flows", but maybe the word "flow" implies something different to you, that would lead to a violation of the 2nd law or something. If so, then that's important, because other readers may be leaving with misconceptions that we didn't anticipate. Spiel496 (talk) 21:28, 7 May 2012 (UTC)

Spiel496 you write "I have no problem with the statement that heat "flows"," I do not doubt you but then do you also accept the Caloric theory of heat? The origin of this theory was the supposition that heat was some kind of fluid that flowed from/into materials according to temperature difference. This doesn't happen with [[3]] friction or chemical change, or does it?

There is a restricted class of heat transfer problems that may be approximated by treating heat as if it were a fluid but care must be taken not to break the 1st law of thermodynamics. What do you think? --Damorbel (talk) 15:06, 8 May 2012 (UTC)

In physics, it is a customary usage to speak of a rate of transfer across a surface as a flow or a flux. The underlying idea is sometimes thought of as 'continuity'. It is not meant to imply 'conservation'. The word 'flux' means flow.Chjoaygame (talk) 17:23, 8 May 2012 (UTC)

Chjoaygame; Spiel496 and many others, what you are talking about is heat transfer which is a commonly used description for a none - equilibium condition arising frequently in thermal engineering such as boiler design and air conditioning where the aim is to transfer thermal energy from one place to another. In some respects this is a (quasi) equilibrium condition but there are a minimum of two temperatures measured, the source temperature and the sink temperature; the rate of energy transfer (Watts, Joules/s) is calculated from the known (or calculated) thermal conductivity of the heat transfer system. Earlier someone gave a link to Fundamentals of Heat and Mass Transfer by De Witt & Incropera. This book draws attention to the common mistake of confusing heat transfer and thermodynamics, the authors write:-

"...take note of the fundamental differences that exist between heat transfer and thermodynamics. Although thermodynamics is concerned with heat interaction and the vital role it plays in the first and second laws [of thermodynamics], it considers neither the mechanisms that provide for heat exchange nor the methods that exist for computing the rate of heat exchange. Thermodynamics is concerned with equilibrium states of matter, where an equilibrium state necessarily precludes the existence of a temperature gradient...." etc., etc., etc. (see p13 §1.2.4).

You will recall that the thermodynamic temperature of the system cannot be defined in this situation because there is more than one temperature, but the objective is not to define a thermodynamic temperature, the aim is to get some hot water for a bath or something or perhaps cool off a bit in midsummer. So you can no doubt appreciate that 'heat' (measured by temperature) is quite different from 'heating' (or 'cooling') i.e.transferring some Joules; heat is the energy density (or energy per particle). If you only have a few paricles very little energy is needed to make their temperature relatively high, the only question remaining is how do you get the particles to absorb the energy needed for the high temperature? (-Damorbel?)

Assuming the just above unsigned is by you: Responding to comment from you was a mistake by me; more wisely, I would not have responded.Chjoaygame (talk) 20:47, 8 May 2012 (UTC)

Um, sorry for omitting the signature. But may I ask why "Responding to comment from you was a mistake by me"? What I wrote is quite logical and supported by a quotation from a relevant source, a source actually cited by you in the talk pages for Heat here; your citation was p14, mine p13 §1.2.4. Don't forget these talk pages are for improving the article, not for telling the world who you want to talk to! --Damorbel (talk) 07:52, 9 May 2012 (UTC)

Damorbel, you've written a lot of words, but you still didn't come up with a false prediction following from the belief that heat flows like a fluid. For example, if we believe the world is flat, then that would imply that if one travels far enough one should reach the edge. But that isn't what happens. Therefore, the world is not flat. Spiel496 (talk) 07:18, 9 May 2012 (UTC)

Spiel496 The question was "...do you also accept the Caloric theory of heat?" To which I add, 'if not, why not?' --Damorbel (talk) 08:01, 9 May 2012 (UTC)

I'm not very familiar with caloric theory. If the theory makes false predictions, then no, I do not accept it. From the WP article, I gather that caloric theory postulates that heat is an actual substance that can't be created or destroyed. However, we observe that heat can be created from friction etc, so the theory is wrong. That doesn't mean everything the theory says is wrong. I don't think the typical reader is going to believe all the tenets of caloric theory just because this article says heat flows. Spiel496 (talk) 14:11, 9 May 2012 (UTC)

Spiel496 perhaps the question should be "is 'flowing a good analogy for heat transfer'?" Perhaps you would like to make a contribution along this line. It is true that temperature difference might be considered as an analogy for pressure difference and thus a temperature difference gives rise to energy transfer. But his flow analogy breaks down so often it is realy quite useless; unless you create some new reality e.g. flowing does not require the conservation of the material that 'flows', then how do you explain that heat is not a conserved quantity, it is energy that is conserved. Thermodynamics is a difficult subject because there are many subtle and counter intuitive interactions between matter and energy, introducing arbitrary interactions like 'heat' flowing (or perhaps it is energy that is 'flowing' - is there a distiction?) just confuse the matter and lead to many miunderstandings.

Look at it this way, what is the point of an encyclopedia if it uses second rate metaphors to explain complex matters? --Damorbel (talk) 14:59, 9 May 2012 (UTC)

So your point is: "Using the word 'flow' implies that heat is a conserved quantity, which contradicts the observation that heat can be created." That's a great starting point for a discussion. I think if you had led with that statement, editors would have chimed in with useful comments about the meaning of "flow" and the best wording for the article. Spiel496 (talk) 16:29, 9 May 2012 (UTC)

"editors would have chimed in with useful comments about the meaning of "flow"." It's never too late! What do you think? How many energy transer processes are to be considered as possible for restoring thermal equilibrium i.e. producing maximum entropy or perhaps just a uniform temperature? --Damorbel (talk) 17:45, 9 May 2012 (UTC)

Somewhat tangent to this section, but in 1st paragraph, shouldn't a more general term be used than "thermal conductivity" like "heat transfer resistance.". Thermal conductivity only applies to the conduction mode of heat transfer and not to radiant heat transfer. 158.35.225.227 (talk) 16:39, 26 June 2012 (UTC)

Hopefully I can interject a bit and better understand Damorbel's point. It seems as though his main point is that in the phrase "heat flow" heat is being treated as though it is a noun. This implies that an object or substance can contain heat, which is false. This is evidenced by the fact that heat is not a state function. Because heat is a path-dependent variable, we must treat it as though the word "heat" is a verb, rather than a noun. However, the big unfortunate truth is that the word heat has been used as a noun for centuries and continues to be used as such. Unless we find a better way of using it (or a better word to replace it) we have to stick with phrases such as "heat flow." For anyone who is interested, here is info for an article that discusses this problem. (American Journal of Physics, 69 (2001), 107. Sirsparksalot (talk) 16:39, 20 July 2012 (UTC)

Wavelength for black-body radiation of bodies with 0 temperature

It should be noted that the entry "Infinite" for the wavelength of a body of 0 temperature is pretty bogus, as such a body simply emits no black body radiation. So it should either be left empty or read something like '-'... — Preceding unsigned comment added by 82.139.196.68 (talk) 15:39, 5 February 2012 (UTC)

Nuclear instability at 0 Kelvin

If an Atom of OO9F18 is at a temperature of 0 degrees Kelvin, how can it have the kinetic energy required to break the PN bond and then capture an electron and change to EE8O18?WFPM (talk) 15:58, 5 April 2012 (UTC)

In a mixture of gases, particles have the same average kinetic energy?

As I understand, as multiatomic gases have more degrees of freedom than monoatomic gases and thus particles have more energy on average at the same temperature, the statement that in a mixture of gases, particles have the same average kinetic energy, does not hold in case of monoatomic and diatomic gas.

Currently the article suggests that in a mixture of helium and hydrogen, particles have the same average kinetic energy:

"In a mixture of particles of various masses, the heaviest particles will move slower than lighter particles, but have the same average kinetic energy. A neon atom moves slower relative to a hydrogen molecule of the same kinetic energy; a pollen particle suspended in water moves in a slow Brownian motion among fast moving water molecules."

--Jaan Vajakas (talk) 12:19, 6 July 2012 (UTC)

Vajakas has a good point, I think. Would the article make its point better if it compared gas particles without internal degrees of freedom? Helium, neon and argon, for example? I don't know what to say about the pollen. I like that part, assuming it's legit. Spiel496 (talk) 17:25, 6 July 2012 (UTC)

Kinetic energy refers to the center of mass motion, at least that's how most textbooks on this subject define this when they make this statement. So, to clarify things, it would be better to actually give an example with multi-atomic atoms and say that its average kinetic energy of <1/2 m v^2> equals 3/2 k T. Count Iblis (talk) 19:16, 6 July 2012 (UTC)

Yes, kinetic energy in this case refers to the kinetic energy due to the translational motion of the center of mass of the molecule. This average is the same for all molecules. PAR (talk) 03:14, 7 July 2012 (UTC)

There seems to be a misundertstanding here, arising from the fact that different species atoms/molecules have different numbers of degrees of freedom. The total energy of a particle (atom or molecule) is the sum of the energy in the different degrees of freedom. For example in the formula given above by Count Iblis <1/2 m v^2> equals 3/2 k T (Iblis' formula is only correct if the 'v' is the RMS velocity as here :${\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {3}{2}}kT$ which incorporates the energy from three axes or degrees of freedom) the figure 3 arises because, for a particle such as a helium atom, there are 3 degrees of freedom since the He molecule is monatomic and only has energy in 3 axes, x, y and z. Diatomic molecules (H₂, O₂, N₂ etc.) have a degree of freedom in the bond axis that makes them diatomic, so another 1/2mv² must be added to the kinetic energy, so the molecular energy becomes ${\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {5}{2}}kT$. It should be noted that the bond energy in molecules will be equal to the energy in the other 3 axes according to the equipartition of energy theorem. Despite this extra energy, diatomic (polyatomic) molecules can still only exchange energy along the 3 axes, x, y and z, there is no direct means for the energy in the bond axis to be involved in the collisions between particles, this means that the temperature is only defined by the diatomic molecules translational axes. However, the energy in all four degrees of freedom does show in the specifc heat of different gases, this can be seen by comparing the specific heats of monatomic gases (A, He, Kr etc) with the diatomic gases (H₂, O₂, N₂ etc.) and polyatomic gases (CO₂, H₂O etc.).

Notice that, because the kinetic energy (${\tfrac {1}{2}}m{\overline {v^{2}}}$) always has the same number of degrees of freedom as the right hand side (${\tfrac {5}{2}}kT$) which means by conventional algebra that the 'degrees of freedom' term falls out of the equation, i.e. the temperature, at equilibrium, is indepedent of the amount of material. --Damorbel (talk) 06:17, 12 July 2012 (UTC)

PAR, Unless one explicitly says otherwise, "kinetic energy" would include vibrational and rotational components, and so H₂ molecules would have more KE than Ne atoms. Would it be accurate enough to insert the word "translational"? So the article would read "... heaviest particles will move slower than lighter particles, but have the same average translational kinetic energy..." A bit wordy, but still readable.

Damorbel, I'm not sure what you're suggesting the article should say, but I do not think this part of the article would benefit from a discussion of degrees of freedom and heat capacity. It's trying to make a simple, easily-visualized point: slow big particles coexisting with fast little ones. Spiel496 (talk) 19:16, 13 July 2012 (UTC)

I think adding the word "translational" is very good. It's accurate and not wordy. PAR (talk) 08:45, 14 July 2012 (UTC)

Thank you, Damorbel, for the explanation and links to the equipartition theorem and the heat capacities. But I don't understand why you claim ${\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {5}{2}}kT$. As I understand, if ${\overline {v^{2}}}$ denotes the average square of speed of center of mass the molecule then ${\tfrac {1}{2}}m{\overline {v^{2}}}$ is the average translational energy of a molecule and in a multi-atomic gas it should still be ${\tfrac {3}{2}}kT$. But if ${\overline {v^{2}}}$ denotes the average squared speed of the constituent atoms then, if the atoms have identical masses (as in H₂), ${\tfrac {1}{2}}m{\overline {v^{2}}}$ would be the average total kinetic energy of the molecule (i. e. including the rotational and vibrational components) and I understand (from the Specific heat article) that in a classical ideal diatomic gas this average total kinetic energy of a molecule equals $3kT$ (in addition to the kinetic energy, a diatomic molecule has ${\frac {1}{2}}kT$ potential vibrational energy on average, so its average total energy is ${\frac {7}{2}}kT$). Jaan Vajakas (talk) 17:08, 20 July 2012 (UTC)

"I don't understand why you claim ${\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {5}{2}}kT$." The 5 comes from the total molecular energy of a diatomic molecule, for a monatomic molecule it would be 3. This shows up in the specific heat of gases, check this table you will see monatomic gases have a Cv = 12.4717 e.g. helium, diatomic molecules = 20.8 e.g. O₂ and polyatomic >=28.46 e.g. CO₂. However when it comes to temperature all molecules are (effectively) monatomic with only the three (translational) degress of freedom, this is because these 3 degrees of freedom participating in exchange energy by collision in (3 dimensional) space, (temperature is a measure of the energy in any (single) degree of freedom) --Damorbel (talk) 06:04, 22 July 2012 (UTC)

So, by ${\overline {v^{2}}}$ you mean the average square of the speed of atoms in the diatomic molecules, not the mean square of the speed of molecule's mass center? OK, then indeed, if a molecule consists of identical atoms (or we use a weighted average) then ${\tfrac {1}{2}}m{\overline {v^{2}}}$ is the average total kinetic energy of a molecule and by the Specific heat article (section Diatomic gas) the formula ${\tfrac {1}{2}}m{\overline {v^{2}}}={\tfrac {5}{2}}kT$ is indeed correct for diatomic gases with light molecules since their molecules are in the lowest quantum state of vibrational energy (so that only two rotational and no vibrational degrees of freedom are added, compared to monoatomic gas). But according to that article, by the laws of classical mechanics, which describe quite well gases with heavier molecules, in diatomic gas ${\tfrac {1}{2}}m{\overline {v^{2}}}=3kT$ and the average total (kinetic + potential) energy of a molecule is ${\tfrac {1}{2}}m{\overline {v^{2}}}+E_{\text{pot}}={\tfrac {7}{2}}kT$ where $E_{\text{pot}}$ is the potential energy of the bond. And if ${\overline {v_{M}^{2}}}$ denotes the mean square of the speed of a molecule's mass center then even in a diatomic gas ${\tfrac {1}{2}}m{\overline {v_{M}^{2}}}={\tfrac {3}{2}}kT$. Do you agree? Jaan Vajakas (talk) 14:48, 22 July 2012 (UTC)

Spiel, all I was trying to do was to explain to the opening post how gases with more than one atom (three degrees of freedom) have the same temperature as gases with more. I probably used too many words! But apart from that, the article has a number of problems e.g. opening statement, 2nd para. "In thermodynamics, in a system of which the entropy is considered as an independent externally controlled variable, absolute, or thermodynamic, temperature is defined as the derivative of the internal energy with respect to the entropy." How can the entropy be considered an externally controlled variable? Is there any meaning at all in this? The first para. is even worse When a heat transfer path between them is open, heat spontaneously flows from bodies of a higher temperature to bodies of lower temperature. The flow rate increases with the temperature difference, while no heat will be exchanged between bodies of the same temperature, which are then said to be in "thermal equilibrium". The first para. is allready introducing 'temperature difference' and 'heat flow' i.e. the 2nd law, before giving more than the vaguest indication of what temperature is all about. --Damorbel (talk) 06:21, 14 July 2012 (UTC)

Temperature and the 2nd law of thermodynamics

As far as I can see there is not one reference given to support the assertion in the section 'Second law of thermodynamics' where it says "It is also possible to define temperature in terms of the second law of thermodynamics which deals with entropy." Further in this section it asserts, also without reference, "... for TC = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K." which is thoroughly in tune with the rest of the article but is more likely to be original research or a POV, but definitely not referenced. I propose this section be deleted. --Damorbel (talk) 20:50, 14 July 2012 (UTC)

Regarding the first statement, rather than delete an obviously valid statement it would be more constructive to find a reference. I will look for one also. Regarding the second, I think it is incomplete. PAR (talk) 01:52, 15 July 2012 (UTC)

"delete an obviously valid statement" How so? By definition the 2nd law is about a system in disequilibrium - surely a system in thermal disequilibrium cannot have a single temperature assigned to it? --Damorbel (talk) 06:19, 15 July 2012 (UTC)

When using the second law to define temperature (and entropy) only the reversible case is utilized. Reversible changes are so slow that each separate system may be considered to be in equilibrium, and therefore each separate system has its own temperature and entropy. Then you can change the thermal connections between two systems and describe the equilibrium situation that eventually develops after the change, assuming the change is so slow as to be reversible. The second law gives a "recipe" (e.g. the Carnot cycle) by which you can define and measure absolute temperature. So, yes, the second law deals with changes in thermodynamic systems over time, but it does not consider the details, only the final equilibrium result, assuming reversible changes only, and this result is unique. PAR (talk) 12:14, 15 July 2012 (UTC)

"Reversible changes are so slow" Really? What does 'slow' mean?

"....the Carnot cycle) by which you can define and measure absolute temperature". Please... how?

The article is about temperature which is 'energy per degree of freedom', characterised by the Boltzmann constant; this appears twice in the article here and here. The Boltzmann constant is the only way to relate temperature and energy, that is why the Kelvin will soon be replaced by the Boltzmann constant as the fundamental constant relating the two; you can read about it here. --Damorbel (talk) 13:47, 15 July 2012 (UTC)

Perfectly reversible means infinitely slow. The slower the change, the closer to perfectly reversible the change becomes. It's a limiting process. If you have a process that so slow that it yields answers that are within 0.01 percent of a perfectly reversible change, and you specify that that, or any slower process is good enough, then you say that the process is "practically reversible". The time it took to achieve these results is "practically infinite", and that's how slow "slow" is.

Its similar to situation with a finite number of particles. The temperature of a system with a finite number of particles is not perfectly defined. The fluctuation theorem tells you how imperfect the definition is. If you have enough particles so that the temperature fluctuations are practically zero, then the number of particles is practically infinite. Its up to you to decide what "practically" means - it depends on how much error you are willing to put up with. If you specify that error, then that error and any smaller error is "practically zero". For most everyday macroscopic systems with everyday measuring instruments, the statistical error can be confidently assumed to be practically zero.

For the second law definition of absolute temperature, see Thermodynamic_temperature#Definition_of_thermodynamic_temperature PAR (talk) 16:06, 15 July 2012 (UTC)

You have not given an independent support for the statement "... for TC = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K." I suggest that this is an example of the perpetual motion school of thermodynamics so popular in Wikipedia! For example it is to be found also in the link that you give above as:-

"Notice that for TC=0 the efficiency is 100% and that efficiency becomes greater than 100% for TC. Subtracting the right hand side of Equation 4 from the middle portion and rearranging gives)

${\textrm {efficiency}}=1-{\frac {q_{C}}{q_{H}}}=1-{\frac {T_{C}}{T_{H}}}\qquad (4).$

where the negative sign indicates heat ejected from the system."

Yet another example in the long history of arguments presented with efficiencies >100% that breach the 2nd law. Have a nice day! --Damorbel (talk) 07:31, 16 July 2012 (UTC)

All I said about that statement is "I think it is incomplete". If we do not allow negative temperatures, then yes, the efficiency for Tc=0 and Th>0 is 100 percent. But you cannot build a perpetual motion machine from this fact. Again, its a limiting statement, a statement about limits, not about any physically realizable setup. In order to have a perpetual motion machine, the C reservoir would have to contain infinitely many particles (impossible) at a temperature of zero degrees (again, impossible) and the time for the process to complete would be infinite. For any real setup, what the statement is saying that for a C-system that is practically infinite at practically zero degrees, you can convert practically all the heat in the H reservoir to work, given a practically infinite amount of time. The efficiency will be practically 100%. Again, it depends on you what the definition of "practically" is. The closer you get to the idealized case, the more tightly you can define "practically". But again, the idealized case cannot be realized. PAR (talk) 17:34, 16 July 2012 (UTC)

Reversal (2)

I have reversred here: [[4]] where it previously said- "...variable because it is defined without concern that the body of interest is composed of many particles, such as molecules and ions of various species. It is an..."

The original text recognises that thermodynamics is the science of particle physics, without it the basis of themal science and atomic theory disappears and most of modern physics with it. If such drastic changes are to appear in Wikipedia may I suggest that there be discussion in the talk pages first?. --Damorbel (talk) 08:00, 13 November 2012 (UTC)

Quantitavely?

I have removed 'Quantitavely' from the text. Temperature is an intensive property, thus it is incorrect to use 'Quantitavely' which is to be used for extensive properties such as energy; this is an important distinction in thermodynamics.

PS Sorry about my duplicate thermometer contribution! --Damorbel (talk) 08:55, 19 January 2013 (UTC)

Ideal gas? Molecules?

The opening section has this text:-

In an ideal gas, the constituent molecules do not show internal excitations. They move according to Newton's first law of motion, freely and independently of one another, except during collisions that last for negligibly short times. The temperature of an ideal gas is proportional to the mean translational kinetic energy of its molecules.

Which is deeply flawed.

1/ An ideal gas is essentially monatomic, so it cannot be a molecule which is an assembly of two or more atoms.

2/ Molecules of all sorts do show internal excitations, that is why molecular gases frequently have higher specific heats than monatomics

3/If the opening section refers to gase it should also mention liquids and solids.

So I intend to change the above paragraph:-

The temperature of all materials is proportional to the mean translational kinetic energy of the constituent atoms and molecules, in fact of all particles in the material. This was explained by A. Einstein in his 1905 paper "Investigations of the Theory of Brownian Movement". This important paper finally established the validity of atomic theory. Enstein's paper explains that the temperature all materials, gas, liquid or solid is proportional to the the square root a particle's linear velocity, be it solid liquid or gas; it has to be linear velocity because it is by linear movement that heat is exchanged; the square root arises because particle energy is proportional to its velocity squared. --Damorbel (talk) 12:03, 19 January 2013 (UTC)

I agree we should avoid constraining the explanation to an ideal gas. However, I removed the bit about the "square root of velocity". There's either a typo or a complete misunderstanding there. One sentence says T~K.E. and the next apparently contradicts it by saying T~sqrt(v). The lead section needs to be accessible to a non-expert, and I don't follow the square root part at all. Maybe you meant velocity is proportional to sqrt(T)? Spiel496 (talk) 22:43, 19 January 2013 (UTC)

I wish I could claim it was a typo but really it had more to do with inattention. You are of course quite correct it should be v ~ squrtT. I should have noticed this myself because the speed of sound is also proportional to sqrtT.

But this discussion is rather a waste of time now because the whole of my contribution on this matter has been deleted and we are back to the position where only freely moving particles .... etc. ... temperature! --Damorbel (talk) 19:29, 20 January 2013 (UTC)

Chjoaygame, regarding the "freely and independently moving constituent particles" contribution, I assume your motivation is to make the language more precise. However, with the addition of each qualifying phrase, the Lead section gets a little harder to read. Can you back up a minute and explain the problem with the shorter phrase "temperature is proportional to the average kinetic energy of the constituent particles"? Does that fail in the presence of any inter-particle forces? Or when quantum effects become important? If the shorter phrase is at least approximately accurate, I suggest we keep it, perhaps with a disclaimer. The interested reader can delve into the article for the complete picture. Keep in mind, this is the Lead. We don't need to cover every subtlety.

Same complaint with the phrase "and the internal energy is considered as a function of the other independent externally controlled extensive thermodynamic variables especially including the entropy". I can't picture the audience who benefits from that language. Spiel496 (talk) 20:44, 20 January 2013 (UTC)

• Spiel496 writes just above: "I assume your motivation is to make the language more precise". My motivation is to state the physics where it's needed. Spiel496 proposes what he calls a "shorter phrase", but what I would call a clause: "temperature is proportional to the average kinetic energy of the constituent particles". In my opinion this is too vague, and strictly read one would say it is inaccurate. I do not agree with Spiel496's proposal: "If the shorter phrase is at least approximately accurate, I suggest we keep it, perhaps with a disclaimer." I think it is better to make the statement accurate from the start; a disclaimer makes the 'shorter' version unwieldy and probably not shorter. Spiel496 proposes that "We don't need to cover every subtlety." I don't think the idea of freely and independently moving particles is too subtle for the lead; it is essential to the physics. We are dealing with people who want to supplant the proper and general thermodynamic temperature with the necessarily reserved kinetic theory temperature. People who can't cope with a precise statement of the thermodynamic definition are free to skip it. People who want to know the proper definition are entitled to find it precisely stated in the lead.Chjoaygame (talk) 21:14, 20 January 2013 (UTC)

• Damorbel writes above: " only freely moving particles .... etc. ... temperature". This seems to look like a quotation from the article but is a misquotation. The word 'only' is not present in the original.Chjoaygame (talk) 21:18, 20 January 2013 (UTC)

freely and independenty moving particles

The kinetic definition of temperature refers to freely and independently moving particles. A microscopic degree of freedom refers to possible microscopic kinetic and microscopic potential energy. It is the microscopic kinetic energy, in particular, the microscopic kinetic energy of translation, that is the usual specific object of interest. For example, Chapman & Cowling 1939/1970 write: "The mean translatory kinetic energy per molecule, ... , is taken to be the proportional to the thermodynamic temperature ..." A gas is a material constituted of freely and independently moving particles, except when they briefly collide or undergo other adventures. A material that is not a gas includes particles that are not freely and independently moving. This means that a microscopic degree of freedom sees a division between its kinetic and its potential energy. The whole degree of freedom has k_BT of energy. For some laws of interaction, especially continuous laws, between the kinetic and potential energy the kinetic energy gets just k_BT/2 of mean energy, but for others it doesn't. For these others, the mean kinetic energy doesn't necessarily get k_BT/2. An ideal gas belongs to the class of material with degrees of freedom with no continuous law of interaction between the kinetic and potential energy. Freely and independently moving particles belong here; they obey the Maxwell-Boltzmann distribution law. They get k_BT/2 for each component of mean translational kinetic energy. That is why one can relate their mean kinetic energy to the thermodynamic temperature. For example, Tolman on page 87 writes:

"..................Hence we may now take the relation

$\beta ={\frac {1}{kT}}\,\,\,\,\,\,\,\,\,\,\,\,(32.11)$

as applying in general to any system obeying the Maxwell-Boltzmann distribution law."

The matter of aggregation of molecules is best discussed, so far as I know, by Sir James Jeans, as cited in the text of the article.Chjoaygame (talk) 20:50, 20 January 2013 (UTC)

Chjoaygame you write:

A material that is not a gas includes particles that are not freely and independently moving ...

Which I take to mean that, in solids, liquids and other structures particles are constrained by interatomic and other forces causing them to be bound together, giving the observed (solid and liquid) properties.

These inter atomic forces are not rigid but elastic, so in these cases the kinetic energy of the particles is exchanged periodically with the elastic potential energy of the interatomic and other forces. As in all dynamic systems with two types of energy storage, kinetic and potential, the result is an oscillation between the two; when, in its oscillation the particle is, for an infinitesimal period, motionless, all the energy is potential; in this state the particle has maximum acceleration so it soon achieves maximum velocity and zero acceleration; in this state all the energy is kinetic.

The important fact is that the potential energy of a particle, in a steady condition, is exactly equal to its kinetic energy, but at different times. Further, at a given moment, the kinetic energy of a particle in a solid state is the same, when the temperatures are equal, as a freely moving particle. It is important to realise that it is only the kinetic component that can transmit 'temperature' (thermal energy) between particles, be they in a gaseous, liquid or solid. --Damorbel (talk) 21:51, 20 January 2013 (UTC)

talk from my talk page

Damorbel has made the following entry on my talk page.

Your revision (today) of the Temperature article

You have made a revision today [[5]] What do you mean by :-

For a material in which there are freely and independently moving constituent particles, the temperature is proportional to the mean translational kinetic energy of those particles,?

I made an edit to extend the introduction, which refferred previously only to ... an ideal gas, the constituent molecules do not show internal... to include all gases liquids and solids.

The point being that the particles of "...liquids and solids..." are not moving freely, they are, as are many gases and vapours, constrained by interatomic forces, that is why they are liquids, solids etc.

Now you have changed it to :-

For a material in which there are freely and independently moving constituent particles, the temperature is proportional to the mean translational kinetic energy of those particles

Why do you write that the particles must be "freely and independently moving ... "? Neither solids nor liquids nor gases with composite molecules have "freely and independently moving ... particles", yet they all have a measurable temperature that is just the same for all particles in eqilibrium conditions, indeed that happens to be the main theory behind the triple point cell. --Damorbel (talk) 20:06, 20 January 2013 (UTC)

I have attempted to reply to this in the previous section here.Chjoaygame (talk) 20:58, 20 January 2013 (UTC)

except for very low temperatures

With respect, I have undone an edit by PAR.

The edit said something important and valuable, but did not fit where it was placed.

The edited text that I undid read as follows: "For a material in which there are freely and independently moving constituent particles, except for very low temperatures where quantum effects become important, the temperature is proportional to the mean translational kinetic energy of those particles, whether they be electrons, atoms, molecules, aggregations of molecules, or pollen grains." From this sentence, I removed the words in bold.

The words "except for very low temperatures where quantum effects become important" are a kind of pleonasm for the words which are left standing. The words that are left standing are explicit that they refer to a special situation, namely that there are freely and independently moving constituent particles, and that it is just those very carefully indicated particles that are intended as showing the proportionality. The quantum effects to which the removed words refer are just the effects that remove the freedom and independence of the constituent particles. Quantum effects are about what happens when orbits of particles no longer extend in effect to infinity, but instead represent bound states of microscopic objects, which are thus no longer free and independent. So the removed words say over again what the remaining words say, adding an explanation that looks like a disclaimer. The wording that remains was originally carefully crafted to avoid a need for such an apparent disclaimer as the removed words seem to imply. The purpose was brevity and accuracy in the lead, indicating the essential physics.

It may be very valuable for the body of the article to contain an explanation of why and how the constituent particles become no longer free and independent when the body is brought to very low temperatures where quantum effects become important. As noted just above, the quantum effects are about binding, which means lack of freedom. Such an explanation would be very welcome, and could go into some detail. But it is not necessary or appropriate as a disclaimer in the presently worded lead.Chjoaygame (talk) 05:39, 21 January 2013 (UTC)

James Jeans

Chjoaygame cites James Jeans in support for his position that 'fixed' molecules (not moving freely) do not exhange kinetic energy, that only freely moving perfect gas molecules do this. James Jeans, in his book "The Dynamical Theory of Gases" (ISBN-10: 0521744784) writes (p2)

The molecules of which a substance is formed will be capable of vibration about their positions of equilibrium, and when these vibrations occur we say the body possesses heat. As the vibrations become more vigorous we say that the temperature of the body increases. [6]

Ths is as good a summary of heat and temperature as you are likely to find. --Damorbel (talk) 07:14, 21 January 2013 (UTC)

Damorbel seriously misquotes me, when he writes of "his position that 'fixed' molecules (not moving freely) do not exchange kinetic energy".

I did not write or think about 'fixed' molecules. That word 'fixed' is an invention of Darmorbel. I did not write or think about molecules that "do not exchange kinetic energy". Such molecules are an invention of Damorbel. My statement did not refer to the perfect gas, and it explicitly considered constituent particles other than molecules; namely, it mentioned electrons, atoms, aggregates of molecules, and even pollen grains. Thus Damorbel's comment contains serious misquotation of what I wrote.

Damorbel is quoting Sir James Jeans' 1904 text. I referred to Jeans' 1940 text, not to his 1904 text.Chjoaygame (talk) 07:28, 21 January 2013 (UTC)Chjoaygame (talk) 07:32, 21 January 2013 (UTC)

more from my talk page

Damorbel has posted the following on my talk page.

James Jeans? 1904?

[7] So I got it wrong did I? So by 1940 he changed his mind did he? Chjoaygame, you are doing it again with your insinuations. If you are saying I got it wrong then why did you not cite like I did? If you merely imply, as you did, that I was incompetent, what you have written becomes an random personal attack.

If indeed James Jeans changed his mind between 1904 and 1940 (I cannot find a 1940 edition of "The Dynamical Theory of Gases". Perhaps you are thinking of "An Introduction to the Kinetic Theory of Gases" which was published for the first time in 1940; perhaps you have been looking in the wrong book ... ! Let me know when you have looked in the book I referenced, I did give a link. --Damorbel (talk) 10:29, 21 January 2013 (UTC)

Before I put up my post here in this talk page, I looked in the book you referenced there.

You misquoted me here on this talk page at Talk:Temperature#James Jeans just above. I was putting the record straight. I had nothing to add. I did not imply that you were wrong. I was not insinuating and I was not implying that you are incompetent.Chjoaygame (talk) 11:54, 21 January 2013 (UTC)

Please do not put personal matters on these talk pages.--Damorbel (talk) 12:21, 21 January 2013 (UTC)

When you misquote me on this page I am entitled to reply about it here; my right to reply to misquoting does not make it personal. It was improper that you tried to divert this matter into my talk page.Chjoaygame (talk) 12:27, 21 January 2013 (UTC)

. . . freely and independently moving constituent particles. . .

After recent discussion, does anybody consider this phrase (opening statement) :-

For a material in which there are freely and independently moving constituent particles,

covers the case for the temperature of gases, solids and liquids in a satisfactory way?

And if so why?

I don't think it is correct to deccribe particles in solids and liquids as "freely moving" because they are constrained by interatomic forces. --Damorbel (talk) 18:54, 21 January 2013 (UTC)

The kinetic theory of gases is largely about freely and independently moving constituent particles. They move on free paths, except for collisions which take place over negligibly short distances in neglibibly short times. The mean free path is an important concept in this theory. Any book on the matter will confirm this. Indeed, as you rightly say, particles in solids and liquids are mostly not freely moving. But, for example, some of the electrons in metals at laboratory temperatures seem to behave as if they were freely moving, and experimental measurements of their velocities as they are emitted from a hot wire find that they have a Maxwell-Boltzmann speed distribution. It is such particles that make sense of the equivalence of the kinetic gas theory and the thermodynamic definitions of temperature. It is such particles that are the proper physical basis for the proposal of a proportionality, between mean translational kinetic energy of constituent particles, and temperature.Chjoaygame (talk) 19:54, 21 January 2013 (UTC)

Sorry but what you write, if I understand you correctly, does not include an explanation of the concept of temperature in solids and liquids. I suggest the introduction to the Heat article would be substantially improved if some text on this aspect of temperature was included. --Damorbel (talk) 20:58, 21 January 2013 (UTC)

In response to your request, I have indicated how the thermodynamic definition covers all states of matter, gaseous, liquid, solid, plasma, liquid crystal, and so forth, and how temperature can be defined for bodies not thermodynamic equilibrium in themselves.Chjoaygame (talk) 23:03, 21 January 2013 (UTC)

The article still has :-

For a material in which there are constituent particles that move freely and independently except for brief collisions, the temperature is proportional to the mean translational kinetic energy of those particles . . .

Which is not correct. The article is confined to :-

constituent particles that move freely and independently except for brief collisions

The very different means of energy exchange for constrained particles (solids and liquids) by interatomic forces is not included. Why not?

There is nothing about this important matter in the whole article! --Damorbel (talk) 10:17, 22 January 2013 (UTC)

The section in the article headed Statistical mechanics approach to temperature is just waiting to be improved. There is plenty to do in it. The desirable improvements to that section would include an account of "the very different means of energy exchange for constrained particles (solids and liquids) by interatomic forces", which would then justify summary statements about them in the lead. Moreover, the article lacks a section on the Kinetic Theory approach to temperature, an approach that is not fully covered by the statistical mechanics approach. Plenty of work there, to put in a section on the Kinetic Theory approach to temperature.Chjoaygame (talk) 16:15, 22 January 2013 (UTC)

Good, you do that for the stastical mechanics and will do it for the opening statement. OK? --Damorbel (talk) 17:32, 22 January 2013 (UTC)

The previous comment seems perhaps to have a typo. When it wrote "and will do it for the opening statement", did it mean to write "and I will do it for the opening statement". Whatever. The talk page does not assign tasks to individuals.Chjoaygame (talk) 18:59, 22 January 2013 (UTC)

I know Chjoaygame means well, but the Lead section has become unreadable. In particular, the 4th paragraph reads like a terms-of-service agreement. I could pick apart each phrase that bothers me, but I don't want this to sound like a personal attack. Please read it out loud to yourself and approach it from the point of view of someone asking the question "what is temperature, really?". Of course, we don't want to "dumb it down" -- I get that -- but we should be able to write something that at least makes sense to a layperson. I have trouble following the text, despite a degree in physics. To someone with less experience in thermodynamics, the text says effectively, "Temperature is a subtle, complex concept that you have no hope of understanding." We can do better. In fact, we could do better by simply rolling back the article to Dec 5th.

I propose we keep the Dec 5th version in place while Chjoaygame, Damorbel and others work out the wording on this Talk page. Spiel496 (talk) 20:25, 22 January 2013 (UTC)

The Lead changed substantially before I completed my above comments. The 4th paragraph I spoke of is not to be found. However, the change was not for the better. The Lead is now even longer and contains topics (such as momentum) which do not appear in the body. The Dec 5th version is still preferable, and I renew my plea to work out these ideas here on the Talk page rather than on the article itself. Spiel496 (talk) 00:21, 23 January 2013 (UTC)

remove/correct errors

Changed paragraph: Two bodies can be out of equilibrium, yet at the same temperature. If they are separated by a permeable membrane which allows particles to pass through, and are at different densities, for example. Only when they have fixed number of particles, and fixed volume will equal temperatures imply equilibrium.

Removed the paragraph:

A system achieves thermal equilibrium as internal temperature differences reduce progressively (see energy .... flows; above). Energy does not literally flow because it is not a fluid (see caloric), it is a convenient concept but a mistaken one. What is popularly called energy (or heat) flow is in fact momentum. This is fairly easy to understand from the thermal models of gases, where particles collide to exchange energy. Again energy is a useful simplification, but it is not a vector quantity so it does not have a vector's directional value that is required for the concept of 'flowing'. So it is by momentum exchange that particles arrive at equilibrium. Frequently, by way of simplification it is said that particle exchange thermal energy 'by means of translational kinetic energy' which is less elegant and less accurate than 'momentum' since the vector component is not correctly included in 'translational kinetic energy'.

Its just too jam-packed with errors to survive. "What is popularly called energy (or heat) flow is in fact momentum". Totally wrong. Heat flow is energy flow, period. "energy... is not a vector quantity so it does not have a vector's directional value that is required for the concept of flowing" - thats wrong, or else mass doesn't flow either. Mass and energy flow because they have a flux vector (mass density x velocity, energy density x velocity), which provides the vector nature. Etc. Etc. PAR (talk) 06:40, 23 January 2013 (UTC)

PAR "Two bodies can be out of equilibrium, yet at the same temperature" Do you mean "thermal equilibrium" ? I have yet to see an author say that thermal equilibrium does not exist in any system, gas, solid, liquid or any combination with uniform temperature. Surely the best example of this is a triple point cell, it is the theoretical basis for the definition of temperature by triple point measurement!

Further, how can energy flow? When mass flows (of course it does) it has velocity which is a vector. But energy transfer doess not require mass flow, for static materials energy is transferred by diffusion of momentum, not particles. Fourier described this in his 19^thC paper Théorie analytique de la chaleur. Also A. Einstein explains radiation energy transfer as being due to photon momentum in his 1917 paper "On the quantum Theory of Radiation".

These are important concepts and are well supported by the references.

The paragraph should be put back. I will accept its removal only if you show an error in my two references. --Damorbel (talk) 07:27, 23 January 2013 (UTC)

The subject of whether heat can be said to "flow" is off-topic. Leave it out of the Lead. Spiel496 (talk) 17:16, 23 January 2013 (UTC)

"Flow' off topic? The section is about equilibrium! Without equilibrium the concept of temperature is meaningless.

Worse than that the concept of heat flowing is rejected in my contribution. I understand from your 'off topic' assertion that it is a viable concept.

Sorry but I am not convinced by your arguments. Would you care to clarify your position on both heat 'flow' or '(thermal) equilibrium'?

These are matters of physics, do you really think that they can be so narrowly separated? It's like saying legs are 'off topic' in an article on tables! --Damorbel (talk) 18:10, 23 January 2013 (UTC)

Yes, the question of whether heat can flow is off-topic. This is the lead section of the article on temperature. It is supposed to give a brief summary of the topics in the article. The main body of the article doesn't mention the issue of whether "flow" is the correct word to describe the movement of heat. Therefore, it is off-topic in the Lead section. Spiel496 (talk) 18:45, 23 January 2013 (UTC)

And yes, I'd be happy to clarify my position on heat flow, but this doesn't seem like the right place. Please leave a note on my Talk page (explaining what goes wrong if one thinks of heat as flowing). Spiel496 (talk) 18:49, 23 January 2013 (UTC)

I have removed a lot of other things that weren't necessarily errors, in the interest of making the Lead more concise. The result is shorter, but still pretty flawed. It may be easier to return to the Dec 5th version as I suggested above, but I decided to give editing a try. Some things left to fix:

• We should restore the language connecting temperature and the vibrational/translational kinetic energy of the particles. And it should precede the introduction of absolute zero, so that the phrase "amplitude of the vibrations" means something.
• T=dE/dS got omitted from the Lead (not by me). It seems important, although I doubt many readers benefit from it.

Some of the things I removed may belong back in, but I urge editors to bring the items up on the Talk page first. Spiel496 (talk) 18:46, 23 January 2013 (UTC)

Spiel496, I am utterly astonished by your conviction that temperature, energy transfer and equilibrium can be separated, temperature can only exist in an equilibrium state and equilibrium states can only be reached by energy transfer (or momentum transfer, if you care).

It is quite irresponsible not to refer to the principle matters in the opening section in an encyclopedia. Leaving relevant material out is properly called 'dumbing down'. I know some people find thermal physics 'difficult' but I don't think they will be helped by leaving critical material out. --Damorbel (talk) 19:06, 23 January 2013 (UTC)

The opening section still talks about energy transfer and equilibrium. What's left out? Spiel496 (talk) 22:59, 23 January 2013 (UTC)

Upper limit

It may appear to be pernickety but I have restored the practical in

There is no practical upper limit to temperature.

Temperature is a measure of particle energy, just like electron volts.

There are however 'impractical' upper limits :-

1/ How do you give the particle extreme energy?

2/ Does the particle actually survive the application of extreme energy? e.g LHC

Oh alright, the second one is really about acceleration! But I do think 'practical' is relevant. --Damorbel (talk) 18:52, 23 January 2013 (UTC)

Another editor's opinion would be welcome, but I would say There is no theoretical upper limit. You are describing what most people would call 'practical' limits. As in, "My car's theoretical maximum speed is 300,000 km/s, but the practical limit is 40 m/s" Spiel496 (talk) 01:12, 25 January 2013 (UTC)

Temperature is a property of all materials, gas, solid or liquid.

The lead contains the statement that "Temperature is a property of all materials, gas, solid or liquid." It is also a property of radiation. I think the lead should allow for this. I will leave it for the current activists to fix.Chjoaygame (talk) 01:55, 24 January 2013 (UTC)

Removed, untrue. Temperature cannot be defined for a system far from equilibrium (i.e. being far from an equilibrium distribution like Maxwell, Planck, Bose-Einstein, Fermi, etc.)PAR (talk) 06:08, 24 January 2013 (UTC)

For consistency, should one not also remove "Temperature is a physical property of matter "? Or add "and radiation"?Chjoaygame (talk) 06:29, 24 January 2013 (UTC)

The extended irreversible thermodynamics people allow a wider definition. I don't fully understand it but it seems nearly that, at least for matter, one can say that the temperature can be defined by the effect of the body on a wall permeable only to heat, provided of course things are near enough to a steady state. I don't think this necessarily requires local thermodynamic equilibrium in the body of interest. The thermometer on the other side of the wall has to have standard properties, for example those of thermodynamic equilibrium. Planck defines non-equilibrium temperature for radiation, one temperature for every wavelength. For matter, 'permeable only to heat' settles it. But for radiation, one can have 'selectively permeable membranes' permeable only to each respective waveband, and thus a contact equilibrium for each waveband, as if the wavebands were chemical substances.Chjoaygame (talk) 06:49, 24 January 2013 (UTC)

the amplitude of the vibrations is also zero

The lead includes the clause "the amplitude of the vibrations is also zero". This is not good enough. I will leave it to the current activists to fix it.Chjoaygame (talk) 02:06, 24 January 2013 (UTC)

I mean to say 'what vibrations'?Chjoaygame (talk) 00:05, 25 January 2013 (UTC)

Temperature is an intensive property, meaning that it does not scale with the size of a system

The lead now includes the following: "Temperature is an intensive property, meaning that it does not scale with the size of a system, ...". This is vague and unsatisfactory for a lead. It is not rescued by the next clause "and that it can vary from one location to another." It is not enough to define intensiveness by saying that it is not a scaling property. I will leave it to the current activists to fix.Chjoaygame (talk) 01:52, 24 January 2013 (UTC)

Done, I hope.PAR (talk) 06:08, 24 January 2013 (UTC)

Not substantially. I think it very useful to say that it can vary from place to place.Chjoaygame (talk) 06:36, 24 January 2013 (UTC)Chjoaygame (talk) 06:37, 24 January 2013 (UTC)

It matches the language from Intensive and extensive properties pretty closely. How much more do we want? Don't we just want to make the point that two 30°C bricks don't sum to 60°C? Spiel496 (talk) 02:38, 25 January 2013 (UTC)

I can't understand what this means: It refers to the state of matter or radiation in a locality, and can vary between locations? It's awkward-sounding. Would it be equivalent to say "Temperature can vary with location."? Spiel496 (talk) 20:01, 25 January 2013 (UTC)

Or "It is a property of matter or radiation that can vary with location"?. Do we really need to say that temperature has spatial variation? The alternative would be a universe with uniform temperature. Everyone knows that isn't the situation. Spiel496 (talk) 20:09, 25 January 2013 (UTC)

It is important that it refers to a state of matter. The state is most primarily one of thermodynamic equilibrium or local thermodynamic equilibrium. The state doesn't have to be one of those, but they are important for basic understanding. They don't need to be spelt out here, but some indication of them should be given, even though implicit; readers have intuition to some extent. The idea of spatial variation is an ordinary language intuitive indication that it is intensive, without the actual technicality right here.Chjoaygame (talk) 23:35, 25 January 2013 (UTC)