
#1
Jun2305, 07:31 PM

P: 250

Hello,
I got into a debate with someone about the term "molecular temperature." I said "You can't define the temperature of a single molecule. It doesn't make sense." And they said. "But look at all these papers where people use the term molecular temperature. They must mean the temperature of a single molecule." I said "I don't know what they mean, but they can't mean that." So can anyone out there answer this? ********************************************************** Here are some examples of its usage: Coherent matter waves of fullerenes: http://arxiv.org/abs/quantph/0412003 http://arxiv.org/PS_cache/quantph/pdf/0402/0402146.pdf Femtosecond laser absorption studies: http://www.chemie.huberlin.de/ernst...bstract27.html Computational molecular dynamics: http://www.nd.edu/~izaguirr/papers/SAC03_MaIz0x.pdf http://cphys.s.kanazawau.ac.jp/icc...html/p249.html Ultracold stuff: http://newton.ex.ac.uk/aip/physnews.393.html http://www.aip.org/enews/physnews/2002/split/6152.html Gasphase electron diffraction: http://www.genetical.com/dc/Scientif...PED/Usage.html Atmosphere?: http://www.sworld.com.au/steven/space/atmosphere/ ********************************************************* So can someone please explain what any of these people mean when they invoke the phrase "molecular temperature"? I seriously doubt that they mean the temperature of a single molecule. 



#2
Jun2305, 08:20 PM

P: 54

In my opinion, the term "molecular temperature" does make intuitive sense. A single molecule can have excited electronic states, vibrational states and rotational states. The molecule may also lie in an external potential well, in which it is bouncing around. All of these excitations contribute to the molecule's "temperature".




#3
Jun2405, 02:07 AM

P: 1,294

It is possible to define temperature for any system that has multiple ways to store a given amount of energy. The key missing point in your understanding is that you don't know wat temperature is.
Is it some kind of measurement of the average energy? No, and this is a common mistake. In order to understand what temperature is, you must understand what entropy is. Entropy is the number of ways a system can arrange a given amount of energy. Think about a cold object. If I add to it some energy, then its entropy goes up significantly because so many particles share so little energy (lots of ways to arrange)/. Think about a hot object. If I add to it some energy, its entropy hardly increases because the entropy is already so large. Entropy is the key to understanding temperature. Once you see how we can define molecular entropy it is easy to define molecular temperature. 



#4
Jun2405, 05:34 AM

P: 416

What is meant by "molecular temperature"?Thermal temperature is a old concept, it is derived from thermal entropy and it applicable only to macroscopic bodies. Statistical entropy is a modern quantum generalization like statistical temperature. It is applicable to single molecules, atoms, or even single atomic nucleus. In fact, from quantum thermodynamics one can predict phase transitions on nucleus. For more information on molecular, atomic, and mesoscopic temperatures can see CPS: physchem/0309002 and references therein on nuclear studies (a copy will be available online in www.canonicalscience.com in brief). Note: In the macroscopic limit both temperatures agree. 



#5
Jun2505, 12:30 AM

P: 250

I just don't see how you could measure the temperature of a single molecule in Kelvins or Celcius. You would have to talk about its energy in units of energy like joules or eV or something. 



#6
Jun2505, 12:42 AM

P: 250

Instantaneously. A molecule will not be in multiple energy states at the same instant. Will it? But please explain to me why if I can define molecular entropy then I can define molecular temperature. I'm curious as to your explanation of both of these terms. 



#7
Jun2505, 12:44 AM

P: 4

If absolute zero is when particles come to a complete hault, then would the hottest temperature be when those particles are zooming around at light speed? If so, what temperature is that?




#8
Jun2505, 12:58 AM

P: 250

What is temperature if not a thermal measurement? 



#9
Jun2505, 01:00 AM

P: 250

And can anyone please explain at least what the folks who wrote the papers on the fullerene matter beams meant by the term "molecular temperature."




#10
Jun2505, 01:04 AM

P: 250





#11
Jun2505, 03:35 AM

P: 54





#12
Jun2505, 01:57 PM

P: 250

As in a strand of DNA or cellulose or something. It could be so long and wrapped up in itself and be of such a size as to have a single temperature? Apologies for the following stream: I was thinking of this too as a possibility. I brought this up to someone else and we got into a discussion about what do we mean by a molecule? Is a big sheet of crosslinked polymer like latex one big (or a few big) molecule(s)? If so, then one could consider a plate of glass one molecule or crystal or a chunk of metal a large molecule? I mean, all the atoms are continuously bonded to another atom in the same structure. We don't usually think of these things a molecules and they really aren't, but for some reason we normally consider very large but still microscopic molecules, such as in biology, as molecules. It's as if we wouldn't have another name for it. Well, macromolecule is a typical term, and I do suppose it may have been introduced to possibly differentiate between small molecules that behave very discretely and a very large polymerictype molecules. So besides all that, it doesn't seem to me that the authors of the C70 matter beam paper(s) are using the term "molecular temperature" this way. Do you think they mean the temperature of single fullerene molecules in the sense that we have discussed above? 



#13
Jun2505, 09:25 PM

P: 54





#14
Jun2605, 04:34 AM

P: 416

One can perfectly do statistics of a single molecule, atom, or nucleus, taking the different quantum states of that system like a "population". The general formula for the entropy of a system is [tex] S = k \ Tr \{ \rho \ ln \rho \} [/tex] where [tex] \rho[/tex] is the density matrix of the single molecule, atom, or nucleus and [tex] k[/tex] is the Boltzman constant. One also know the energy [tex] E[/tex] of a single molecule, atom, or nucleus, therefore [tex] \frac{1}{T} \equiv \frac{\partial S}{\partial E} [/tex] I think that you error is in believing that entropy is a macroscopic quantity applicable only to a great number of molecules, what is not true. From above definition of temperature one can obtain kinetic temperature (average of kinetic motion) and thermal temperature (internal energy [tex] U[/tex] by unit of entropy for an Avogadro number of molecules) like special cases. 



#15
Jun2705, 03:19 PM

P: 250

So where do you draw the line? At what point do decide that a molecule is large enough to have its own temperature? And at what size does a molecule stop being a molecule? Are you so sure? See, they used the term "internal energy" when speaking of the molecules. Why would they use the term internal energy in the excerpt you chose? They could definitely calculate the internal energy of one fullerene molecule. Are you saying they can also calculate the temperature? The way I read that excerpt is that they had a heating stage right near the grating to increase the temperature of the beam which is a result of varying or increasing the internal energy of the molecules. Do you see why I'm having such a hard time of this? The normal definition of temperature doesn't fit here. I sincerely doubt they mean to express in their paper that a C70 molecule has enough variation in it's states of energy to be able to calculate (couldn't measure it) an instantaneous temperature in Kelvin. I think they just threw the word molecular in before temperature to make it sound cool. I hink they just mean the temperature of the molecular beam. {edit: Yes, I see now, by actually reading the paper instead of just skimming, that they intend to mean (or mean to intend?) that the term molecular temperature refers to the temperature of single molecules.} 



#16
Jun2705, 05:19 PM

P: 250

{No, I'm just a chemist who took the word of certain professors back in the day...} This is the first time I've seen this equation. Of course, since I am a simple chemist, I've only seen something like: [tex] S = k \{ \ln \Omega \} \ [/tex] It's this sort of understanding (or really this level of understanding) and this defintion of entropy that I am working with. Or really I am thinking along the lines of relating entropy and temperature via the heat capacity of a given substance. These are all "macroscopic" terms in this line of thinking, of course. But anyway, are you saying that perhaps the equation you have above is a quantum modification or a generalization of the oldschool Boltzmann Principle? I always thought of the Bolzmann constant as was a way to relate energy to temperature, especially since it's expressed in terms of J/K. I guess here you are defining temperature as a relation between entropy and total energy? In this case would the entropy be a component of this total energy? If that is indeed what you mean by [tex]E[/tex] since it's vague to me what [tex]E[/tex] you are talking about here. Any time I see this sort of thing (where temperature is in an equation that can apply to a single particle) I assume that the temperature in the equation is the "ambient temperature" or the temperature of the surroundings. For example, when someone talks about the temerature dependence of some molecular or lattice vibration, they don't mean the temperature of the single vibration or the temperature of the single molecule, but the temperature of the surrounding medium. But, I'm probably wrong in this way of looking at things. I was really looking at a temperature as an average and nothing more. I guess you are saying effectively the same thing as Nicky. That since there is an ensemble of energy states within a single molecule at a given instant, whether they are different manifestations (ie, vibrations, rotations, electronic states, etc), that these energies can all be averaged into a temperature? So, in the oldschool Boltzmann principle, the value for [tex] \Omega [/tex] could be very small, but as long as it's more than 1, all is good? For instance when they say: It's almost like they wanted to say internal energy, but said temperature instead. Or here: But then they MUST mean the temperature of single fullerenes here: I'm convinced now, of course, that these folks are talking about the temperature of single fullerene molecules, but am I being too presumptuous in thinking that "molecular temperature" (or atomic or nuclear) cannot mean the same thing as traditional bulk temperature? They do talk later about molecular analogs to blackbody radiation, thermionic emission, and evaporative cooling, and it is obvious to me how these analogies are drawn, so the temperature they speak of is merely a molecular analog and not the same thing as a bulk temperature. Is it like thermal entropy vs. informational entropy where people use the same word to actually mean two different (but maybe analogous) things? 



#17
Jun2805, 07:37 AM

P: 416

Your BoltzmannPlanck formula is a special formula, it is not the proper definition of entropy like many (all?) physical chemistry and statistical thermodynamics textbooks argue. Only when the system is at microcanonical equilibrium being closed, without longrange correlations, external EM fields, absence of gravitatory effects, etc. the quantum state of the system is [tex] \rho = \frac{1}{\Omega}[/tex] and the BoltzmannPlanck formula [tex] S = k \{ \ln \Omega \} \ [/tex] follows from the Von Neumann definition by direct substitution. [tex] S = k \ Tr \{ \rho \ ln \rho \} [/tex]. but in general the quantum state is not defined by the inverse of number of available states. You are relating entropy and temperature using specific concepts aplicable only in determined situations. The definition of temperature is that i wrote. It is the standard definition of temperature in physicists books. It is know since 1930 at least, but irrelevant chemists textbooks ignore rigorous formulations and still work with heat engines (19th century thermodynamics). In CPS: physchem/0309002 i did a criticism to a 2002 paper by a group of very famous chemists (one was Evans) published in PR claiming for an experimental violation of second law of thermodynamics in nanoclusters. They used arguments from usual chemical thermodynamics (even a very very wrong argument from the Levine on physical chemistry, Do you know the book?). Of course all the paper was wrong. Since chemical thermodynamicians have no idea of rigorous thermodynamics. At least, two physicists published a formal comment showing that article was completely wrong with basic misunderstanding of elementary 20th century thermodynamics. A specialist from institute of microelectronic contacted with me and said that my criticism was correct, the only violation of thermodynamics "was in the title of paper by Wang et al." I have atempted to modify the ideas of chemist and correct their really great errors, but many of them ignore modern stuff and continue to publish wrong papers and books; many physicists, biologists, and enginners simply don't read chemical literature. In some cases, enginners have a more elevated level than chemical thermodynamicians like celebrated Klotz (do you know?) [tex]E[/tex] is the internal energy of the system, the notation [tex]E[/tex] is used in statistical theories and the notation [tex]U[/tex] in thermal macroscopic. However, one can introduce the total energy (internal more kinetic) into [tex]dS[/tex]. Temperature is not average. It is the definition that i said. After, in special systems and situations, it "looks like". For example, aplying the above definition to an equilibrium ideal gas of classical puntual molecules one recovers the idea of temperature like average of kinetic motion (velocity). [tex] C_{z} \equiv T \left(\frac{\partial S}{\partial T} \right) _{z} [/tex] Thermal (or bulk) temperature is above definition that i wrote [tex] \frac{1}{T} \equiv \frac{\partial S}{\partial E} [/tex] when aplied to a macroscopic system [tex] \frac{1}{T_{bulk}} \equiv \frac{\partial S_{bulk}}{\partial E_{bulk}} [/tex] Informational entropy and information temperature are other concepts; are more conceptual (mathematical) than physical. For example, one can talk of informational temperature of a trasmited message for a coaxial line but it does not signify that the coaxial is heated. 



#18
Jun2905, 04:33 PM

P: 250

That's it? It's funny, I looked through 3 P.Chem books readily available to me and the definition of temperature is never given in those terms and the equation defining temperture is not there. They all discuss it in terms of the zeroth law and how to construct a temperature scale based on an ideal gas, and that's it. I couldn't find a copy of the Levine book but I know of it. I see so many possibilities for engineers to carry the work of chemists to applications that it's crazy. Sometimes I want to try to start these things myself, but I am discouraged with "Let some engineer worry about that...":) But I looked it up and here is a desription that might make you squirm. A new, millennium edition of the classic treatment of chemical thermodynamics Widely recognized for half a century for its firstrate, logical introduction to phenomenological thermodynamics, this classic work is now thoroughly revised for the new millennium. The Sixth Edition continues to cover the fundamentals and methods of thermodynamics with exceptional vigor and clarity, while incorporating many new developments. I believe they are discussion something closer to what you wrote before that. I think they are talking about internal energy states (vibrational, etc). I work mostly with nanoparticles and the like and this may be good to know for future reference. I might have to start looking more into physics books instead of chemistry ones. It might give me an edge in understanding and I won't have the embarassment of "violating the 2nd law...":) 


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