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Topic: Warm; hotter; that's it. (Read 939 times) |
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Noke Lieu
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Warm; hotter; that's it.
« on: Aug 26th, 2004, 11:21pm » |
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Might sit nicely in wanted, but here goes.
I get troubled doing the washing up sometimes. My brain starts throwing questions around that I don't know the answer to.
For example: Does temperature have an upper bound? Surely, it has to, no? 
What do you reckon?
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towr
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Re: Warm; hotter; that's it.
« Reply #1 on: Aug 27th, 2004, 1:01am » |
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::It is limited by the amount of energy in the universe, but that may not be constant or limited.. (supposedly it came from somewhere, and perhaps more could come into existence the same way)::
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Wikipedia, Google, Mathworld, Integer sequence DB
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rmsgrey
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Re: Warm; hotter; that's it.
« Reply #2 on: Aug 27th, 2004, 6:47am » |
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If you pick a short enough time-scale, the amount of energy in the universe is very undefined as a consequence of the Uncertainty Principle, so for very brief moments, the average temperature of the universe can be arbitrarily large. A black hole evaporating through Hawking Radiation also gets pretty close to infinitely hot (quantisation of the area of the event horizon probably keeps it finite), and, last I heard, the Big Bang supposedly started off as infinitely hot (but actual models only start at around 10-43 seconds or so after the event, by which time the temperature was finite).
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honkyboy
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Re: Warm; hotter; that's it.
« Reply #3 on: Aug 27th, 2004, 8:13pm » |
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To answer the question, yes. Only considering a single point, and not total energy, or average temperature of the universe, what is the physical limitation to the upper bound of possible temperature? Surely a particle cannot be pushed past the speed of light. If this is not the ultimate reason for an upper temperature boundary than what else is?
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Grimbal
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Re: Warm; hotter; that's it.
« Reply #4 on: Aug 28th, 2004, 6:24pm » |
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But a real particle accelerated to the speed of light holds infinite energy. So this does not provide an upper limit to the energy in particle movement.
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honkyboy
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Re: Warm; hotter; that's it.
« Reply #5 on: Aug 29th, 2004, 1:07pm » |
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Oh, yes, thank you Grimbal. I c
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Noke Lieu
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Re: Warm; hotter; that's it.
« Reply #6 on: Aug 30th, 2004, 6:27pm » |
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Well, these are (roughly) the thoughts that went through my head. Followed by the one that I couldn't figure out...
the temperature must be of something. Heat it enough, the atoms of that something will surely fuse after a point. Which will result in a large release of energy. surely this will continue...
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rmsgrey
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Re: Warm; hotter; that's it.
« Reply #7 on: Aug 31st, 2004, 9:09am » |
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I'd have thought that once you get hot enough, nuclei would break down giving you a sort of quark soup. If you get up to high enough energy levels, you stop being able to distinguish quarks and leptons (electrons, neutrinos and some weird(er) relatives). In theory, if you get up to the Grand Unification Energy (assuming I've remembered the right catch-phrase) you stop being able to tell the difference between hadrons (matter-type particles) and bosons (force-carrying particles, eg photons).
Beyond that, I don't think any plausible theories go
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Grimbal
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Re: Warm; hotter; that's it.
« Reply #8 on: Aug 31st, 2004, 1:40pm » |
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This is very scientific and souds very impressive. But the truth is much simpler. The upper limit of temperature depends on what thermometer you use.
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JocK
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Re: Warm; hotter; that's it.
« Reply #9 on: Aug 31st, 2004, 1:59pm » |
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Quantum mechanical and relativistic issues just confuse the picture here. Rather than speaking about the temperature, one should speak about the energy per degree of freedom in a physical system with many degrees of freedom for which equilibrium has set in so that equipartition of energy holds.
(The temperature T is related to the energy E per degree of freedom via E = (k/2)T, where k/2 (Boltzmann's constant divided by 2) happens to deviate from unity only in case the system of physical units has not been chose properly  .)
In any case, the energy per degree of freedom is bounded from above and below: it can not reach value zero, and it can not reach infinity. In between, anything goes.
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xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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Patashu
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Re: Warm; hotter; that's it.
« Reply #10 on: Sep 2nd, 2004, 4:48am » |
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Cold is merely the absence of heat, not the opposite. Like darkness is the absence of light. Thus, it can be finite while heat isn't.
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Icarus
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Re: Warm; hotter; that's it.
« Reply #11 on: Sep 14th, 2004, 8:56pm » |
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Temperature measures the ratio of the change in heat in a system to the change in entropy. To obtain large temperatures, you can either add extreme amounts of heat, or you can limit the change in entropy. The first means is limited by the amount of energy available in the universe. Theoretically, this value does not change, and has never changed in the entire history of the universe. Conservation of energy is perhaps the most fundamental of all physical laws - and is equivalent to saying that the laws of physics do not change over time.
But entropy does not have any such limitation. By arranging a system to undergo minimal change in entropy when heat is added, you can obtain as high a temperature as you like, without having to invest tremendous amounts of energy into the process. Indeed, extremely high temperatures have been obtained in the laboratory by exactly this approach.
One experiment that was described in my Thermo book obtained such temperatures by going the other way: negative absolute temperatures: the component atoms or molecules of a system are allowed only a finite number of energy states, then adding more heat to the system eventually forces the majority of the molecules into the upper states. At this point, adding more heat causes entropy to decrease instead of increase. I.e. the temperature of such a system is below absolute zero.
The system used for the experiment was the nuclear magnetic resonances of a collection of atoms. I don't remember the details, but they were able to create situation where each nuclei had only a finite number of resonance states it could be in. Adding heat to the system (which happened naturally through interaction between the nuclei and the atomic lattice they were a part of) caused the nuclei to crowd into the upper states, decreasing entropy, and sending the temperature of the system skipping over the unreachable value of 0 into the negative realm. As more heat flowed into the system, the temperature continued to plummet towards -[infty]. As I recall the report, the temperature evenually skipped over -[infty] as well (since the system had a finite - if very large - number of nuclei, its values actually stepped though descrete steps rather than changing continuously - this is how it skipped over absolute zero). When the temperature skipped over -[infty], it skipped to an extremely large positive temperature, from which it eventually fell back down to the ambient temperature of the lattice.
So the answer is no. There is no upper limit to temperature. Neither is there a lower limit, even through there is a value in the middle (absolute zero) which is unobtainable.
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Icarus
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Re: Warm; hotter; that's it.
« Reply #13 on: Sep 15th, 2004, 7:59pm » |
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I had some trouble following the author's prose. It sounds like in the end he (she?) says that negative temperatures are not possible after all (as equilibrium states). But a more careful examination reveals that this argument only applies to situations with an infinite number of possible energy states: to have a negative temperature, the population of each state has to grow exponentially with the energy level. Since this would require an infinite number of particles, it cannot be achieved.
However, it can be achieved when the number of energy states is finite. And this is exactly what happened in the experiment I mentioned.
The trick to both negative and extreme (even infinite) positive temperatures is not more heat, but less entropy.
The way Temperature was defined in my thermo book (due, I believe, to Caratheodory) was to note that while the differential of heat transfer, dQ, is not necessarily exact (ie, it is not the differential of a variable of the system), the 2nd law of thermodynamics demands that it has an integrating factor:
dQ = T dS
for some thermodynamic variables T and S (dS is an exact differential). Furthermore, the values of T and S are determined up to a multiplicative constant (ie, if dQ = X dY, then there is a constant k such that X = kT and Y = S/k). The temperature is defined to the variable T. Demanding that the triple point of water be 273.16 kelvins fixes the Kelvin scale. S is defined to be the entropy of the system.
(In the above, I have taken dQ to be positive when heat is flowing into the system - otherwise we would want dQ = - T dS.)
Turning the equation around: T = dQ/dS. And thus high temperatures can be obtained by either increasing the heat flow into the system, or decreasing the resulting entropy change.
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logix128
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Re: Warm; hotter; that's it.
« Reply #14 on: Sep 22nd, 2004, 7:39pm » |
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on Aug 27th, 2004, 6:47am, rmsgrey wrote:::
If you pick a short enough time-scale, the amount of energy in the universe is very undefined as a consequence of the Uncertainty Principle, so for very brief moments, the average temperature of the universe can be arbitrarily large. A black hole evaporating through Hawking Radiation also gets pretty close to infinitely hot (quantisation of the area of the event horizon probably keeps it finite), and, last I heard, the Big Bang supposedly started off as infinitely hot (but actual models only start at around 10-43 seconds or so after the event, by which time the temperature was finite).
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::couldn't the extreme gravity of the black hole restrict the atomic vibration?::
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