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Q & A: Heat conduction, radiation and vibration

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Most recent answer: 06/06/2009
Q:
Sorry for this long winded discussion but I don't think I can explain what I am exactly trying to say without doing so. I guess my confusion is over the concepts of heat with regards to conduction, radiation and vibration. For instance it seems that conduction is nothing more than one atom colliding with another and transferring momentum in the process. In this way, the particles of a gas in a box move faster at higher temperatures and collide at a higher rate than when at a lower temperature. But heat does not seem to be synonymous with linear speed. For instance, heat is often described as the vibration of the particles in a system. Also, a particle cannot know how fast it is moving, therefore linear speed is not the heat in the system...it is merely a consequence of the heat. However, in a collision, I can imagine that not only would there be a transfer of momentum, but that the particles in the collision would ring like tiny bells as a result of the collision, and that THIS is perhaps, the heat. If so, then in order to conserve energy, part of the collision energy is transferred into linear speed, and the rest as vibration in the particles (heat). But I think the vibration analogy is only partially applicable for two reasons: 1. A physical bell (or any macroscopic object for that matter), can vibrate at an infinite number of different modes simultaneously. But an atom is restricted, because, 2. The "vibration" per say would just be the time it takes for the affected electrons to return to their ground state orbitals, correct? If this is correct, then any atom in isolation and in collision with a fixed number of photons, can not radiate heat any longer than one cycle of vibration for each one of the electrons that absorbed a photon and re-emitted it, and the "frequency" of any one cycle would depend on how high the electron was kicked out of its ground state. Therefore, the time it would therefore take an isolated atom to completely lose its heat would be the frequency of the lowest energy photon involved. I am assuming that the time it takes an electron to be kicked up and then settle down equals the frequency of the photon . But the gas in the box is not an isolated atom...it is an incredibly HUGE amount of atoms all colliding with each other and constantly transferring momentum and heat, and therefore constantly having their electrons kicked out of their ground states and back again, over and over. So it seems that conduction is not as efficient as pure radiation in transferring heat because during conduction, part of the energy of the collision is "wasted" as transferred linear momentum. But also it seems that no conductive transfer can EVER be without radiative heat transfer as well...each heated atom is in the process of trying to return to its ground state and therefore is constantly radiating energy away as released photons. So I offer a hypothetical situation: Suppose the box has walls that are perfect insulators (the box is a perfect whitebody), and that there is a heating pipe that enters into and out of the box, and this pipe contains flowing, heated water. But imagine that the pipe itself acts like a perfect check valve or diode...it only allows heat to pass one way...into the box. In this situation, would not the temperature in the box slowly rise to infinity, since radiation of the heat of the water molecules is constantly being added to the interior of the box? This part bugs me. If the energy of the radiated photons is equivalent to 100deg of heat per photon, then these photons cannot cause any of the atoms of the gas to vibrate (go from ground state to higher state and back again) any faster than the frequency of these photons. Hence, once all of the atoms of the gas have reached 100deg, all of the interactions are still only 100deg interactions and the heat should stay constant at 100deg. I can only assume then that the growing amount of energy in the box is transferred into linear momentum (the linear speed of all the atoms of the gas). But maybe this is the solution. Since linear momentum is constantly increasing, a healthy portion of this overall increasing momentum is being transferred into higher heat values with each new collision. In other words, higher collision energies means part of that collision energy will be portioned out as higher linear speed, and the rest as higher energy photons (higher frequency photons, meaning deeper penetrations into the electron shells of the atoms by these photons, meaning that the deeper electrons will be kicked up out of THEIR ground states into higher orbitals and drop back down again. And since the energy of these deeper ground states is higher, then like stronger rubber-bands, these electrons will snap back quicker than ground state electrons in higher orbitals. Walla, higher heat). Or as best as I can surmise! Thank you for any replies, Tom
- Tom (age 51)
Las Vegas, NV, USA
A:
Wow- that's a record for length, but it's got some real meat to it, so I'll try to partially answer. First, let me recommend that you get a nice beginning text on thermal physics, because you're very much on the trail of some key ideas, but have parts a bit scrambled up. A good starter is "Unit T" by Thomas Moore. Somewhat more complete and advanced, you could try  "Statistical Physics: Berkeley Physics Course, Vol. 5" by Fred Reif.

Now top some specifics. In a gas, heat is indeed mainly just carried by atoms (or molecules) bumping into each other. The thermal energy does indeed, as you surmise, consist of the energy of translational motion, the energy of electronic excitations, and (in molecules) the energies of rotations and vibrations. Thermal energy automatically distributes between all these different modes. Some of these are unimportant at room temperature, for reasons that made no sense classically and thus led to the discovery of quantum mechanics. Opposite to your guess, the translational energy is mainly responsible for the thermal conduction in a gas, The internal energy contributes to the heat capacity but not to the conductance.

As you intuited, it makes no sense to describe the translational motion of a single atom by a temperature. For a collection of atoms, all heading random directions compared to the center of mass of the collection, the energies of translational motion can typically be described by a temperature, regardless of whether those other forms of energy are present.

Your speculations about the connection between typical oscillation frequencies and the time that energy stays in the molecule show the sort of curiosity we wish more of our students had. They are, however, not right. The typical dwell times of energy in internal modes are limited by some quantum mechanical effects (but not limited to just one period) as well as by effects of collisions between the molecules.

Your question about a perfect check-valve is a central one that occurs to everyone who starts to study thermal physics seriously. It turns out that no physical process will cause heat to flow spontaneously from a cooler to a hotter object. That means that there can be no perfect check valve! The valve itself becomes leaky due to its own temperature. There's a great description of this effect in Richard Feynman's "Character of Physical Law".

I may have missed some parts of the question, but that should do for now.
Mike W

(published on 06/06/2009)

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