Heat conduction in solids: Why is it so slow?

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Kasuha
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Re: Heat conduction in solids: Why is it so slow?

Post by Kasuha » Thu Nov 25, 2010 7:47 pm

Sorry to disturb but I'd like to know how, using your neat theory, would you like to explain the fact that if you hit an anvil with hammer, the anvil becomes warmer in the place where you did hit it.

I'd also like to know how you'd like to explain that gases, liquids, and solids extend their volume when heated up at constant pressure - or increase the pressure at constant volume. And why they lose heat when pressure decreases.

And finally - how comes the black body radiation spectra so well match chaotic motion, because with circular the spectrum would look completely different.

And when you become bored by thinking about that, you may read a bit about history of heat.

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Tim_BandTechDotCom
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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Sat Nov 27, 2010 2:18 am

Chelle wrote:
Tim_BandTechDotCom wrote:Also enjoyed the acoustic dust experiment, though I suspect the rotation there is a side effect of the transducer.
Don't you think it might be caused by Static Electricity, that goes over into a current due to the frequency pattern, generating an electric motor?
I was thinking that the CW and CCW standing waves, if the transducer is a voice coil type of speaker, could be due to some slight out of axis action, either due to the coupling of the speaker to the membrane, or just due to the voice coil itself being slightly out of center. Just picture dinging it out of center a bit, then that orbital motion sustaining itself through the energy supply of the motion.

I don't feel strongly about the circulation current, but suppose that during high pressure (voice coil up) the dust is compressed, then while the voice coil drops it's like the dust's momentum is freeing it from contact. This isn't really a full development of that circulation current though. Ahh... perhaps it is like soil loading: at the center the best loading occurs, so that the central dust is lifted most effectively, leading to flow up and out the center; eventually causing circulation.

Anyway, the trouble with heat as vibrating atoms is most apparent in solids. Crystalline solids don't have much freedom, and as far as I can tell the freedoms that do exist are all acoustic in nature; mechanical action. These go so far as the elastic limit of the solid and up to the point that the inertia of the atomic structure fails to respond to a high frequency stimulus. I think this point is worth studying, and I see Kasuha is onto it a bit.

- Tim

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Re: Heat conduction in solids: Why is it so slow?

Post by chelle » Sat Nov 27, 2010 8:35 am

Tim_BandTechDotCom wrote:Anyway, the trouble with heat as vibrating atoms is most apparent in solids...
You might want to check: http://en.wikipedia.org/wiki/Molecular_vibration
A molecular vibration occurs when atoms in a molecule are in periodic motion while the molecule as a whole has constant translational and rotational motion. The frequency of the periodic motion is known as a vibration frequency. The three atomic molecule have three modes of vibration irrespective of whether these are linear or nonlinear. The molecules with n(n must be greater than 3) atoms has 3n−6 normal modes of vibration, whereas a linear molecule has 3n−5 normal modes of vibration because rotation about its molecular axis is simply a rotation of the reference frame and cannot be observed.
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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Mon Nov 29, 2010 12:19 am

Kasuha wrote:Sorry to disturb but I'd like to know how, using your neat theory, would you like to explain the fact that if you hit an anvil with hammer, the anvil becomes warmer in the place where you did hit it.

I'd also like to know how you'd like to explain that gases, liquids, and solids extend their volume when heated up at constant pressure - or increase the pressure at constant volume. And why they lose heat when pressure decreases.

And finally - how comes the black body radiation spectra so well match chaotic motion, because with circular the spectrum would look completely different.

And when you become bored by thinking about that, you may read a bit about history of heat.
I don't think that it is boring at all. If anything the existing theory strikes me as incomplete. We are in a gray age I think, where much progress has been made, but some of the foundational steps are still up for grabs, and this means that if those fundamental theories change that the top accumulation will be dubious. In terms of the anvil and hammer I've not read any convincing description within the existing theory, which fuels my statement here on the incomplete nature of the modern state. It is fair to say that we are farther along than ever, but that does not mean that we have crossed any sort of a finish line. As to what is still open for discussion: this is a meaningful step to consider, and within academia this discussion does not seem to go on very much. There are mechanisms that can be used to explain this, but regardless, we can pose all problems as open, and this keeps the discussion much more lively.

Now on to the hammer and anvil. I think there are some general statements to make that are important within this context. One is that all mechanical energy will eventually be converted to heat unless it endlessly vibrates (mechanical vibration, that is), and even the best resonators do diminish, and even if they radiate some of their 'sound' that even that sound will be turned into heat at some point, or some other form of energy, but generally we accept heat as the loss mechanism in most of physics, electronics, and mechanics.

Next, we should not forget that there are other processes going on, such as work hardening, and that should the hammer swing hard enough against the anvil that the material may deform or if work hardened perhaps even fracture. A blacksmith allowed me to use his setup earlier this summer and warned me not to hit the anvil directly, but always to hit the work, which is generally hot and soft, and especially in that state the delivery of the hammer's heat is more profound.

I prefer to consider a crystalline solid model, and the anvil is close, but is composed of grains of more crystalline material, and as that material becomes brittle then that is the work hardening, which causes fractures, which is exactly what we might see if the hammer his a crystal with sufficient force. This seems a digression, but we've exited a clean model of a crystalline solid and gentle forces on it, so I am grappling with the problem and can't help but see these side effects. Now, what we really want is a mechanism of how a hammer blow which is mechanical translation can turn into heat, which is under my own proposal a rotational mechanism.

One means to arrive closer to an answer is to consider that a resonant bar will not yield to this heat transformation as readily as will a bar that is not so resonant; at least not as rapidly. I do not have numerical answers for these details, and in ordinary circumstances we have the radiation of sound energy outward through air typically, which is an impedance that should be removed from the problem. So ideally we would be in Einstein's elevator, with no bottom floor, in a vacuum, and we would arrange the hammers to hit a bar so that the bar does not leave the reference frame. Since we've gone to gedanken land let's just get rid of the hammer altogether, and create the initial conditions of the bar flexed well within its elastic limit.

Given these perfect conditions, for a perfect bar of even dimensions (the resonant case), and staying within the standard atomic model, the best mechanism that I see is interactions between the electron shells and the nuclei of the atoms. We could regard the action of the nuclei as delayed relative to the actions of the electron shell, which we should think of as symmetrically bonded in chains in three directions; a standard cubic lattice arrangement (Cubic P in Kittel). Additionally we have the transverse versus longitudinal action, and we see both exist in a bar which has been flexed and is in free vibration. Indeed what we witness is that portions of the bar do have rotational components, and are varying at the frequency of vibration, which is a function of the bars long dimension, and the density of the bar.

To expose this rotational behavior of the bar let's just look at one end of the bar and consider its position at the maximum extents of its oscillating motion. We see that at these positions an elongated side of the bar and a compressed side. Thus we have two longitidunal modes out of phase with each other if we consider the directions of propagation to be longitudinal. But also we have to admit that the motion of the end is orthogonal to that mode, and so accelereration is occuring in the orthogonal direction as well, and so there are forces present which are of the transverse mode. Regardless of these complications of the standardized modes of wave propagation, we see the end of the bar rotates a small angle theta between the two extents, and so any interaction between the electron shells and the nuclei that can impart the rotational component can be absorbed into the nuclei. I have to stress that I do not have this mechanism, and further that the ability to impart this rotational momentum into an object whose mass is all at its center of mass (the standard atomic model) is dubious. This is one reason that I suggest that the standard atomic model could be flawed. While the isolational freedom of the nucleus to rotate is good (loosely coupled), its rotational moment is too small, especially at the low frequencies of mechanical action we are considering as for say a one meter bar of aluminum vibrating at its fundamental frequency.

Next would be to explain a rise in this thermal conversion process for a bar that is not very resonant(say twice as wide at one end as the other) and I will just quickly suggest that it is the transverse mode that can be converted easiest if we regard adjacent courses of atoms to be out of phase slightly; this phase problem increasing with the non resonant form.

OK. I wrote way too much here, but that somewhat means that you have asked for too much. What I would like from you now is the standard explanation of how heat comes to be generated from a low frequency mechanical vibration in a resonant bar, and a reference to that description on the internet would be most helpful. I am not asking for your own interpretation, but since thermodynamics is dead and done the accepted account by the pros. I seriously doubt if you will find one.

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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Thu Dec 16, 2010 11:50 pm

Tim_BandTechDotCom wrote: OK. I wrote way too much here, but that somewhat means that you have asked for too much. What I would like from you now is the standard explanation of how heat comes to be generated from a low frequency mechanical vibration in a resonant bar, and a reference to that description on the internet would be most helpful. I am not asking for your own interpretation, but since thermodynamics is dead and done the accepted account by the pros. I seriously doubt if you will find one.
Still haven't heard anything here. Just did a fresh search and find nothing directly related to the topic of how a hammer blow turns into heat. This is because the discrepancy between mechanically vibrating atoms and heat as vibrating atoms is ignored. We know that the rate of propagation of a local perturbation of mechanical energy through a long bar of material is extremely rapid relative to a local heat perturbation. The fact that the distinction is not clearly explained requires that the heat interpretation remain open.

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Re: Heat conduction in solids: Why is it so slow?

Post by adam_jeff » Wed Jan 12, 2011 1:03 pm

The rate of heat propagations is slow because the amplitude of the vibration is small. This means that the perturbation to neighbouring atoms is also small. the energy in a vibrating atom is a function of the amplitude and the frequency of vibration. Increasing the heat energy increases the frequency of vibration, not amplitude.
Sound energy on the other hand consists of low frequency, high amplitude vibration. Since the displacement of the atom is much larger, the effect on neighbouring atoms is also much larger. That's why sound travels faster.

You touched on another reason when you mentionned specific heat. In most materials, a small temperature increase actually holds quite a lot of energy. In the aluminium bar you said that 4.5 watts would be transferred [ I didn't check your calculations ]. Well that's equivalent to an audible noise level. Maybe the rate of energy propagation isn't all that different for sound / heat - just that we need a lot more heat energy for a measurable difference than sound energy.

To explain the hammer / anvil thing is easy. When the hammer makes contact it displaces atoms in the anvil. A few (surface) atoms receive large displacement - this affects neighbouring atoms and the resulting sound eave travels outwards. But many other atoms receive a much smaller displacement. They start to oscillate about their equilibrium position ( determined by electrostatic forces within the cristalline lattice). And voila, that's heat.

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Re: Heat conduction in solids: Why is it so slow?

Post by Kasuha » Wed Jan 12, 2011 2:17 pm

Regarding the heat transfer - I have finally found how the thing I had on mind is called in english (hooray!). It's coupled oscillators.
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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Tue Jan 18, 2011 7:33 pm

adam_jeff wrote:The rate of heat propagations is slow because the amplitude of the vibration is small. This means that the perturbation to neighbouring atoms is also small. the energy in a vibrating atom is a function of the amplitude and the frequency of vibration. Increasing the heat energy increases the frequency of vibration, not amplitude.
Sound energy on the other hand consists of low frequency, high amplitude vibration. Since the displacement of the atom is much larger, the effect on neighbouring atoms is also much larger. That's why sound travels faster.
You are posing a nonlinearity here that is not convincing. Are you suggesting that if I were to shift one end of a metal rod by one micron that the other end might not move one micron in the same direction? Would this be a small amplitude vibration? The characteristic of this lower limit does not exist as far as I know. If this is a continuum behavior then as the amplitude is increased we would the see the rate of propagation gradually rise, which we do not observe. The discrepancy between the speed of sound in a metal rod versus the conduction heat is many orders of magnitude. It seems to me that a mechanism that would yield your interpretation would be necessary.

I do appreciate your attempt, and it is unique, but I don't believe that it is convincing. Still, that you offer up such an explanation exposes that you are open to the discrepancy. Here you have maintained both heat and sound as vibrating atoms consistent with existing theory, but as far as I know there is no condition on amplitude of vibration.
adam_jeff wrote: You touched on another reason when you mentionned specific heat. In most materials, a small temperature increase actually holds quite a lot of energy. In the aluminium bar you said that 4.5 watts would be transferred [ I didn't check your calculations ]. Well that's equivalent to an audible noise level. Maybe the rate of energy propagation isn't all that different for sound / heat - just that we need a lot more heat energy for a measurable difference than sound energy.
Well isn't this another disproof of your own explanation? At 4.5 watts the heat would have turned into the higher rate of propagation form wouldn't it? I assure you that the rate of propagation of 4.5 watts of heat energy is remarkably slower than the 4.5 watts of sound energy. The sound energy can be transferred in milliseconds whereas the heat energy will take many minutes. Please do check the computations that I did. We could do the similar computation for sound.

To explain the hammer / anvil thing is easy. When the hammer makes contact it displaces atoms in the anvil. A few (surface) atoms receive large displacement - this affects neighbouring atoms and the resulting sound eave travels outwards. But many other atoms receive a much smaller displacement. They start to oscillate about their equilibrium position ( determined by electrostatic forces within the cristalline lattice). And voila, that's heat.
No, when you state that they start to oscillate this oscillation is based in lattice interactions. They cannot just oscillate on their own, until, that is, we introduce rotational freedom. The 'vibrating atom' interpretation requires interaction, and this is exactly the criticism that I have of the standing heat interpretation: it must be more loosely coupled since collisions propagate through the lattice rapidly.

Thanks adam_jeff for your response. I'll try to check back in some time soon.
- Tim

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Re: Heat conduction in solids: Why is it so slow?

Post by adam_jeff » Wed Jan 19, 2011 9:57 am

1. The difference is between an oscillation and a one-way movement. If you shift the metal rod by one micron, then after an extremely short time the other end will also move by one micron. But if you oscillate one end of the rod with an amplitude of one micron, the other end will oscillate with a smaller amplitude.
In any case, I'm not arguing for heat as a slow-moving wave. The wave speed (phase velocity) might be the same as for sound. But because the wave is damped, the rate of energy transfer from end to end is smaller. You might think of it like this: if you transmit a short sound at one end of the rod, it travels through the rod and when reaches the other end, there is no sound 'left behind' halfway down the rod (although there is an infinitessimal amount of heat). But when heat travels from one end of the rod to the other, the whole rod ends up heated. You cannot move all the heat from one end to the other of the rod, because the heat 'wave' is damped over the distance of just a few molecules, so you always 'leave behind' more heat than reaches the end.

2. No it's not a disproof, it's complementary. I'm saying that, averaged over a long period, the rate of energy transfer can be similar. That doesn't mean that the energy reaches the other end of the rod after the same time, because as I explained above, the energy moves in a different way - with sound, it leaves one end and travels to the other; with heat, it spreads across the whole rod.

3. An atom in a crystal lattice can oscillate on its own, if only for a very short period after which the perturbations spread.

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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Mon Jan 24, 2011 2:25 pm

adam_jeff wrote:1. The difference is between an oscillation and a one-way movement. If you shift the metal rod by one micron, then after an extremely short time the other end will also move by one micron. But if you oscillate one end of the rod with an amplitude of one micron, the other end will oscillate with a smaller amplitude.
In any case, I'm not arguing for heat as a slow-moving wave. The wave speed (phase velocity) might be the same as for sound. But because the wave is damped, the rate of energy transfer from end to end is smaller. You might think of it like this: if you transmit a short sound at one end of the rod, it travels through the rod and when reaches the other end, there is no sound 'left behind' halfway down the rod (although there is an infinitessimal amount of heat). But when heat travels from one end of the rod to the other, the whole rod ends up heated. You cannot move all the heat from one end to the other of the rod, because the heat 'wave' is damped over the distance of just a few molecules, so you always 'leave behind' more heat than reaches the end.

2. No it's not a disproof, it's complementary. I'm saying that, averaged over a long period, the rate of energy transfer can be similar. That doesn't mean that the energy reaches the other end of the rod after the same time, because as I explained above, the energy moves in a different way - with sound, it leaves one end and travels to the other; with heat, it spreads across the whole rod.
But you have already described them as the same mechanism operating at different power levels. Low power is heat, high power is sound. If we can pass 5 watts of either sound energy or heat energy through the rod then this is an inconsistency.
adam_jeff wrote: 3. An atom in a crystal lattice can oscillate on its own, if only for a very short period after which the perturbations spread.
Well I appreciate your willingness to carry on this argument. If your #3 is true, then it will be a very important part of a proper theory. Can we extend this to the atom in vacuum? Here it is easy to see that the only type of oscillation that the atom can support will be rotational in nature.

The interaction of a ball bouncing against a wall is not consistent with the lattice interpretation, for the wall is made of balls equivalent to the ball under study. The degrees of freedom of the fluid states are greater, and this is where the traditional interpretation of heat took its meaning. Entering the crystalline state has inherently reduced those freedoms.

As I understand it you are claiming that an atom could take a positional behavior like
x = a + 1E-12 sin( t ) meters
without interacting with its neighbors, where a is a constant and merely implies the relative position of that atom. The modern understanding of the atom, especially within a crystalline lattice, is that the positions are electrically coupled, and electrical signaling is at the speed of light, so that rather than a speed of heat issue, we could nearly claim that even the speed of sound is suspect. But we do have the momentum of the nucleus in the problem, and an elasticity of even the hardest known materials to work with. Still, has anyone derived the rate of sound propagation in material based upon these? I'm sorry to say that I have not gotten this far. As I review Kittel there is something called Brillouin (sp?) zones. He also claims to disregard high harmonic frequencies (wavelengths smaller than the atomic distance) as imperceptible, which I have a hard time with. He seems to be quite cryptic, and in a textbook this is not becoming. It is a signal that what he claims to be fundamental is not necessarily so, and this is essentially my statement on the body of thermodynamics. Still, until a clean replacement theory arrives then this criticism is only marginally useful.

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Re: Heat conduction in solids: Why is it so slow?

Post by adam_jeff » Wed Feb 02, 2011 2:51 pm

To clarify my general point that heat and sound can both be vibrations within the lattice but behave diferently, perhaps this page will help:
http://en.wikipedia.org/wiki/Phonon

To clarify point 2: There's a difference in what it means to transfer 5W of heat energy and 5W of sound energy.
Let's say we transfer 5 Joules of sound energy from one end of the rod to the other and it takes one second to travel (ie 5W). Then 5J has left one end and the same 5J has arrived at the other.
If we take a cold rod, then in order for 5J of heat to arrive at the far end then far more than 5J will have to leave the near end: you need enough energy to heat the whole rod too.
Now take the 'steady state' where the rod is hot at the near end and cold at the far end, with a gradient between the two and heat flowing from hot to cold. Then we could say that every second 5J of heat leaves the hot end and 5J arrives at the cold end.
To clarify point 3: I'm not claiming that an atom in a crystal lattice can move without this affecting its neighbours. However, after the movement of the first atom there is a (very small) time delay before the next atom moves. That is the point I was making and the only one which is necessary to support 'my' theory (aka normal physics as I understand it).
The delay given by the speed of light is only the delay until the 2nd atom starts moving. The delay which is more interesting for the onwards propagation of the sound wave / heat is the delay until the 2nd atom reaches a displacement equal to the displacement of the first, i.e. the distance between them is the same as it was in the beginning. This delay is much greater than given by the speed of light, due to the inertia of the atoms.
I am not aware either if the speed of sound in a material can be derived from factors such as their rigidity, density, lattice shape etc. but I agree it seems reasonable (though not necessarily easy!) to be able to do this.

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Re: Heat conduction in solids: Why is it so slow?

Post by adam_jeff » Wed Feb 02, 2011 2:58 pm

Hah, I guess I should have read the basics before I answered that last part:
http://en.wikipedia.org/wiki/Speed_of_sound
The speed of sound is given by square root (coefficient of stiffness / density), known as the Newton-Laplace formula.

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Re: Heat conduction in solids: Why is it so slow?

Post by CharmQuark » Thu Feb 03, 2011 6:50 pm

Equilibrium wrote:Maybe because phonons are grid stable on non conductor solids and they behave like a gas in a conductor solid??

Water isnt conductor but if you add some salt to it it became conductive because the phonons??

CQ is alright if i ask??

I'm afraid asking, posting in several post could drive me mad :angry-screaming: :angry-steamingears: :scared-shocked:
I have never once said you couldn't ask anything :thumbup:
Anyone who doesn't take truth seriously in small matters cannot be trusted with large ones either by Albert Einstein.

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Re: Heat conduction in solids: Why is it so slow?

Post by Tim_BandTechDotCom » Tue Feb 15, 2011 4:36 pm

Ahh. Someone seems to be having trouble here with the control freakish nature of moderation. Welcome to the real world of human interaction; one that is filtered out of the facial journals, but not at all deleted beneath the skin. Delete the shortcomings, but they are still shortcomings. Now we have an opportunity to work in the open and what happens? Well, if this post gets through at least it happens less than one could think; still here we are on a censored media and posts whose ownership is all lhcportal.com. If you want something better take it to usenet: the first cloud.

Above here Jeff speaks of passing 5 Joules through a metallic rod in one second. I agree that if the rod is of sufficient diameter this may be done with acoustic or mechanical propagation; the difference in these two being fairly transparentp; i.e. we can operate on a continuum of periodic motions from say 0.1 Hertz to 100 kiloHertz and perhaps observe some dynamics, but mostly a well behaved system.

I do believe that if we attempt to pass 5 Joules per second through the rod as thermal energy that we will have some trouble. Let's suppose that the rod is made of aluminum and is 2.0 cm x 2.0 cm square extrusion. If the rod is one meter in length then at 250 W/(mK) I am getting a 50 degree temperature difference from end to end.

The point is that atomic vibration does not account well for the loosely coupled heat flow that requires this initial condition. How does one state the influence of one atoms vibration upon its neighbors? We have set up a condition that is asymmetrical in order to achieve this gradient, and our atoms are coupled by electronic bonds which are operant near the speed of light. But for the mass in the system there is little to work with, and so long as the mass is entirely at the atomic center then the freedoms of the problem are too severely restricted, for the rotational inertia of this atomic model is nill, which limits its interactive modes to translational interactions.

The attack on thermodynamic interpretation leads to an attack on the atomic model.
The best way to achieve the loose coupling that is heat flow is via rotational momentum within the atomic bounds, but this will require energy storage in this mode. Where do we see the rotational freedoms of the nucleus studied? I guess we have to get to MRI principles to see this. To what degree are there atomic components versus molecular components? Are the bounds between the solid state and the liquid state clearly defined? This structural integrity becomes a scalar problem. Consider for instance the rotation moment of inertia of a molecule of water with nucleated mass versus distributed mass. Clearly the distributed mass version carries more moment of inertia under rotation. This is where I predict the evidence will show up the clearest if a new atomic model is necessary.

- Tim

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