# Understanding Heat

Heat or thermal energy as understood is some kind of vibrations of molecules / atoms of the matter. If the molecules are tightly bound in case of solids, it is to-and-fro motion what we call vibration, or, it may be random motion of molecules in case of liquids/gases/plasma.

Sound, being waves, is also a vibration of matter. Why, then, if we heat one end of a solid rod, assuming rod is at least few feet in length, does it take ages for the heat to reach the other end, whereas sound reaches in no time ? (sound travels at 1400 m/s approx in solid)

Doesn't it show that heat is more an intra-atomic feature rather than an atomic or molecular motion? Given the fact that electrical good conductors are also good conductors for heat, can we assume that heat is chaotic motion of electrons (the "electron gas") or some other sub-atomic particle? The model should be correlated or validated for all the phenomena that involve heat, some of them listed below:

• Solid melts as it is heated, liquid vaporizes when heated.
• Hot material emits light (frequency of which depends upon temperature)
• Light is absorbed converting to heat.
• Microwave produces enormous heating in certain material (eg. a pan of water in a microwave oven)
• Throttling of a gas through a nozzle produces cooling (or absorbs heat)
• Mechanical friction produces heating
• Compression of gas produces heat
• Heating causes expansion in solid, liquid and gas (though mechanism may differ among the 3 states)
• Heat diff can produce an EMF and vice-versa in a thermocouple (Seebeck / Peltier effect)
• Expansion of rubber band produces heat, contraction absorbs heat
• Passage of electric current through metal produces heat
• Magnetic hysteresis produces heat
• Sound and other mechanical motions dissipates into heat
• Certain chemical reactions (exothermic) produce heat , whereas some (endothermic) absorbs it.
• Change of the state of matter produces/absorbs heat without raising the temperature (latent heat of fusion , latent heat of vaporization)
• "Heat or thermal energy as understood is nothing but motion of molecules of the matter." This is wrong. Heat is neither temperature nor internal energy. – Eric Duminil Nov 30 '20 at 13:55
• @Eric Duminil : Where did I say that it is temperature or Internal energy? – pongapundit Dec 17 '20 at 6:49
• "motion of molecules of the matter" could be used to describe temperature or internal energy. They are state functions (en.wikipedia.org/wiki/State_function). But heat is a process function (en.wikipedia.org/wiki/Process_function) and cannot be assigned to a body. For example, a lot of heat is flowing from the Sun to the Earth, as radiation. And it flows in vacuum, so your definition cannot apply. – Eric Duminil Dec 17 '20 at 10:01
• en.wikipedia.org/wiki/Second_sound – R. Emery Dec 21 '20 at 6:51

The analogy is a very good one, because heat transfer is in fact modelled by phonons, which you could also use to describe sound waves.

The crucial difference is that sound waves have a much longer wavelength (at least in the range of some millimetres) than thermal phonons (not more than a few orders of magnitude bigger than the atomic lattice scale). These small-wavelength phonons can easily scatter at any lattice impurities, while the sound waves need macroscopic pertubations (like air gaps in an insulated glazing) to do so.

• I don't really know about phonons, but I see a fundamental problem here- why should all vibrations associate with a wavelength? All waves are vibrations, but all vibrations are not necessarily waves. – pongapundit Jul 3 '11 at 5:44
• Yes they are. You can fourier-expand any vibration into frequency components, and each of these frequencies corresponds to some wavelength. – leftaroundabout Jul 3 '11 at 10:04
• Very enlightening! – Richard Terrett Jul 5 '11 at 6:58
• @leftaroundabout: I think you are confused wavelength with amplitude. Wavelength has precise relationship with frequency of vibration (for a given material, say iron or wood or air). There must be a fundamental difference between vibration due to sound waves and that due to heat. How do you model a sound wave using phonons? Curious to know. Just using a complex jargon and a jigsaw logic doesn't explain the things to a lay person like me. I am thinking in direction that heat is a intra-atomic phenomena, while sound vibrations involves molecules. – pongapundit Dec 17 '20 at 6:56
• And one more fact to correlate here is that the sound wave eventually dissipates into heat energy. – pongapundit Dec 17 '20 at 7:21

leftaroundabout gave an excellent explanation for the thermal conduction of insulators. However, in the case of metals, a significant amount of energy is carried by the excitations of electrons (the width of their Fermi-Dirac distribution). The thermal conductivity is then related to how far an excited electron can travel before being scattered, and is therefore related to the electrical conductivity. In most metals, the electrons will have a greater contribution to the thermal conductivity than the phonons.

• A very important point! – leftaroundabout Jul 4 '11 at 12:29

I feel that when a physicist speak about Heat he/she has a flow of energy in mind. Suppose that you have a rod and that the two extrema are held at different temperatures. Then the Fourier law states that there must be a flow of Heat from the hotter end to the cooler. When a physicist speak, instead, of the molecular motion he/she is thinking to the internal energy of the body.

Now when molecules and atoms are involved, it more likely that we must enter into the quantum world. By the way, we can make some few heuristic semiclassical consideration, namely we can apply Boltzmann statistics to the quantum structure of atomic and molecular spectra. A body that is immersed in a certain environment will be in thermal equilibrium state. Atoms and molecules receives energy from the thermal bath, but they also radiate energy in such a way the the total balance is "no energy exchange", therefore no energy flow, i.e. no heat flow.

We must note though that when we deal with atomic or molecular excitation levels, we are considering relatively tiny amounts of energy. Take as a reference the binding energy of the electron in the hydrogen atom, this being roughly 13.6 eV. Sounds excitations involves way more energy than this and in this case you can forget that the body has a quantum nature. You can treat it as a continuum and apply the laws of classical mechanics, i.e. the theory of elasticity and forth.

• It's more like the other way around: sounds excitations involves way less energy. You don't get around $E=\hbar\omega$ there, which means that a $440\:\mathrm{Hz}$ has an energy of only $1.8\cdot10^{-12}\:\mathrm{eV}$! [wolframalpha.com/input/?i=440Hz*2pi+hbar+in+eV] – leftaroundabout Jul 2 '11 at 20:39
• What I was trying to say is that you have to hit a rod of steel with a hammer to produce an audible sound, and this is way more than just a few eV. In this regime you can surely apply classical mechanics. – Phoenix87 Jul 3 '11 at 8:09
• The hammer may have a noteworthy energy, but without sufficient frequency this cannot be used for any kind of excitation at all. Consider an asteriod far from the sun: this has plenty of kinetic energy WRT the solar system, but the frequency is almost zero, so no excitation whatsoever can take place. – leftaroundabout Jul 3 '11 at 10:09
• I'm sorry but I don't really get your comment. What do you mean by "sufficient frequency"? Also I don't get the asteroid example. If the asteroid is travelling at constant speed w.r.t the remote stars than there must be a frame of reference where the asteroid is not moving... – Phoenix87 Jul 3 '11 at 16:16
• Exactly. Such a frame of reference only exists for a "sufficiently constant" motion, that is, for one with a low enough frequency. – leftaroundabout Jul 3 '11 at 17:49

Here is a numerical simulation of heat transfer in a thread which is only one atom thick, each number is an atom, 8 is an atom with 8 units of kinetic energy, and so on:

First left side has more heat energy:

8 0 0 0

After one collision between neighbor atoms:

4 4 0 0

After one more collision between neighbor atoms:

4 2 2 0

After one more collision between neighbor atoms:

3 3 1 1

As you see, there is some heat traveling at speed of sound. At the beginning of the simulation, when there was a heat difference of 8 between neighbor atoms, large fraction of heat energy traveled at speed of sound.

(Smell does not travel at speed of sound. If some smell was transferred when molecules touch, then smell would travel like heat energy)

• contrast that to sound traveling: 8000, then 0800, then 0080, and finally 0008 (ignoring minor volume loss) – Dale Jul 5 '11 at 3:14
• -1 as this simulation does not really address the question. You are basically solving a discretized diffusion equation. The real question is why does heat obey a diffusion equation while sound obeys a wave equation, given that both have the same physical origin, at least for the phonon contribution to thermal conductivity. – Edgar Bonet Jul 5 '11 at 8:29
• (continued) Also, your picture is wrong at the atomic scale, as thermal phonons propagate like waves. This is because vibrations in a solid are a collective motion. They are not independent atomic vibrations, with only random energy transfers between neighbor atoms, as your simulation suggests. pongapundit understood this issue, and that's why he is posting this question. The diffusion model only becomes valid at scales larger than the phonon mean free path, and leftaroundabout explained the physics quite clearly. – Edgar Bonet Jul 5 '11 at 8:30
• Well my view is that conduction of heat in solids resembles conduction of heat in gases, much more than conduction of heat in solids resembles propagation of sound in gases or solids. – jartza Jul 7 '11 at 7:11
• At the macroscopic scale you are perfectly right! But at the atomic scale, solids and gases are quite different. Atoms in a gas move more or less independently from one another, whereas in a solid they have collective motions. The difference between sound and heat in solids is then more a matter of whether you look at scales shorter or larger than the phonon mean free path. So your simulation is OK provided you realize that the “simulation cell” has to be larger than this mean free path. Now, the original question was explicitly addressing the atomic scale. – Edgar Bonet Jul 7 '11 at 9:29