Not in the classic mass & velocity sense I suppose, but if I inject a quantum of heat into a substance, can I predict what the temperature will be a given distance away from the point of heating after a period of time? And if I give the surface a blast of heat energy, can I determine the speed at which the surrounds will heat up?
Thanks
M
Yes you can determine how fast heat is likely to dissipate through a medium based on the three modes of heat transfer - radiation, conduction and convection - and the properties of the medium. Likening this to inertia and momentum is not very useful IMHO, particularly as it is dependent on the medium through which it travels and not the ‘heat’ itself.
What exactly is a “quantum of heat”? Heat is energy moving from a low to a high temperature. I suppose a single virtual photon or somehting is quantised, but I’m not sure I follow what you mean by this expression.
It’s trivial if you know the thermal density, heat capacity and conductivity of the substance itself and it is isolated in a vacuum. If it’s touching other objects including a gas then it gets trickier. But teh answer remians yes, within limits.
Not sure what you mean by “blast of heat energy”. IR radiation? Hot air?
Anyway if you know how much energy you’ve put into the object and you know its vital statistics and those of the surrounds (gas compositon, temp, flow etc) then yes, you can determine the speed at which it will heat up.
It is in fact pretty easy to predict the future thermal behavior of a body after you inject a package of heat.
If you think of the body’s temperature profile as being the sum of various sine and cosine waves with frequencies such that there are 1 and 2 and 3 waves etc across a dimension of the body, then these sine and cosine waves will all decay exponentially but maintain their frequency and phase. The relaxation times for these decays will be inversely proportional to the square of the frequencies and to the ratio conductivity over heat capacity (AKA thermal diffusivity).
If you think you recognize the Fourier transform in this approach, you’re right. This was actually the problem that Fourier developed his transform to solve.
Actually if an object gains heat its mass does increase. I realize that’s not your question but I thought I’d throw it in for the hell of it.
Heat doesn’t need to move; it’s simply thermal energy.
In crystalline materials, heat is quantized in phonons, which are also the quanta of sound.
It’s usually defined as energy in transit, but it can be considered a measure of energy inherent in a system by virtue of the movement of particles in that system.
Cool video in that link! It should be emphasized that this is only true for crystalline solids, as you say. I don’t think the OP wanted to confine the discussion to only those types of materials.
Can you expand on this concept, I’m not familiar.
Sure. Einstein’s relativistic equation that relates energy, mass, and momentum is:
E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup]
Or setting c = 1
E[sup]2[/sup] = m[sup]2[/sup] + p[sup]2[/sup]
Where E = energy, m = mass, and p = momentum
So if p = 0 (object at rest) then E = m or m = E
So, anytime an object gains energy that can’t be transformed away its mass increases.
Again, just for the hell of it, here’s a few other unintuitive things the above equation says:
Even though a single photon has no mass, a system of photons that has a center of momentum frame does have mass.
A system consisting of a rock and a photon has more mass then just the mass of the rock.
A vault that contains a nuclear explosion has the same mass both before and after the explosion.
Mass cannot be converted to energy.
Heat is a form of energy. Any form of energy which doesn’t change the total momentum of a system is part of the mass of that system (that’s actually exactly what mass is). So the heat of an object is part of the object’s mass. It’s absolutely miniscule compared to other forms of mass, but it’s there.
For really cool physics, when the phonons interact with elastic collisions, they behave similar to the particles of an ideal gas. And exhibit the emergent behaviors of ideal gases, like, for example, sound. So, under certain conditions, the sound “particles” in a crystal can themselves form propagating longitudinal “sound” waves, called second sound.
And because in crystalline materials, thermal energy propagates via these same phonons, the second sound manifests as fluctuations of heat. Literal heat waves.
Materials have conductivity and a certain heat capacity. This is analagous to a resistor in series with a capacitor. If the heat itself has inertia the result should be the possibility of oscillation in the heat flow. Is there any such thing?
See my previous post. Second sound is such a thing, but only occurs under very specific conditions.
I think I used to know this, but if I did, I no longer remember it, so let me ask someone who seems to know this stuff.
In the Cooper pairs explanation of superconductivity phonons come into the picture in some way or other. Would you, or Chronos if he’s still around, be so kind as to enlighten me?
Ah yes. I read your post but didn’t see it’s signifiance until I re read it.
I hope you don’t mind, but can you continue to fight my ignorance?
I thought that’s what the point of E= m c^2 was?
Mass can’t be converted to energy, because mass is always energy. It’s just energy which doesn’t have any momentum. And no matter what you do with a truly closed system, the amount of energy which doesn’t have momentum will remain exactly constant, so mass, in a strict sense, is conserved.
However, it’s often practical to look at non-closed systems, or to break a system up into subsystems. When you do this, mass may appear to be converted to energy. For instance, if I take an electron and a positron (antielectron) at rest relative to each other, the system consisting of those two particles has a certain mass. If the two collide, then they’ll turn into two high-energy photons, which fly away in opposite directions at the speed of light. If I look at the system consisting of the two photons, I’ll find that the total mass of that system is exactly the same as the total mass of the electron and positron. However, it might also be interesting to look at the photons one at a time. If I do this, I’ll determine that each individual photon has no mass, and that all of its energy is kinetic energy.
Chronos is a real honest to God physicist, and I’m not. Nevertheless I feel compelled, in a nit picky way, to disagree with him.
I think it’s very misleading to think of mass evaporating or something, and then out pops energy. Mass isn’t a thing, it’s a property of a system with energy that can’t be transformed away. If you’re consistent in defining your system then mass is absolutely conserved, just as energy is.
When you combine quantum mechanics with special relativity you wind up with a theory where the number and type of particles can change. So it’s a convenient shorthand for physicists, who know what they’re talking about, to say that mass and energy are interconvertible. But I think it’s misleading as hell to people who aren’t physicists.
If you’re going to use the term then I think that it should be made very clear that you’re talking about a local mass defect and not a global one. Otherwise it can seem pretty confusing when it’s said that a vault containing a nuclear explosion weighs the same both before and after the explosion. If it weighs the same then how can mass have been converted to energy and why did the pressure inside the vault increase?
It seems much clearer to say that some of the potential energy of the nuclei has been converted to kinetic and electromagnetic energy. In other words one form of energy has been converted to another. Why confuse the issue by saying that mass is converted to energy when clearly it has not.
Cooper pairs are charge carriers that are coupled together by phonon interactions.
In free space, two electrons will experience a repulsive force due to their direct electromagnetic interaction. Basic Coulomb’s Law, plus magnetic effects from motion.
In a crystalline material, in addition to that force, there will also be forces due to the atomic lattice and all of the other electrons. In a conductor, the net effect on the almost free (valence) electrons is that they move freely, but with a complicated energy-momentum relation.
Phonons (quantized lattice vibrations) will also have complicated energy-momentum relations. Phonons are not charge carriers because they can not convey charge from location to another, but do have energy and momentum, and are important for understanding the properties of a material.
So, the crystalline material will have electrons and phonons. These can interact in different ways. Simple electron-phonon scatter is the quantum-mechanical source of electrical resistance. Electron-phonon-electron scatter is more complicated. A simple diagrammatic explanation:
Initial conditions, arrows represent momentum:
<---e e---> <---p
Electron interacts with first electron, slowing it down:
<---e <--p e-->
Electron interacts with second electron, slowing it down, too:
<---p <--e e-->
The electrons are now moving away from each other more slowly. Thus, the net effect of the phonon is an attractive force.
Note that total momentum is conserved.
In free space, photons mediate between electrons, causing a net repulsive force. In the material, phonons can do the opposite. Under certain conditions (depending on the exact energy-momentum relations of both the electrons and phonons), the electrons will experience a net attractive force. This bound pair of electrons is a Cooper pair.
Cooper pairs are charge carriers, but unlike electrons, they are bosons. Electrons are fermions, which prevents any two electrons from occupying the same state. Bosons do not have that prohibition. The Cooper pairs can all fall into the same low-energy state without conflict. This is what allows superconductivity. It is analogous to a superfluid and a Bose-Einstein condensate.
Sorry, that turned into a condensed matter lecture. Hopefully a few of you can get the gist of it. 
Edit: corrected meaningful typo.