Re: [Phys-L] heat content

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> > To exclude the possibility that someone thinks that some of the energy
> > of the system might have to do with the translational motion of the
> > center of mass of the system, I tend to say that the internal  energy
> > of the system increases, rather than just saying that the energy of th
> > e system increases.  I don't think I should have to include the
> > adjective "internal" but it helps clarify things.
>
> I agree with the sentiment, but in practice one needs to be somewhat more
> cagey.  Start by considering a pendulum.  It undergoes some center-of-mass
> motion, which which we can call a /collective mode/.  To a very good
> approximation the collective mode is decoupled from the thermal properties
> of the materials.  The decoupling is not a law of physics, but we can /arrange/
> for it by means of suitable engineering, e.g. invar rods et cetera.  So far so
> good.
Let me try to explain what my point here is.  I think it will take some doing.  I'll start with an assertion and try to back it up.  What we refer to as the kinetic energy of a particle is not really energy of that particle but rather energy of a system whose center of mass is at rest relative to the inertial reference frame in which the particle is said to have that kinetic energy.  As far as the explanatory and predictive power of the concept, what we call the kinetic energy of a particle only matters insofar as it is the kinetic energy of a system consisting of that particle and something else with which that particle is interacting, will interact, or could conceivably interact.  For instance, if we have two elementary particles on a collision course with each other and you want to know what set of elementary particles there might be after the collision, what matters is the energy in the center of mass frame of the system and we cans say that each particle makes a contribution to the total energy of the system that (before the particles are interacting) is its mass plus the kinetic energy associated with that particle as measured in the center of mass frame of the system of two particles.

In accord with this notion of energy, the energy of an elementary particle is its mass (up to a factor of c^2), always.  If the particle is interacting with something else, e.g. a proton in a magnetic field, the control mass system consisting of whatever is causing the magnetic field to exist, the magnetic field, and the proton has some energy of interaction, but it is not the energy of the particle.  The particle, by virtue of its motion relative to the center of mass of the system, may be making a kinetic energy contribution to the system, but that energy is the energy of the system, not the particle.

In accord with this notion of energy the energy of a system is its mass.  All energy of a system is energy in the center of mass frame of the system.  Kinetic energy associated with the motion of the center of mass of the system is energy of some larger system whose center of mass is at rest with respect to the inertial reference frame in which the original system is said to have said kinetic energy.  As such, with respect to the original system, in the words of Bernard Cleyet, such energy is external energy.

In the center of mass frame of a spinning disk, all the energy is energy of the control mass system consisting of the disk.

 In the earth frame, where the (control mass) system is the bob of a simple pendulum, the potential energy and  motion of the center of mass of the bob energy are external energy--they are not energy of the system in question.  They are energy of the earth+pendulum system.  They contribute to the mass of the earth+pendulum system, not to the mass of the bob.

I think it would be inconsistent for someone to consider the mass of a particle to be invariant but to consider what we generally refer to as the kinetic energy of a particle to actually belong to that particle.  If it were to belong to that particle then it would contribute to the mass of the particle.  I think that if someone were to object to the notion that what we call the kinetic energy of a particle cannot actually belong to the particle on the basis that it is not a physics statement but rather a philosophical statement, then they must have the same objection to the statement that the mass of a particle and its rest mass are one and the same thing.

I think the notion that what we call the kinetic energy of a particle does not really belong to the particle eliminates what I perceive to be a problem, namely that the energy of a particle depends on the inertial reference frame from which we view that particle.  In accord with the notion that what we call the kinetic energy of a particle does not really belong to the particle, the contribution that the particle, by virtue of its velocity, makes to the total energy of a system, depends on what control mass system is under consideration.  If the velocity of a particle relative to the center of mass of system B is greater than the velocity of the same particle relative to the center of mass of system A, then of course it will be making a greater contribution to the total energy (the mass) of system B.

I don't think one would have to drastically change one's language to incorporate this notion if anyone were to accept it.  What I do with the fact that the gravitational potential energy associated with the interaction between a baseball and the earth is energy of the earth+ball system, not energy of the ball, is to say that for such cases the energy is really energy of the earth/baseball system but for accounting purposes I am going to assign it to the baseball.  We can do the same thing with the kinetic energy associated with the motion of the baseball relative to the earth.  As regards the kinetic energy associated with some particle relative to an inertial reference frame, one can say that it is part of the energy of some system whose center of mass is at rest in the reference frame in question.

It is in this sense that I say that, for any control mass system, all energy of the system is internal energy.