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Re: CONSERVATION OF ENERGY



Having broken ranks slightly with David Bowman on the matter of
pressure being a potential energy density in Benoulli's equation,
I now find myself in the position of differing, again slightly,
from John Mallinckrodt on the matter of internal energy. In a
posting which I consider quite instructive otherwise, John breaks
ranks with conventional thermodynamics when he says:

I hasten to add however that I *am* willing to separate out bulk (i.e.,
"center of mass") translational kinetic energy and distinguish it from
internal energy because it--in sole contrast to all other forms of
system energy--is frame-dependent and, therefore, clearly *not* a
property "of" the system.

Here I understand your reluctance to consider kinetic energy as
being internal to the system, but in classical equilibrium
thermodynamics that's just where it belongs. Let's take Ludwik's
iron block as our system. It is initially at rest. I push on it
with a constant force F over a distance s. In thermodynamics one
would say I had done work W = Fs on the system and thereby
increased its internal energy by an amount dU = Fs, all other
termodynamic coordinates being equal. "Where" is this internal
energy? it is in the translational kinetic energy of the system!
It is certainly possible to treat the work you did as a separate
kind of work, but what is gained by doing so? Would you treat
work done by twisting the system (thus conferring upon it a
rotational kinetic energy) differently from Fs? Both processes
are classified as (reversible) work in conventional terms. What
about work which simply goes into compressing an elastic system?
Same thing - the elastic potential energy is internal energy.

Ask yourself what you would do if the system consisted of a
large table and a marble? You push on the marble instead of the
system as a whole. Is the marble's kinetic energy part of the
internal energy of the system? Now let us exchange the masses of
the marble and table. Same process. Same question.

I understand the problem people are having with these concepts.
Too much meaning is being heaped upon the word "internal". Some
discussants want this to be something which remains within the
physical boundaries of the system. Some discussants further want
to require the system boundary to remain rigidly fixed in space.
Some want only to count "thermal" energy, a fallacy well treated
in John's note. The truth is that in classical equilibrium
thermodynamics there is only one kind of energy, the internal
energy of the system. There are two processes by means of which
energy can be transferred from one system to another. If energy
is transferred solely by the agency of a temperature difference
the transfer process is called "heat". All other processes by
means of which energy is transferred between systems are called
"work". All of these terms are used in other contexts; they all
appear in dictionaries with other meanings, but when we speak
them in the context of classical thermodynamics they have
precisely the meanings I have given here, and no more!

In Fermi's admirable treatise on the subject he does not use the
term "internal energy"; he calls it simply "the energy". Perhaps
we have got ourselves into this conceptual confusion because we
didn't follow his lead. After all, he does everything we can do
with our term - except getting in this muddle! He does it all in
160 pages, too, including the index*!

Leigh

*No, I didn't get this out of the trash behind LeConte Hall. I
purchased it in 1956 for $1.75, the list price then. I see it
is listed at Amazon for only $5.56, and even the list price has
only increased fourfold in forty years.