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[Phys-L] ?conservation of _internal_ energy



Maybe you folks can help me out here.

Most (albeit not all) thermo books emphasize the «internal energy»,
denoted U or E_in. It equals the plain old energy E minus the
center-of-mass kinetic energy of the parcel minus potential energy
terms such as gravity.

I have never been able to make sense of this «internal energy».

Most of the introductory-level books restrict attention to
situations where there is no CM KE and no GPE, so the «internal
energy» is identically equal to the plain old total energy, and
I have to wonder why they bothered to introduce this fancy new
concept if they weren't going to use it.

The distinction between U and E is significant in fluid dynamics.
Maybe I'm missing something, but AFAICT the «internal energy» is
not conserved. To see this, consider the contrast:
a) One parcel expands in such a way as to compress a neighboring
parcel. U is conserved in this situation. So far so good.
b) One parcel expands in such a way as to /lift/ a neighboring
parcel. It seems to me that U is not conserved.

For more on this, see
https://www.av8n.com/physics/thermo/state-func.html#sec-internal-energy

I have never needed to figure this out, because I've always been
able to duck the question. Rather than figuring out U, I just
reformulate everything in terms of E and proceed from there.

So let me ask some questions.
*) We know that U is conserved in trivial situations, but
is it conserved in nontrivial situations, when the parcels
are actually changing speed and changing elevation?
*) Is dU = work + heat?
*) If so, is that consistent with the work/KE theorem?
It seems to express a work/U theorem, which is not the same.
*) Is it consistent with the usual definition of force?
It seems that if (M g h) is missing from U, then (M g)
is missing from the force, which seems like a problem.
*) Is it consistent with the principle of virtual work?


This is not a burning practical issue, because in every situation
I care about I've been able to reformulate things in terms of the
plain old energy. However, it does come up in pedagogical discussions.
People ask why I don't use U. Am I missing something? Is there some
better way of thinking about U?