I thought of one more way in which «internal energy» is confusing:
It is interesting – but highly misleading – to note that if no energy
or matter can cross the boundaries of the system, then the «internal
energy» is constant. This is practically begging people to reason by
analogy to the plain old energy, which leads to the wrong answer about
conservation of «internal energy», as we see from the following table:
Constant Conserved
in an isolated
system
Energy : yes yes
«Internal Energy» : yes no ← surprise!
Some very basic questions are still on the table:
*) We know that U is conserved in trivial situations, but do
you claim it conserved in nontrivial situations, when the
parcels are actually changing speed and changing elevation?
*) Is dU = work + heat? (assuming const # of particles)
*) 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?