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Re: [Phys-L] ?conservation of _internal_ energy



The folks on this list often go deeper into these fields than my experience
allows me. I have a question about the post that included:

"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."


If parcel one is a gas, parcel one would lose energy as it lifted parcel 2.
Parcel 2 would gain gravitational potential energy if the earth is in the
system.
If Earth is not in the system, wouldn't the earth do negative work to the
parcel removing energy from the system? So the energy would not be
constant, but it would be conserved. We could still account for energy
entering and leaving the system and the changes within the system.

In a hurry, which is very rarely a good time to type up an email, but
sending this out anyway.
Paul


Paul Lulai
Physics Teacher
St Anthony Village Senior High
St Anthony Village MN 55418

On Tue, Jan 12, 2016 at 10:24 PM, John Denker <jsd@av8n.com> wrote:

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?
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