Re: ENERGY WITH Q

["Carl E. Mungan" <mungan@USNA.EDU>]

John Denker wrote:


> To summarize:  A key part of the algorithm is noticing where the ener=
> gy=20
> went, and whether you can keep track of the details.  If you can't ke=
> ep=20
> track of the details, it's probably thermal.

I basically agree with your analysis of course. But I am wondering
how robust it is, whether it is a bit circular. Don't you essentially
have to know the answer "in advance" so to speak. The question was,
does the energy go into thermal or nonthermal modes, and the answer
is, look at where the energy goes and count modes.

Here's another example to analyze. Maybe it will shed some more light:

A ball of clay hits a hard surface and comes to rest on it. How much
of the initial kinetic energy gets converted into thermal energy of
the clay? If you like, you may also count the immediately adjacent
portion of the surface, although I am assuming it is hard enough and
thermal conduction is low enough that its thermal energy will not
change.

Before answering too quickly, let me add that I do not necessarily
require the surface to be stationary. It might be. Or it might
originally have the same velocity as the clay and decelerate very
slowly to rest, ie. be the floor of an elevator.

And here's another question that would really help my understanding.
Are the following adjectives more or less synonymous as applied to
some energy changing process:
- nonconservative
- dissipative
- irreversible
- thermal
Try to answer from the point of view of an undergraduate student who
has had mechanics II and thermodynamics II (ie. one course of each
after the intro sequence, so that he can reasonably have been
expected to have encountered all 4 of these terms previously) rather
than from a pedant's point of view.

Robert Cohen wrote:

> Can we say that both friction and tension change the thermal energy of
> objects but friction changes it in the block and tension changes it in the
> person holding the string?

That seems partly reasonable but partly overly facile. The tabletop
and string presumably also have some changes in thermal energy. What
happens if the string is rather elastic? What if the string is
attached to a wall instead of a person: are you sure the wall gains
most of the thermal energy?

Ludwik Kowalski wrote:


> The main point is the 100% KE --> Eth conversion, not
> how the H=deltaEth is distributed at any particular
> moment. If you wait long enough (in a perfectly sealed
> room) then the final outcome should be the same in both
> cases, a change of temperature of everything in that
> room by 0.0000...1 C.

I cannot argue with this but I am not sure it is very helpful. Let us
review the situation. The standard First Law is:

W + Q = delta (E_mech) + delta (E_internal)

Note that E_mech + E_internal is the total energy of the system. For
convenience, I have arbitrarily split off part of the energy which I
call mechanical energy. Why do I do this? Because I can calculate
that portion from the work-energy theorem in mechanics:

pseudowork_nc = delta (E_mech)

where the left-hand side is the sum of the integral of the net
nonconservative force acting on part i of the system dotted with the
displacement of part i's center of mass. Here I choose identifiable
macroscopic parts of the system such as blocks, spinning wheels,
pulleys, the earth, etc.

John D's point (I think) is to question the W+Q on the left. He wants
to replace it with one term, call it net energy in.

Now your point (I think) is to question the two terms on the right.
You want to replace it with one term, call it thermalized energy at
infinite time.

Hmm, we're left with one term on left and one on right. I have
considerable doubts about this equation being particularly useful
beyond the general statement that energy is conserved. I was hoping
to solve some real problems. Find out how far blocks slide,
individual pieces warm up, gasoline consumption, etc.
--
Carl E. Mungan, Asst. Prof. of Physics  410-293-6680 (O) -3729 (F)
      U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu    http://physics.usna.edu/physics/faculty/mungan/