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Re: first law of thermo



John M. Wrote:

O.K. You're entitled not to get excited by solutions of simple
problems, but last week you drew me in to this discussion by claiming
that Carl's solution was wrong. In one message you said it was "not
even close" and in another you said it was off by "roughly a factor
of two." It seems to me that we could have saved a lot of confusion
if you had simply told us that you find it boring!

Carl said many things, many of which were just fine,
some of which were correct but boring, and one of which
was wrong. He understandably dropped the wrong part
from subsequent discussions. If you insist on bringing
it up again, it will still be wrong.

Specifically, he calculated the non-bulk kinetic energy
and set it equal to the thermal energy. This is OK for
ideal gasses but severely wrong for almost everything
else ... off by a factor of two in typical cases.

===============

If you calculate one kind of work and then try to set it
equal to the wrong kind of change in energy you'll probably get the
wrong answer, but the mistake will be 100% yours. If you want to say
there is only one work/energy theorem then you'd better be sure that
you don't go around using different definitions of work or energy.

I agree that using different definitions can cause problems.
I hope John M. doesn't think I'm causing the problem. I
thought I was POINTING OUT this very problem by identifying
inconsistencies in the way other people were doing things.
Please don't shoot the messenger. In particular, other
people were telling _me_ about "the" work/KE theorem ... and
I was objecting.

I don't trust a formalism which produces the right answer
if you know the right answer and produces lots of wrong
answers just as easily.

At least we agree on something!*

OK.

As an example and/or analogy, consider the rule that
says odd numbers are prime.
-- yes, some numbers are odd.
-- yes, some numbers are prime.
-- yes, some numbers are odd and prime.
-- but it's not a reliable guide. You could say to the
student that sometimes it's a mistake to apply the
odd==>prime rule, and blame the student for making
such a mistake, but that seems to me to be bad science
and reeeeeally bad pedagogy.

Almost any rule, no matter how useless, boring, and misleading,
can be made technically correct by putting enough restrictions
on its domain of applicability. If you do that, however, you
take on a heavy responsibility to never state the conclusion of
the rule without also stating the limitations. So far in this
thread I've been repeatedly told that Work_cm = delta KE_cm
but I haven't seen one word about what the limitations are.
I know that it's _sometimes_ true. I know that _some_ odd
numbers are prime.

But I still think the rule is restricted to trivial situations
and useless or worse in typical situations. And you can't
prove the value of the "rule" by showing me one or two trivial
examples.

The "bulk" property of energy is a red herring.
It has no significance to thermodynamics.
It is a waste of class-time to introduce the concept.
What matters is entropy or the lack thereof.

"What matters" and what is a "waste of time" depends on the situation
and the question. So, again, fine; you don't like it. That doesn't
make it wrong.

I believe I have been careful to call
-- wrong things wrong
-- misleading things misleading
-- etc.

I stand by my assertion that separating the energy into
"bulk" energy and "non-bulk" energy is a red herring, with
no significance to thermodynamics. You can contrive
restricted situations where it is not wrong, but any
resemblance to real thermo is a coincidence or contrivance.