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SOCRATIC DIALOG, PRETENDING TO BE A STUDENT.
Replying to what is below,
A simple machine used to compress a spring corresponds to
a calorimetric setup in which "latent heat" is accumulated,
perhaps in a solar house for subsequent release. Thus energy
(mechanical or thermal) can be said to be "work done on a
system" or "heat supplied to it".
Such generalization may surface naturally in a Socratic
postlab dialog. Should we immediately say NO, NO, NO?
How should the dialog continue to correct the misconception?
I will be happy to play the role of a student, if somebody
takes on the role of a teacher.
my high school teacher wrote:
OK. I would ask the student to explain to me how he would
compress a spring by heating the system, expecting that he
would contrive some sort of engine to do so. I would then
ask him if he had stored all of the heat in the spring. &c.
He should soon see the error of the parallelism he has
drawn between latent heat and a compressed spring.
*************************************************
Your question should not be answered by me, dear teacher.
I did not say it is possible to compress a spring by heating it.
I know it becomes a little longer but it is not compressed,
unless we prevent it from becoming longer. Perhaps we
can heat the spring without heating "walls" (to keep its
length constant). If we do this we have another illustration
of the idea that:
Put the spring on a piston in a cylinder containing gas. Attach
the end of the spring to a rigid support so that it cannot move
with respect to the top of the cylinder. Heat the gas and
compress the spring. How much energy did you store? How much
energy did it cost you to do so? Was all the energy stored in
the spring? (This operation may be done reversibly, by the way.)
Can you think of a way to store all of the energy expended in
the spring?
.. energy (mechanical or thermal) can be said to be
"work done on a system" or "heat supplied to it".
We heat the system and its potential energy is increased.
The only energies we learned about so far are kinetic and
potential. I am saying that work and heat can perhaps also
be called forms of energy. You are implying that this is
wrong. Should I accept this on the basis of your authority
or should I expect a good explanation in terms of what
I know so far?
I'll teach you about another kind of potential energy. You
already know about two (which you took on faith); a third
should not overly strain your credulity. Will that help any?
By the way, I was contemplating a possibility of measuring
(or at least estimating) the amount of heat (caloric, as they
used to say) entering the spring and comparing it with the
amont of potential energy stored. I suspect that the two
would be identical for a spring of negligible mass, provided
no heat is allowed to escape. What do you think?
If you constrain the ends of the spring and heat it directly
you will store only a small fraction of the energy as elastic
potential energy. There is an important difference in the
*quality* of the energy storage. Do you really think it is
possible to make a spring of negligible mass (heat capacity)?
How would you engineer such a spring? Using real numbers for
your calculation, by how many degrees celsius would you have
to raise the temperature of a steel spring to store an amount
of energy equal to the elastic energy stored when the steel
is strained by 1% in length? (Stated that way the calculation
should be independent of spring geometry.) Do you still think
a steel spring of negligible heat capacity can be made?
.. energy (mechanical or thermal) can be said to be
"work done on a system" or "heat supplied to it".