Thermodynamics of energy storing objects (such springs,
chemical compounds or sources of emf) is a much more
advanced topic than a typical chapter on elasticity. We do
not speak about the equation of state of steel while describing
its behavior in terms of elastic moduli. A spring is ideal, its
temperature does not change no matter how much we stretch
or compress it.
Compressing a spring by heating (by which I mean
putting it in thermal contact with a reservoir of higher
temperature, T) while the length L is forced to be constant,
can be turned into a thermodynamic problem but not in an
introductory physics course. Instead of doing this we simply
observe that, in the first approximation, L=Lo*(1+alpha*dT).
We do not say that this is a state equation. We do not explain
alpha in terms of electric forces which minimize potential
energies. We do not say that processes are reversible.
Both alpha and Y are assumed to be constant. Thermalization
of mechanical energy in rapidly bent wires, or compressed
springs, is ignored in an introductory chapter on elasticity.
Hook's law has no provision for dT, even if we know how
to express k in terms of Y, or vice versa. A calculation of k,
when Y is given, is quite simple for an ideal steel rod (which
knows how to change its length without changing the cross
section) but it becomes very difficult for coiled rods etc.
That is why I think that Socrates had no right to ask the
fictitious H.S.S. character for a numerical comparison
between the potential energy stored in a chemical compound
and in a compressed spring. It was not a fair question.
Seeing the analogy was already a big accomplishment.
All this does not mean that we should be prevented from
discussing the topic. The purpose of this message is to
emphasize that discussing an exotic topic among us is
quite different from making physics meaningful in
an introductory physics course. Both are exciting and
worth focusing on, but not at the same time.
Happy Thanksgiving to everybody (except big birds).
Ludwik Kowalski