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Re: [Phys-l] operational definition on heat



On 09/12/09 17:09, carmelo@pacific.net.sg wrote in part:

The quantitative
definition on heat can be defined, for example, with the use of
Calorimetry.

That may be true in a small way, but it is wrong
in a big way.

If you define heat in terms of simple calorimetry,
you might get away with it ... provided the entire
inquiry is confined to a particular type of simple
calorimetry.

When you warm something up, heat goes in, and when
you cool it off, heat comes out, as controlled by
the temperature and the heat capacity and maybe
the latent heat. The path "up" is the same as the
path "down", retracing each step in reverse. You
can consider the heat that comes out to be the
_same heat_ as the heat that went in. This type
of heat is a function of state. It seems to be
a conserved quantity. Call it caloric if you wish.
You can talk about Hess's Law in terms of conservation
of heat.

Alas what is true for caloric and simple calorimetry
is not true of thermodynamics in general. The latter
application is much more demanding.

By way of analogy, a sundial keeps time very well
if you use it properly. But if you attach a small
sundial to your arm, and pretend it is a wristwatch,
it doesn't work so well. The latter application is
much more demanding.

What works for simple calorimetry does not work for
steam engines or rocket engines or batteries, with
or without dissipation. It also doesn't work for
friction or dissipation of any kind.

In thermodynamics in general, that is to say in all
of thermodynamics except for certain very narrow
subsets, heat is not conserved. Heat content is
not a function of state.

This is a pedagogical nightmare for multiple reasons.
For one thing, students (like most other folks) tend
to be unduly enamored of definitions. They always
want you to give them "the" canonical definition so
they can learn it by rote. School often exacerbates
this tendency. Alas this flies in the face of real-
world experience and common sense, which tell us
that words often have multiple partially-overlapping
partially-conflicting meanings.

Secondly, students (if they are not completely clueless)
show up with some hunches about heat. If you give
them a "definition" that confirms their hunches, it
makes them happy. But we really shouldn't be letting
the inmates run the asylum. Happy in the short term
leads to unhappy in the long term, because notions of
heat as a conserved quantity will have to be unlearned
at some point.

Sometimes teaching is hard. Sometimes you need to
make tough choices about where to start. Sometimes
this requires starting with a brutally simplified
approximate notion, and then spiraling back to
refine it later .... but this is *NOT* one of those
times! Here's why: In the case of simple calorimeter,
if you care about heat capacity, you can perfectly
well define heat capacity in terms of energy:

Cv := ∂E / ∂T at constant V [1]

In particular you do not need a definition of heat,
operational or otherwise, since we already have
everything we need, namely a nice operational way
of carrying out experiments to measure heat capacity
in accordance with equation [1].

Let's be clear: it is perfectly possible (and indeed
highly advantageous) to define heat capacity without
defining heat. Consider "heat capacity" to be an
idiomatic expression; that is to say, you should
not try to understand it by examining the individual
words "heat" and "capacity". As Voltaire said, the
Holy Roman Empire was neither holy, nor Roman, nor
an empire.

Common sense says we should care about things that
actually matter, such as how to measure heat capacity.
In contrast, fussing about things that don't actually
matter, such as the definition of heat, is academic
in the worst sense of the word.