Re: energy, work, heat

[John Denker <jsd@MONMOUTH.COM>]

At 05:57 PM 9/3/99 +1000, Brian McInnes wrote:
> I would like to propose the thesis that
> (1) we all agree on a "work-energy" theorem for a particle;
> (2) we disagree on a "work-energy" theorem for an extended body' and
> (3) we must look at the consequence of the different definitions on
> applications of the First law of thermodynamics.

My take on this is that
 0) The vast majority of physicists believe that energy obeys a local
conservation law.  That is, the change in total energy within a smallish
volume is equal to the amount of energy transferred across the boundary of
said volume.
 1) The work-energy theorem is a corollary of the energy-conservation law,
where the transferred energy has been divided into "work" and "all other
forms of energy".  For a single particle, the interpretation of this is
straightforward.
 2) For an extended body, one needs to account for the possibility of
transformations of the internal energy  (e.g. converting the inconspicuous
potential energy of springs or chemicals into conspicuous kinetic energy),
but otherwise the interpretation of the work-energy theorem is straightforward.
 3) The first law of thermo is another corollary to the energy-conservation
law, where the transferred energy has been somewhat arbitrarily divided
into "work", "heat", and "all other forms of energy".

Of course, as the saying goes, "no matter what you are doing you can always
do it wrong."  For one thing, it is always possible to undercount or
double-count various contributions to the total energy.  Also,

> Some define work done by any force as the integral of the dot product
> of the force and the displacement of the centre of mass of the body.

That "definition" is inconsistent with the meaning of work as used in the
work-energy theorem, because the center of mass is not at the boundary.
Such an inconsistency will immediately lead to trouble, such as:

> a non-zero value for work done by the push of wall

OK? -- jsd