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On Fri, 16 Nov 2001, Ludwik Kowalski wrote:http://www.csupomona.edu/~ajm
Is it OK to say that P is also the energy per unitvolume
(because N/m^2=J/m^3)? We know that P decreasesalong the tube
as the cross sectional area becomes smaller. Thesituation
looks like an energy transformation; process.Bernoulli tells
us that P decreases by the same amount by whichthe KE (also
per unit volume) increases. What is wrong withsaying that P
is the "mechanical energy of pressure," per unitvolume? Is
this energy kinetic or potential?
Here are a few considerations that I think you will
find argue
against considering pressure itself as an energy
density:
1. If the pressure of an incompressible fluid is to
properly
represent some form of energy density, you ought to
be able to
come up with a raft of processes where that form of
energy is lost
and other, more well known forms appear in its
place.
2. You ought to be able to account for that energy
in all
processes. Consider, for instance, a 1 cm^3 diamond
under 50
kbars of pressure. What happens to those 5000 J of
"pressure
energy" when the pressure is removed?
3. The internal energy density of air at room
temperature is about
3.5p by virtue of the fact that it is essentially a
diatomic gas.
In general, the internal energy density of a gas
will depend on
what kind of gas it is and the temperature and can
always be
expressed as some number times p simply because p
has *units* of
energy density. But how does all this square with
the idea of p
itself *as* an energy density?
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona