On Fri, 16 Jan 2004 12:56:25 -0800, Grant Erwin

I'm not looking for a demonstration, Ned. A simple explanation would do.
If you find it "impossible" to explain then that's one thing, but could
you at least try? I'm very frustrated with people who simply assert complex
facts without trying to explain them. They do teach thermodynamics to college
freshmen, and I don't usually fail to understand concepts from freshman physics.

No doubt, and I don't doubt that you'd understand thermo as well with
some effort, if you cared to invest it, but you may have to hurt your
head more than you want to or think it's worth. . Nobody
understands it without some effort. It's a mess.

Unfortuantely, that's *exactly* what thermo profs do: assert complex
facts with equations without explaining. I never did get a
satisfactory explanation of entropy. "What is entropy"? "It's S".
Mmph.
"Yessir, but what is the meaning of it?" "It's the integral of Q/ T
over a path of integration." Oh, right, that clears it right up and
thankyouverymuch you old jerk. Passed course (got a B) by
regurgitating equations with no idea what they meant in any intuitive
or sensible context, as did the rest of the herd.

I've cracked a few books over the past few weeks and I think I sort of
understand what's going on now, but not nearly well enough to explain
it clearly and succinctly even to myself. It's not magic, but it
isn't a simple matter lending itself to a simple intuitive
understanding with simple analogies. There are too many different
and interdependent things going on: change of pressure, temperature
and volume, and energy content in the form of pressure time actual
volume (cu ft of gas at given absolute pressure) vs energy content as
heat which is not the same as temperature except perhaps in terms of
mass. I'm not trying to be obscure, that's as clearly as I can
state it given my admittedly limited present state of understanding.
This cat has a lot of tails on it.

The only "simple" observation I can offer from what I've learned from
my recent Excedrin time with the books is that energy in the form of
heat * in excess of that manifesting itself as an increase in
pressure of given volume or volume at given pressure by rasing
temperature* may not be recoverable as work. It has been
asserted several times that when gas is expanded then work is
necessarily done. I think that's an incorrect inference though I may
be accused of splitting nits for saying so. There's little or no
dispute that the available energy in the expanded gas is less, so the
energy hadda go somewhere -- but not necessarily as work. Some of it
may have been converted to heat content -- which (again) is not the
same as temperature because temperature also depends upon pressure and
volume. It doesn't leave the regulator to ambient because the
regulator doesn't run hot, so it must remain in the downstream gas --
but at least some of it may no longer be available to do work.

We've seen many places that PV = nT but T is temperature, not heat.
The recoverable portion of the heat conveyed to the downstream gas is
that which increases V (or effectively reduces V drawn from the
reservoir to Gary's point) in the regulated P pipe downstream.

Maybe the difference could be found by calculating the V and T of the
downstream gas (P is set by the regulator) from the equations in
Machinery's handbook, calculate available energy from that, and then
calculate the heat energy at that T from the relationship Jim Rozen
noted using the Stephen-Boltzmann contant for energy (per molecule, I
think) as 3/2 power of temperature. The arcane math and terminology
of termogoddammics was derived from first principles in the first
place, so maybe it'd be easer to get ahold of by doing that for one's
self.

I'll admit to not being that curious. But that may well be how a
termogoddammics course should be taught, at least for openers.
Students then might get some feel for where the hell the math
conventions, definitions and terms came from.

The exhaust gas is usually colder than ambient but not as cold as it
might be were the regulator not there because it's expanding from a
lower pressure. I think the unaccounted-for "where did it go?"
energy is heat content lost out the exhaust even though the exhaust
is still colder than ambient.

One of the laws of thermodynamics asserts that no useful work can be
extracted from the heat energy in a gas that's already at or below the
temperature of the "sink" -- in this case, ambient. That energy is
still there, but it's not available to do work. If you send that
exhaust air in a perfectly-insulated container and bring it to
Minnesota during January, I'll recover some of that energy back as
work!

At that point I called a halt to my Excedrin time in favor of Miller
time, quietly bowed out from fracas and the hell with it.
But I'm still following along!