Re: multi-step reasoning and Joule-Thompson

["John S. Denker" <jsd@MONMOUTH.COM>]

Joseph Bellina wrote:
> Thanks to all who pointed out that the Joule-Thompson gedanken is a case
> in which the volume changes but no work is done, at least in the case
> where one has a perfect vacuum on one side...I'm not so sure about the
> real case where there is no perfect vacuum.

1) The analysis doesn't require a "perfect" vacuum.  Vacuum
is just an easy-to-state initial condition;  other initial
conditions work the same way. Why would perfection have
anything to do with it?  Why does the question even come up?
After the first nanosecond, there will be a nonzero amount
of gas on both sides of the valve anyway, no matter what
the initial conditions.

2) As others have pointed out, it is easy to analyze the
case where there's initially gas A on one side and gas B
on the other side, and they each diffuse into the other.
No vacuum required.  No ideas beyond elementary equilibrium
thermodynamics required.

> This is a good example of how our private vision informs our
> communication...the issue behind many of my comments about what does or
> does not happen in a classroom.  I had been thinking entirely in terms of
> a chamber with a movable piston, so that things stay in equilibrium.

3) In the classic J-T experiment, a porous plug is used so that
the expansion is locally quasi-static.  The methods of equilibrium
thermodynamics apply directly.   Compare item (1) above.

4) A moving piston does no work, if there's no force on it.  Example:
bellows, as discussed previously.  Another example:  pumping up an
ordinary air-matttress.  As it goes from 1/3rd full to 2/3rds full,
the volume doubles.  But if you take P to be the absolute pressure
(1 Atm) the work involved is certainly not PdV.  Not anything like
that.  The bottom-line physically-correct answer is that a negligible
amount of work is being done.  There are several ways to calculate
this.
I prefer to calculate it using the gauge (not absolute) pressure, which
is negligible.  If you absolutely insist on using absolute pressure,
there is another (more complicated) way of getting the right answer,
but unthinking application of the PdV formula will give the wrong
answer, wrong in principle and wrong by a huge amount.