Re: [Phys-l] T dS versus dQ

[Bernard Cleyet <bernardcleyet@redshift.com>]

I find the following exercise quite interesting.  I presume each step is done over an "infinitesimal" time  (max. entropy change).

Is it valid and is it appropriate to "our" discussion?

http://jchemed.chem.wisc.edu/JCEDLib/symmath/collection/031/Isothermal_Expansion.pdf

bc substitutes googling for thought.

p.s. from John's and Carl's analysis one would necessarily use an explosive actuated piston to achieve a significant entropic compression.   A quick calc. reveals that my suggestion of using a 0.22 calibre powder actuated fastener is order(s) of magnitude insufficient.  Assuming 100 m/s  is sufficient for a measurable result, the mass must be < ~ 20 gm for the pistons.

OTOH does not a free expansion of a cylinder at 2 k PSI into another at one atmosphere or rough vacuum result in a sig. temp diff. than slowly thru a porous plug?  Even tho the cylinders have relatively high conductivity and thermal mass (sinkability), a short TC thermometer would show a difference?


On 2010, Feb 11, , at 16:30, John Mallinckrodt wrote:


cut

> Notice that a) not until the piston speed is nearly half the rms  
> speed of the gas molecules does this formula give final temperatures  
> that are even as large as those predicted for an infinitely slow,  
> isentropic compression and that b) for piston speeds much greater  
> than the rms speed, the formula gives enormous final temperatures  
> that would never begin to be realized due to rapid conduction of heat  
> to the walls.  I conclude that the formula has very limited  
> applicability and, thus, as Carl does, that the Adiabatic Gas Law  
> apparatus suffers no noticeable ill-effects due to the non- 
> quasistatic nature of the compression.
>
> John Mallinckrodt
> Cal Poly Pomona
>
> Carl Mungan wrote:
>
> > I think there's no practical problem with the Adiabatic Gas Law
> > apparatus. To be adiabatic (no heat transfer) the process cannot be
> > too slow because in the real world no thermal insulation is perfect
> > (especially since there's not just conduction but also radiation to
> > worry about). On the other hand, to be reversible (isentropic) the
> > process cannot be too rapid - compared to typical molecular speeds of
> > the gas. Well these two limits leave a big working range - any quick
> > motion of the piston by a human arm is bound to be just fine. Carl