Re: [Phys-l] App. for Was: Re: T dS versus dQ

[John Mallinckrodt <ajm@csupomona.edu>]

Bob LaMontagne wrote:

> With the hope that I won't get shouted down for daring to mention  
> this topic again, may I respond to JM's quoted comment:


I promise; no shouting.  ;-)

> But how excruciating must the detail be? If one envisions a  
> cylinder that is absolutely impervious to any energy transfer  
> through its walls, fitted with a piston and containing Nitrogen  
> only, and a stop inside the cylinder that prevents the piston from  
> compressing the gas to less than half its original volume - and  
> then one applies a force with one's hand to push the piston to the  
> stop in 10 seconds - and then repeat with identical apparatus but  
> do the compression in 0.001 seconds, and then let the two pieces of  
> apparatus sit for a while until all waves. etc., dissipate, will  
> there be any difference in their final states

Yes.

> - and specifically what?

I can't say, and only in part because you haven't provided nearly  
enough detail.  At the very least you'd have to know the precise  
function x(t) that describes the position of the piston as it  
compresses the gas, but that certainly wouldn't be enough.  In  
addition you'd need to know the detailed shape of the cylinder so  
that you could get a handle on how the disturbance propagates through  
the gas and back to the piston again.  But even once you provided  
enough information, calculating the precise amount of work done from  
first principles would be *very* tough sledding; I dare say impossible.

> The final volumes are identical, will the final temperatures and  
> pressure be higher?

Both will be higher than they would have been had the process been  
quasistatic.  This is a simple deduction from the fact that the  
entropy will be higher because of the fact that dissipation has  
occurred.  They will also almost certainly be different.

> If this is not a sufficient specification of process and boundary  
> conditions, what else need be specified?

See above.

JM

> On 2010, Jan 20, , at 11:04, John Mallinckrodt wrote:
>
> > It's interesting to me that the analysis of the rapid versus slow
> > compression of a thermally insulated gas can cause so much confusion
> > and I think the reason has to do with the fact that it can't be
> > easily done by simply talking about work and energy (and it can't be
> > done *quantitatively,* period, without knowing about the process and
> > the boundary conditions in excruciating detail.)  By considering
> > things like the potential energy loss of a heavy piston as it falls
> > or the kinetic energy added to and then delivered by the piston, it
> > can be tempting to suppose incorrectly that the rate of the process
> > is irrelevant to the final state.