[FRIAM] Entropy Redux

[Santafe]

Volume and Temperature are state variables.  Pressure is a state function of the other state variables (including composition, which I assume you mean to be the same in the two volumes, though this was not said).

If volume and temperature (and composition) are the same now, then the pressure state-function of the others is the same as well.  “State function” means history doesn’t matter, given any sufficient set of values to fix the state, which V and T (and composition) would be.

So expected movement of a divider is zero.  An actual divider would undergo a Brownian motion if there were no mesoscale movement in the air volumes.  But it there is movement in the air volumes, and your divider is soft, then it will be sloshed around according to whatever that other movement is.



> On May 28, 2025, at 11:58, Nicholas Thompson <thompnickson2 at gmail.com> wrote:
> 
> Side by side, butt-to-butt, two cylinders of air, of equal volume and equal temperature, but different histories. They are separated by a frictionless sliding divider which is now pegged.  Before compression or heating, both started with air at 10 degrees C, and after compression or heating, both arrive at 20 degrees C. The left one has arrived at its present temperature and volume by being compressed, the right-hand one by having its volume set to the same value as the left and then having contents  heated.  All compartments insulated, all manipulations quasi-static.  Now, remove the peg, allowing the partition between the two parts to slide, one way or the other.  Which way would it slide and why. What would your explanation be?  Please don't read others' answers until you have submitted your own.
> --
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology
> Clark University
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