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Re: [Phys-l] T dS versus dQ

Bob LaMontagne wrote:

Sorry - I was trying to follow the thread - someone had proposed letting a weight fall through mgh to a stop. If there is no stop then the mass certainly oscillates. However, again following the thread of adiabatic, the oscillation follows the same P-V adiabatic curve during the oscillation as it does in the slow adiabat (neglecting for the moment the sound wave, etc., points that have been raised on this thread).

... which is the same thing as saying "ignoring any irreversibility in the process," which, in turn, is the same thing as saying "assuming that the gas is at all times effectively in an equilibrium state."

It overshoots the final stopping point (h) along that adiabat and then retraces itself - the net result being the area under the reversible quasi-equilibrium process - mgh.

But again, *only* if we can ignore any irreversibility, which we explicitly can't if we want to remain true to Carl's original problem specification.

The minor triumph of thermodynamics that I alluded to before is that, for a given final volume, we know immediately that the work done, the final energy, the final temperature, the final entropy, and the final pressure in Carl's scenario will all be higher for *any* process-- oscillatory, jerky, smooth, or otherwise--during which the gas is *ever* once out of equilibrium than they would be for a "slow" (or "quasi-static" or "reversible") adiabatic process, i.e., an isentropic process. This is a relatively simple consequence of the second law.

The somewhat confounding experimental fact is that, for liter-sized containers of gas, one can closely approximate an isentropic process even with fairly rapid piston motions. But that is simply a matter of experimental precision. Indeed, pedagogical lab experiments often make use of this fact and may leave students (and faculty?) with confused ideas about "adiabatic" processes. For instance, Experiment #3a on pages 11 and 12 in the lab manual for Pasco's Adiabatic Gas Law Apparatus (see, explicitly instructs students that "the gas should be compressed as rapidly as possible to make the experiment approximately adiabatic." The reason for the instruction is to get around the fact that the gas is NOT thermally insulated and it works DESPITE the fact that the rapidity itself technically insures that the process does NOT precisely follow the adiabatic gas law.

John Mallinckrodt
Cal Poly Pomona