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Re: [Phys-l] T dS versus dQ

The force for a sudden movement is greater because of the mass of the accelerating piston - and it will be less to decelerate the piston to stop it. If the gas is ideal, the pressure as a function of volume - hence the force of the piston on the gas - will be the same. If the piston is pinned - as Carl proposed - and is allowed to drop until it hits a stop, the force of the piston against the gas is still just the force of the gas against the piston - any excess force goes into the acceleration of the piston.

Unless the system is allowed to radiate the sound waves to the outside, it seems the final temperature is again the same as before since the sound waves soon become part of the random molecular motion. It seems that the final entropy is the same as for the slow reversible case.

Bob at PC

For that matter, the motion doesn't even need to be
supersonic; I reckon Carl mentioned that just by
way of emphasis. Any reasonably _sudden_ motion of
the piston will launch sound waves which will sooner
or later become thermalized, raising the temperature.

To say the same thing yet another way, the force
required for a sudden movement will be greater than
the force required for a gradual movement. This
means the F dot dx (aka P dV) will be larger than
you might have expected.