Vacuum Expansion: Understanding the Final States of Closed Systems

[Chuck St. Lou]

I have uploaded a diagram of two closed systems in which no work can or heat can be leave the system (See attached file). One is a free expansion of a gas into a vacuum and the other is a piston with the same gas on one side and a vacuum on the other side. After the piston is released and is pushed by the gas to the vacuum side what is the final difference of states of each system after equilibrium?

 

[Mapes]

There's no difference between the two systems. If this is a follow-up to https://www.physicsforums.com/showthread.php?t=288946", note that the posters there were assuming that the piston was attached to the outside world and that energy was being removed in the form of work.

 

[vanesch]

The state will be the same, eventually. The reason is that your perfect piston will be *accelerated* by the force done by the gas on the piston. The work of the gas on the piston will be transformed into kinetic energy of the piston.

Now, or your piston is *really* perfect, and will hence collide elastically on the wall, and bounce back, recompressing the gas to its original volume V1, and expand again, and bounce back, and so forth,...

Or you will allow for some dissipation (be it in the form of *sound* and vibrations) due to this movement of the piston. It can also be that after the first expansion, the piston is *glued* to the wall, in which case its kinetic energy is dissipated as heat into the glue who did the braking.

In any case, the work done on the piston is converted into heat again, and given back to the gas (assuming negligible heat capacity of the piston itself).