# Net work being done on or by the gas and the user from a volume expansion, and how doing work affects the energy of ideal gas particles

My question is well-contained in the following exercise:

Here is my thought process:

• The enclosed volume is doubled, so the pressure decreased while the volume increased.

• Even though the pressure decreased, the average kinetic energy of each ideal gas particle hasn't been increased, as it hasn't been directly supplied energy - what this volume expansion has effectively done is increase the amount of time a particle moving in $+z$ will take before hitting a container. This strikes me as a free expansion, as the pressure has decreased and the volume increased without necessarily any change in kinetic energy of the gas particles and thus no temperature change.

• I use the sign convention for the first law of thermodynamics as $\Delta U = Q + W$.
• Since $W = -\int PdV$, and the volume change is positive, $dV$ has a positive signature, so $W$ is overall negative. This implies then, that work is being done by the system, and thus by the gas, and net work is being done on the user. This conclusion is basically a resuscitation and guess from lecture notes. My intuitive reasoning behind this is really bad.

I don't like how I thought this through, but this is what came up with. I'm not confident with the second and fourth bullet points in particular. To be honest, I can't imagine how any work can be done on the gas unless the particles are given energy. Here, to me changing the volume just changes the amount of space the particles have before colliding with the walls of the container.

Thus, my questions are two-fold:

• Is net work here being done on or by the gas inside the syringe? Is net work being done on or by the user? What about my thought processes are wrong?

• How can work change the internal energy of a system if it isn't directly increase the energy of the individual gas particles (perhaps I'm trying to get at saying - without heating the system?)?

I'm also inclined to think this is a free-expansion, as it seems to me this is merely a case where a partition is removed.

• What direction is the force that the gas exerts on the piston? How does this compare with the direction of the piston displacement? What direction is the force that you have to exert on the piston? How does that compare with the direction of the piston displacement? – Chet Miller Nov 30 '17 at 22:13
• The direction of force the gas exerts on the piston, if it is indeed exerting a force on the piston, would be in the direction it moved - so along $+z$. It should align with the direction of the piston's displacement, no? The direction of the force that I would have to exert on the piston... should be also to the right as well, which would also be the same direction as the piston displacement? Perhaps I'm wrong. I mean, the forces should align with the direction of the displacement, that would make sense. – sangstar Nov 30 '17 at 22:24
• This is all correct!!! So does the gas do work on the piston? And, do you do work on the piston? – Chet Miller Nov 30 '17 at 23:41
• I certainly do work on the piston by physically moving it to the right. And while I do agree with you that about the direction of the force the gas exerts on the piston and how it would be parallel to the displacement of the piston, I'm not yet convinced that the gas actually exerts a force on the piston to begin with, so I can't instantly say the gas does work on the piston. – sangstar Nov 30 '17 at 23:43
• Suppose that you are moving the piston very slowly, much more slowly than the gas molecules? Certainly then you would agree that the gas is exerting a force on the piston, After all, it would be exerting a force if it were not moving at all? Do you really feel that there is a significant effect on the force if it moves at 1 cm per year compared to not moving at all? – Chet Miller Dec 1 '17 at 0:10