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.