Conceptual Question on Elementary Thermodynamics

[Ricky2357]

1. The problem statement

Suppose we have a thermodynamical system whose state is modified by external forces. This results in a change of the internal energy of the system. If we designate by $$W_{ext}$$ the total work done during the process by the external forces acting on the particles of the system, then the conservation of energy requires that
$$\Delta U=W_{ext}$$

In the classic example of the container filled with gas whose volume can change by means
of a movable piston, the particles of the gas collide with the surface of the piston causing it to move by a small distance $$\Delta x$$ (see figure attached).
Since no external forces act on this particular system we must have
$$W_{ext}=0$$ and thus $$\Delta U=0$$. But this can not be since the internal energy of the system clearly changes.

2. Relevant Questions

Where is the flaw in my thinking?

 

[Mapes]

Most of your reasoning is fine. Your attachment isn't visible yet, but if you've defined your system as the gas only, then the piston's mass and friction result in external forces. If you've defined your system to include the piston, then the internal energy of the system doesn't change; the gas cools slightly and the piston heats up slightly from friction. Does this help?

 

[Ricky2357]

If we define the system as the container, the gas and the piston and assume that there are not any forces of friction present, then no external forces act on this system, yet the internal energy of the system changes.Is this right?

 

[Mapes]

No, the internal energy doesn't change. How could it?

EDIT: To be more clear, the gas would be cooler and the piston would be moving.