We have a box filled with gas, and a piston that can move horiziontally. There's no external pressure (such as air pressure, etc). Now, If we compress the gas by applying an external force to the piston, we do work on gas, right? Therefore [math]\Delta W[/math] should increase (I'm assuming that [math]\Delta U = \Delta Q + \Delta W[/math]). This makes sense to me. I note that the volume decreases in this process. This force seems to have done work against the random collisions of the piston.
In an adiabatic expansion, it's said that the gas does work. Against what? Plus, it's said that Q is decreased. Since this's an isolated system, this means W has increased. The gas does work, and still W increases?!? How doesn't this violate conservation of energy?
(there seems to be an error in signs somewhere, but I'd prefer an explanation with physical reasoning, rather than speaking pure-equation-wise)