When we compress a piston, its total internal energy increases, however I don't understand why.
As the piston compresses, the temperature should change, as the total energy density increases.
As a piston compresses, work is done to compress the gas. However, this is solely fighting a differential in pressure, as well as the force to accelerate the piston. It seems none (or very little) of this energy should be imparted to the gas – so why does the internal energy significantly increase?
The last one is somewhat explicable, however, when we pull back on a piston, uncompressing the air, we're not taking energy away from the air. While the overall energy density changes, the total energy itself shouldn't, as no process is removing energy. However, it does – so where is the energy going?
Ultimately I think this comes down to: where does the energy go, and how does it get there?
Best Answer
The first law of thermodynamics says "the increase in internal energy of a body is equal to the heat supplied to the body minus work done by the body". Assuming there is no heat flow (for simplicity), this says "the increase in internal energy of a body is equal to the work done on the body". Since you are doing work on the gas, the internal energy increases.
So where does the internal energy come from? The work you're doing on it!
Think of pushing the piston. You're clearly using some force to do it, and you're exerting this force over a distance. Force times distance is work, which is a form of energy. You can picture all the little molecules bouncing off the surface of the piston as you move it. Since the piston is moving, they have a little more energy after they bounce off of it -- kind of like hitting a tennis ball with a racket. That's how they get the energy.
BTW, temperature is proportional to energy, not energy density.