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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?

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"None of this energy is imparted to the gas" - Yes, it is. Pressure is force per area, and this force is the time-average over all the little incidents where gas particles hit the walls of the piston. If you compress the piston, you're imparting extra energy onto those particles that hit the wall during that compression period. –  Lagerbaer May 6 '13 at 19:33
    
@Lager Doesn't that make the total imparted energy highly variable? –  Emrakul May 6 '13 at 19:34
    
what you mean with 'none of this energy is imparted to the gas'? The kinetic energy is transformed in potential electrostatic repulsion between atoms and friction, which becomes heat –  lurscher May 6 '13 at 19:35
    
@lurscher It's only reducing the volume of the gas, and doesn't have an active force on the gas –  Emrakul May 6 '13 at 19:37
    
@Emrakul Yes it does, as are all things in thermodynamics. But since we're dealing with so many particles, all these fluctuations average out. –  Lagerbaer May 27 at 19:12

1 Answer 1

up vote 5 down vote accepted

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.

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