Thermodynamics & 2nd law

[Templar]

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)

[5614]

When a gas expands it is doing work on the surroundings. ΔW is negative.

 

ΔW = PΔV where P is pressure (constant) and ΔV is change in volume.

 

There is no thermal energy transfer. ΔQ is zero.

 

As ΔU = ΔQ + ΔW and ΔW is negative and ΔQ=0 we can conclude that ΔU is also negative.

 

Because the internal energy (ΔU) has decreased the temperature will decrease.

 

Summary:

Gas expands by doing work on surroundings.

No ΔQ.

ΔU is therefore negative.

This causes the temperature of the gas to decrease.