What are the implications of work and pressure changes in thermodynamics?

[dhoyda]

Lets say we have a gas under pressure in a cylinder with my hand on the piston. I let my hand go and the piston shoots off the cylinder and the gas escapes to the atmosphere.

I take that same arrangement of gas in the cylinder under a piston and I arrange a scenario so that the gas expands to a pressure equal to that of the atmosphere. Note that the piston is still fitted on the cylinder just in a different location.

Now, I can push that gas down to the same pressure it was in the first scenario by the force of my hand on the piston head. I have done some work.

But if I want to take the gas that has escaped into the atmosphere and push it down to the same pressure with the piston that it was before I must do additional work by getting it out of the atmosphere not to mention the work that was done by pushing it down.

So the work that is the same in both cases is the work i expended to push the piston down on the gas.

What have I stumbled upon in my analysis?

 

[Zeppos10]

I really wonder what you have stumbled upon in your analysis.
If your gas happens to be air there is little diffence between the 2 cases.
If your gas is carbondioxide (to show it might be a real problem) you can expand till the pressure is 1 atm=101325 Pa (case 2). The pressure of CO2 in the atmoshere is about 30 Pa, so a lot more expansion would be needed to get there (case 1).
Maybe you can reformulate your question now ?