# Volume work, absolute and relative pressure confusion

1. Feb 28, 2009

### kandelabr

hello.

i can't figure out where i'm wrong. this is the problem:

we have a cylinder, closed with a piston. the absolute pressure inside the cylinder is p0, atmospheric pressure is patm. the air inside expands isothermally to some (specific) volume vend.
i derived the equation for isothermal work directly from this one: dW = F(s)ds.

here it is (sorry for handwriting... uses less time (will learn TeX one day... )):

the final equation seems just fine, but you've probably noticed the big fat asterisk. here's why:
p0 is absolute pressure and it exerts F(s0) on the piston. but there is also patm, which does negative work equal to patm * A * (send - s0). this fact hasn't been taken into account anywhere.

where am i wrong (the thermodynamics probably isn't wrong, right? :) )

2. Mar 1, 2009

### Staff: Mentor

What you are calculating is the work done by the gas on the piston, not the net work done on the piston. The gas is not subjected to atmospheric pressure--it's contained in the cylinder.

3. Mar 1, 2009

### kandelabr

oh, i get it.
but if now i want to know how much work i can get from this piston, i need to include atmospheric pressure.