# Finding work for a gas in a piston cylinder

1. Oct 9, 2015

### jdawg

1. The problem statement, all variables and given/known data
A gas in a piston-cylinder assembly undergoes a process for which the relationship between pressure and volume is pV2=Constant. The initial pressure is 1 bar, the initial volume is 0.1 m3, and the final pressure is 9 bar. Determine the final volume and the work for the process.

2. Relevant equations

3. The attempt at a solution
V2=sqrt((p1)(V12)/(p2))
V2= 0.03333 m3

W=∫ pdV
W=∫ C/(V2) dV
=C[-1/V]
=C[-1/(V2-V1)]
=[(p2V22)-(p1V12)][-1/(V2-V1)]

=[((900000Pa)(0.0333m3)2)-((100000Pa)(0.1m3)2))][-1/(0.0333-0.1)]

I think the answer is supposed to be W= -19.97KJ, I'm not sure what I'm doing wrong.

2. Oct 9, 2015

### Staff: Mentor

Your integration is incorrect, and your determination of the constant C is incorrect. $C=p_1V_1^2=p_2V_2^2$

3. Oct 9, 2015

### jdawg

Oh ok, the constant part makes sense. How is the integration wrong though?
I thought ∫1/x^2 dx = -1/x ?

4. Oct 9, 2015

### Staff: Mentor

Yes, that's correct, but you substituted the integration limits incorrectly.

Chet

5. Oct 9, 2015