Thermodynamics problem (zemansky 3.1)

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Titan97
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Homework Statement


Printed textbook problem 3.1 about a thin-walled metal container of volume V leaking gas through a stopcock into a cylinder with a frictionless piston at atmospheric pressure P0, asking to show that the work is W = -P0(V0 - V).


Homework Equations


$$W=-\int PdV$$

The Attempt at a Solution


The gas fills the cylinder slowly and any increase in pressure of system is countered by the upward motion of piston. So the process is quasi-static.
But how do I find final amount of gas in the cylinder?
 
You did not show the complete problem. Vo is not even defined.
 
They apparently expect you to assume that the temperature of the gas does not change during the process, and that even the gas in the original container equilibrates with the temperature of the surrounding air. They also expect you to assume that the final pressure of the gas in the container equilibrates with the pressure of the gas in the cylinder.

Chet