Is Work Done When a Gas Expands into a Vacuum?

[db725]

Homework Statement

A gas is separated from vacuum by a membrane. Let the membrane rupture and the gas fill the entire volume. Neglecting any work associated with the rupturing of the membrane, is there work done in the process:

a) If we take as our system the gas and the vacuum space
b) If we take gas as a system

Homework Equations

W =∫PdV

The Attempt at a Solution

My answer: If we take our system as the gas and the vacuum space, because there is no volume change and the gas fills the empty space we get zero work done in the process. Is it wrong to analyse work in a purely mathematical way by that integral above?

Answer:No work done

My answer:If we take the gas as our system there is work done as there is a volume change.

Answer: No work done. Something along the lines of no resistance at the system boundary.. What does that mean?

Why is there no work done?? :(

I find it really difficult to understand the concept of work even though it seems really simple. I try to look at it from a mathematical way and still get it wrong. What's the best way to go about it.

Any help would be greatly appreciated

 

[LawrenceC]

W =∫PdV

The above equation only applies to a quasiequilibrium process. This process is not a quasiequilibrium process.

The system boundary includes both the gas and the vacuum portions. No work can be identified at the system boundary. Therefore no work has been done.

 

[db725]

Thanks LawrenceC, makes so much more sense now.