Is Work Done When a Gas Expands into a Vacuum?

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SUMMARY

The discussion centers on the concept of work done when a gas expands into a vacuum, specifically analyzing two scenarios: treating the gas and vacuum as a single system versus treating the gas alone as the system. In both cases, it is concluded that no work is done during the expansion due to the absence of resistance at the system boundary and the lack of volume change in the first scenario. The integral W = ∫PdV is applicable only in quasi-equilibrium processes, which does not apply here, reinforcing that no work is performed in this gas expansion scenario.

PREREQUISITES
  • Understanding of thermodynamic work concepts
  • Familiarity with the equation W = ∫PdV
  • Knowledge of quasi-equilibrium processes
  • Basic principles of gas behavior in thermodynamics
NEXT STEPS
  • Study the principles of thermodynamic work in detail
  • Learn about quasi-equilibrium versus non-quasi-equilibrium processes
  • Explore the implications of system boundaries in thermodynamics
  • Investigate the behavior of gases under different thermodynamic conditions
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Students of thermodynamics, physics enthusiasts, and educators seeking to clarify the concept of work in gas expansion scenarios.

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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
 
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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.
 
Thanks LawrenceC, makes so much more sense now.
 

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