Solving the Piston Problem: Calculating Time for No Molecules Left

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Discussion Overview

The discussion revolves around calculating the time until no gas molecules remain in a closed system with a frictionless piston. Participants explore concepts related to diffusion, collision frequency, and mean free path in the context of gas behavior under specific conditions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the relevance of mean free path in calculating the diffusion coefficient and its role in determining the time until no molecules are left.
  • Another participant questions the characterization of the problem as a piston problem rather than a diffusion problem, suggesting a need for clarification.
  • A participant provides specific parameters of the system, including the mass of the piston, area, external pressure, and initial temperature, while mentioning the calculation of initial moles using the ideal gas law.
  • There is a request for a method to calculate the time until all molecules of gas A are gone without resorting to complex integration.
  • A later reply asks for the original question to be quoted verbatim, indicating a desire for clarity in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the framing of the problem, with some focusing on diffusion aspects while others emphasize the piston mechanics. The discussion remains unresolved regarding the best approach to calculate the desired time.

Contextual Notes

The discussion lacks clarity on the assumptions regarding the behavior of gas molecules in the system and the specific definitions of terms like "piston problem" and "diffusion problem." There are also unresolved mathematical steps related to the calculations proposed.

mojo4king
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Hello,
Piston question,i need to work out the time when no molecules are left in the gaseous system..
I have worked out the relative velocity..if i multiply that by the mean free path to get
the diffusion coefficient am i getting any closer to the answer?
I can work out the change in time using an equation involving collision frequency but i'm
guessing mean free path has to be involved somewhere..
This question had been bugging me for weeks!
Regards.
 
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I've only just seen it and its already bugging me! Could you be more specific? Why is it a piston problem and not a diffusion problem?
 
closed system,frictionless piston initially filled with gas molecules A, piston mass 100g,area 10cm2,10cm from bottom,pressure outside 1atm,temp. iniside system 900oC, i have already calculated the initial number of moles using pv=nrt...

Next using the collision flux multiplied by the area i have determined the initial rate.

Final question is how would i calculate the time after which no molecules of A will remain in the gaseous phase in the system (doesn't require complex integration).

Many thanks.
 
Please quote the original question verbatim.
 

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