Solving the Piston Problem: Calculating Time for No Molecules Left

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To determine the time when no molecules are left in a closed gaseous system with a piston, the discussion focuses on calculating the diffusion coefficient using relative velocity and mean free path. The initial conditions include a frictionless piston filled with gas at high temperature and pressure, with known parameters such as mass and area. The user has already calculated the initial number of moles and the initial rate using collision flux. The final question seeks a straightforward method to calculate the time until all molecules of gas A have dissipated without complex integration. Understanding the relationship between collision frequency and mean free path is crucial for solving this problem.
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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