Kinetic Theory: How many molecules enter pinhole in vacuum?

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Homework Help Overview

The discussion revolves around a problem in kinetic theory related to the flow of molecules through a pinhole in a vacuum. The scenario involves calculating the number of molecules that enter the vacuum through a small opening, given specific pressure conditions and temperature.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the use of differential equations to model the problem but express concerns about missing initial conditions and volume information. Some suggest focusing on the ratio of molecules per volume (N/V) and propose using arbitrary volumes to simplify calculations. Others question the need for velocity information and the applicability of the Maxwell Distribution for velocity calculations.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and offering insights into how to approach the calculations. Some guidance has been provided regarding the use of N/V and the potential for simplifications, but no consensus has been reached on the method to obtain a numerical result.

Contextual Notes

Participants note the constraints of the problem, including the lack of initial molecule count and volume, which are critical for a complete solution. There is also an emphasis on the order-of-magnitude nature of the answer being sought.

Lagraaaange
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Homework Statement


Pressure in vacuum is 10^-3 Torr. External Pressure is 1atm and 300K. Pinhole of 10^-10cm^2 made in vacuum. Assuming all molecules striking hole pass through, how many molecules leak into vacuum in 1hour?
Answer: 10^17 molecules

Homework Equations


Flux = <v>*N/4V
Rate = Flux times A

The Attempt at a Solution


I can make an DE: dN/dt = <v>N/4V*A and solve this but I have no info on N0, initial molecules. I also don't have volume. So I don't see how to obtain a numerical result.
 
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Ask yourself what pressure is.
 
You only need N/V, molecules per volume, which you can get with the given information.
Alternatively, take an arbitrary volume, it will cancel out in the calculations anyway.
 
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I don't see how I can get this with the information
mfb said:
You only need N/V, molecules per volume, which you can get with the given information.
Alternatively, take an arbitrary volume, it will cancel out in the calculations anyway.
P/kT = N/V = 2.45molecules/m^3 = ρ
Also <KE> = 3/2KT = 6.21E-21J = m/2 *<v^2>.
Now particles within vΔt make it to hole; also those within AvΔtρ make it.
Now I'm stuck. I can't get v since I don't have m. Also I'm unsure whether to invoke a Maxwell Distribution to get all velocities.
 
Looks like they are only asking for an order-of-magnitude answer. So, you can use any reasonable value for the mass of a molecule.
 
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