Finding the Initial Rate of Gas Leakage from a Small Hole in a Cubic Container

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To find the initial rate of gas leakage from a cubic container with a small hole, the relationship between pressure, density, and velocity is crucial. The formula p = ρc²/3 indicates that the velocity of gas molecules must be considered, particularly how many are directed toward the hole. The proposed leakage rate of av/3 assumes that one-third of the gas particles are moving toward the hole, but it lacks clarity on how the pressure difference affects this rate. A more detailed explanation of the equations and their application is needed to confirm the accuracy of the solution. Understanding the impact of pressure on gas flow is essential for determining the correct leakage rate.
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Homework Statement


A cubic container with sidelength l has a small hole with cross sectional area a (a<<l). The gas has density ρ and pressure P. Find the initial rate of gas leakage given that the outside pressure is 0.


Homework Equations



The question mentions the formula p=ρc2/3 so I know I have to use this.

The Attempt at a Solution



Assume that 1/3 of the particles are moving in a direction towards the hole. Any molecule in a cylinder of base a and length c will leave the hole in one second so is the leakage rate av/3, and then I can substitute out c with the formula? Is this the correct answer?
 
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Any molecule in a cylinder of base a and length c will leave the hole in one second
Not bad - but your result does not appear to take the pressure difference into account.

I'd have wanted to see that explicit - can you explain what your equations mean and how you are using them.
I suspect you have it right, but cannot tell exactly from what you've written down so far.
 
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