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

[vmedica]

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?

 

[Simon Bridge]

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.