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## Homework Statement

If you poke a hole in a container full of gas, the gass will start leaking out. In this problem, you weill make a rough estimate of the rate at which gas escapes through a hole.

If we now take away this small part of the wall of the container, the molecules that would have collidedwith it will instead escape through the hole. Assuming nothing enters through the hole , show that the number N of molecules inside the cotainer as a function of time is governed by the DE equation

dN/dt=-(A/2V)*sqrt(kT/m)*N

## Homework Equations

Possible equations that pertain to this problem

P=-m*(delta(v

_{2})/delta(t))/A

v

_{x}=sqrt(kT/m)

PV=Nmv

_{x}^2

## The Attempt at a Solution

PV=(-m*(delta(v

_{x})/delta(t))/A)*V=Nmv

_{x}^2

N=((-m*(delta(v

_{x})/delta(t))/A)*V) /mv

_{x}^2

m cancel and and I am left with :

N=((-(delta(v

_{2})/delta(t))/A)*V) /v

_{x}^2

N=((-1/delta(t))/A)*V) /v

_{x}^1= (-V*(delta(t))/A)/(v

_{x})

N/delta(t)= -V/A(v

_{x})=V/(A*sqrt(kT/m))

Something is wrong with my calculating because I think I am suppose to integrate N and my A nd V are in the wrong places.