If a lyophilizer chamber had a volume of 8404 liters, already excluding the shelves, hoses, etc., and it had a measured leak rate of 0.5 mTorr/hr, what size would the leak hole be if it were a single simple pinhole through the wall?
Let
Let
Let
<= Molecular Wt for Air
Let
<Microscope view of pinhole.
A detailed calculation, allowing for all angles of approach of molecules to the surface and providing for the distribution of molecular veloities shows that with
nm (the mean velocity in meters/sec), a correct velocity equation is
where n' is the number of molecules per m3and n is the number of collisions per m2 per second.
Thus the units of
and the units of
and the units of
From kinetic theory,
Thus
or
<= EQU (1)
Separately, one can see that the mass (w)of molecules striking an opening per square meter per second is <=EQU (2) and units of
Now combining equations 1 and 2 we get
and
<= Ideal Gas Law
with a little algebra,
The mass that is striking the unknown area(of the pinhole) per sec can be determined from the DP/hr given in the problem.
First find the number of mole (n) per sec that are leaking through the pinhole.
where 
and the units of 
and the units of 
or 
and 
that impinge on the opening.
and 
