INDUSTRIAL AND ENGINEERING CHEMISTRY
7 80
In this range of pressures the rates of transfer of both momentum and energy vary linearly with the pressure and this fact has therefore been applied t o the development of a number of designs of low pressure gages. We may now consider briefly a few relations which have been deduced from the kinetic theory of gases, which are of importance in high vacuum investigations. At low pressures, the rate a t which molecules strike a surface is given by the relation Y
=
nv, molecules cm.-2 set.-'
l/4
(6)
Vol. 40, No. 5
For organic vapors, as pointed out by Hickman, the value of M / T is approximately 1. Hence, the value of G is about 0.6 p (grams per square meter per second)-that is, at p = 1 micron, the maximum theoretical rate of evaporation is 0.6 gram per square meter per second, or about 4.7 pounds per square meter per hour. Finally, there exists a difference between the rate of flow of gases a t normal pressures and the rate of flow at low pressures.
For the whole range of pressures the rate of flow of gas through a cylindrical tube can be expressed by the relation
which can be expressed in the form Y
= 3.513 X 1019p/d/MT
where p = pressure in microns. For nitrogen a t 25 C., Y = 3.84 X 1017p , molecules see.-’ Since the number of molecules, Ns, required to form a layer one it follows molecule thick (monolayer) is about 18 X 1014 that the time, to, required to form a monolayer, assuming that each molecule condenses on the surface, is O
1YS
to = - = 2 X lO-S/p seconds Y
that is, at p = ,
micron, to is about 2 seconds.
These relations are of importance, as shown by L. Apker, in determining the rate of contamination of a clean surface in a high vacuum. Actually, not every molecule incident on a surface “sticks.” There is a constant re-evaporation which increases with the temperature, and as shown by Langmuir, the fraction of the surface covered at equilibrium, e, at any pressure p , is given by a relation of the form
e=-
bp
1
+ bp
(7)
where b is a constant which is proportional to the “life” of the adsorbed molecules on the surface. Equation 6 also gives the rate at which molecules evaporate from a surface at very low pressures of residual gases. From this equation it follows that the rate of evaporation is given by the equation,
G
=
-
5.833 X 10-5 p d M / T gram cm.-2 sec.-l
(8)
where Q = micron liters per second p 2 - pl = difference in pressures (in microns) a t the two ends of the tube a = radius and I = length of tube (in em.) L, = mean free path a t the average pressure, pa= 0.5 (PZ PI) = ap,/L1 L1 = mean free path a t 1micron, in em. 2 = function of a/L. which increases from the value 0.81 for a/L. > 100 to 1.0 for a/L, 0.1 If we plot log Q versus log p a , the slope has the value 1 a t low pressures and the value 2 at high pressures, with a transition from 1 t o 2 in the range a/La = 100 to a/L, = 1 approximateiy. At the lower range of pressures, Q varies linearly with p z - pl; at the higher range, Q varies with the product, (pz pl)p,.
+
