The performance of ideal vacuum system

According to the kinetic theory of gases, when the temperature of the gas in the vessel is constant

PV= constant

The formula for the time differential, and in the pump with the same volume velocity S = dV/dt under the conditions of the container under the conditions of integration, then, if the pressure of t=0 is Po, then

P=p0e- (s/v)

As a kind of ideal gas filled in and the wall outside except reflected without some other effects, and the volumetric efficiency of constant pump, the pressure will be the relationship between the expression of the equation of time. At the beginning of the extraction phase of the vacuum container before using the mechanical pump, basic meet the assumptions, the function relationship between the pressure and the time to draw in the semi logarithmic coordinate of the approximation is a straight line.

In theory, the pressure should be decreased exponentially with the increase of time, which is determined by the time constant of V/S. Today, many vacuum systems in the laboratory, pumping speed (1/s) more than 10 times the volume (1), so the time constant of 0.1s.

It is interesting to study the prediction of this concept, the pressure will drop from 10-3Torr to 10-9Torr. in 1.4s, if the time constant is 1, from 10-3Torr to 10-12Torr is as long as 21s. This is obviously inconsistent with the actual situation, this is not because the theory is wrong, nor in the pressure range assumption within basically constant pumping speed calculation is wrong, but the actual situation and we assume that the model does not match.