Vacuum and the Kinetic Theory of Gases

1 Vacuum and the Kinetic Theory of Gases To understand the importance of vacuum, one first needs to realize that in any gas at room temperature and under atmospheric pressure (also defined as 1 atm, 101.3kPa, 760 Torr, etc.), there exists 2 X 10 molecules flying around in random directions at velocities that are in excess of 100 m/s (this is mass and temperature dependent) with the average velocity best described using the kinetic theory of gases. As these molecules move, there is a finite probability that they will collide with some solid surface, i.e. container walls, sample surface, and so on. Indeed, there are over 10 collisions/cm. s under atmospheric conditions, which is what results in the pressure measured. 

The kinetic theory of gases implies that the resulting pressure (P) can be expressed as  

The collision rate (Z ) can be written upon substitution of Relation 4.2 as  

This is the Hertz-Knudsen relation expressed in SI units. This relation can be made more accessible by expressing pressure in units of torr and merging all the conversion factors into a single constant, i.e.  

This provides the colhsion rate in units of coUisions/cm. s. Note Although torr is not the SI unit for pressure (the Pascal is), the Torr is the most commonly used unit of pressure for many of the surface analytical techniques. Conversion factors between the different pressure units are listed in Table 4.1. These aspects are all covered in detail elsewhere (Redead et al. 1968,1993). 

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