KEMS equation, derivation

The central KEMS equation can be derived now that the Knudsen cell vapor source and mass spectrometer have been described. This follows directly from the vapor flux in the molecular beam selected from the distribution of material effusing from the Knudsen cell (molecular beam flux equation) and the definition of the ionization cross section (Equation 48.18). However, in accordance with the aim of identifying factors that affect the measured ion intensity and that are unrelated to sample temperature and composition, it useful to rewrite Equation 48.18 in terms of the number of ions produced per second in the elementary volume dv in the region defined by the intersection of the molecular and electron beams, ni(E) [71,80] (this is prior to the formation of the ion beam) ... 

We have devoted a large section to the derivation of the KEMS equation, relating ion intensity to vapor pressure. As noted, it would be beneficial to understand some of the variables in this relationship further. In particular, an independent measurement of the total vapor flux would be helpful. This could be accomplished with an in situ weight loss measurement or target collection system. Improved molecular beam definition could include better positioning of the cell, with more precise x-, y-, and z-coordinates. 

Double-pipe exchangers are often piped in complex series-parallel arrangements on both sides. The MTD to be used has been derived for some of these arrangements and is reported in Kem Process Heat Transfer, McGraw-Hill, New York, 1950). More complex cases may require trial-and-error balancing of the heat loads and rate equations for subsections or even for individual exchangers in the bank. 

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