Analysis of Molecular Flow in an Isothermal Enclosure

Abstract

Previously presented analyses of the molecular flow of saturated vapor from a condensed phase in an isothermal enclosure have introduced simplifying approximations early in the treatments. Consequently functions and subtle inconsistencies have appeared which can be recognized, identified, and understood only by returning to the original formulation. A more desirable procedure is to pursue rigorously as far as possible the problem before introducing approximations. The presently described analysis differs from the others in the following respects: (1) The precise system described and the fundamental assumptions employed are defined initially. (2) For a cylindrical (and a generalized) enclosure it is shown that the form p=p_e(1—Δ) with p_e equal to the equilibrium pressure and Δ a function of the parameters of the cell is a convenient one for the purpose of effecting approximations. (3) The exact physical system corresponding to the classical equation, p_e=p[1+(S₀/S₁)], in which S₀ is the area of an orifice and S₁ is the evaporating area (both on a spherical surface), has been found to be a spherical enclosure for which Δ can be easily calculated. (4) The single approximation leading to the formulation of Whitman and of Motzfeldt has been found and Δ has been evaluated. An intercomparison is given.