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A venting equation commonly used to describe the transient evolution of pressure within a volume containing an outgassing or offgassing source and a restrictive vent conductance under conditions of molecular flow has been solved analytically. Solutions are found for sources of finite thickness characterized by classical diffusion-limited behavior (proportional to inverse square root of time), as well as responses for thick material sources often observed in testing that are characterized by a more general form of power-law decay, up to inverse time behavior associated with surface desorption. Solutions involve evaluating integrals where both numerators and denominators of the integrands diverge with time, making wide-ranging transient solutions difficult to directly compute numerically. Usually, one can avoid evaluating these integrals by assuming quasistatic conditions at long time scales. A novel approach is used in this work to analytically produce solutions by generating bespoke mathematical functions, some of which solve integrals that have apparently had no previous analytical solution.
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