Thermodynamics Problem: Finding Heat Transfer

[Jacob White]

Homework Statement

In vacuum and weightlessness, at the bottom of a cylindrical vessel (a cup), there is a layer of solid substance. This
substance sublimes slowly (evaporates from the solid phase into
gaseous phase) and pushes thereby the vessel to the opposite
direction. The mass of the vessel is M, and the initial mass of
the substance m ≪ M. The cross-sectional area of the vessel
is A, and the pressure of saturated vapours of the substance
at the temperature T is p0. What is the acceleration of the
vessel? Provide answer for two cases: (a) the mean free path
length λ of the molecules at the saturation pressure is much
smaller than the length of the vessel, and (b) much larger than
that.

Relevant Equations

a=pA/M

I have come across this problem from this booklet: https://www.ioc.ee/~kalda/ipho/Thermodyn.pdf

 

[Jacob White]

Sorry for that mess. But this is my first post and I have accidentally post it without description

I have managed to done b) but I have some doubts about a). The answer suggests(at least I think so) that saturated vapour would form around the layer and exerted force Psaturated * Area. But this is rather strange assumption. Why it wouldn't escape to vacuum? Although the λ ≪ L, there is no wall at the other end and it is highly unlikely that some molecules would turn back. Could someone explain that? I would be very grateful.