Response to the following problem:
A vessel of volume V contains a gas that is kept at constant temperature. The gas slowly leaks out of a small hole of area A. The outside pressure is so low that no atoms leak back.
(a) Prove that the pressure at any time t is given by
P = P0e-k’t
Where Po is the initial pressure.
(b) Calculate k in terms of V, A, and (w).
(Note: Assume that all the atoms arriving at the hole pass through.)