All Problems

Transport Phenomena

Problem 2.234

An ideal gas of molar mass MM is enclosed in a vessel of volume VV whose thin walls are kept at a constant temperature TT. At a moment t=0t=0 a small hole of area SS is opened, and the gas starts escaping into vacuum. Find the gas concentration nn as a function of time tt if at the initial moment n(0)=n0n(0)=n_{0}.

Reveal Answer
n=n0et/τ, where τ=4V/Sv,v=8RT/πMn=n_{0} \mathrm{e}^{-t / \tau}, \text { where } \tau=4 V / S\langle v\rangle,\langle v\rangle=\sqrt{8 R T / \pi M}