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Transport Phenomena

Problem 2.234

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

Reveal Answer
n=n0e−t/τ, where τ=4V/S⟨v⟩,⟨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}
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