Blundell Thermal Physics · Problem 7.8

Molecular effusion

Physics — Statistical Mechanics · effusion-pressure-decay-oven

Problem

Show that the time dependence of the pressure inside an oven (volume

V

) containing hot gas (molecular mass

m

, temperature

T

) with a small hole of area

A

is given by

p(t) = p(0)e^{-t/\tau}, \tag{7.25}

with

\tau = \frac{V}{A}\sqrt{\frac{2\pi m}{k_\mathrm{B}T}}. \tag{7.26}