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Homework Statement
A container of volume 10−3 m3 has a pressure of 10−7 mbar.
Surrounded by air at 1 bar and 290 K, how long does it take the pressure inside to rise to 10−6 mbar when air effuses through a small hole of area 10−17 m2?
Homework Equations
The Attempt at a Solution
[tex]Flux ø = \frac{1}{4}n<v> [/tex]
Starting from continuity equation:
[tex]øA = -\frac{dN}{dt}[/tex]
[tex]\frac {1}{4} \frac{NA}{V}<v> = -\frac{dN}{dt} [/tex]
[tex] n = n_0e^-{\frac{1}{4} \frac {A<v>t}{V} = n_0 e^-{bt} , b = {\frac{1}{4} \frac {A<v>}{V}[/tex]
Am I right to assume that temperature in the box is the same as temperature of the surrounding air, 290K? Since average temperature of air molecules entering the box is 290K, the average temperature in the box is also 290K, which is constant.
[tex] \frac {P_f}{P_i} = \frac {n_f}{n_i} = e^{-bt} [/tex]
Solving, [tex] t = 1.94 * 10^{12} s [/tex] The result is astronomical!