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How Long Does It Take for Pressure to Increase in a Punctured Container?
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[QUOTE="Charles Link, post: 5906896, member: 583509"] Your original differential equation is incorrect. You are assuming the effusion only goes in one direction is this problem (that is ok), but the equation should read ## \frac{dN}{dt}=\frac{A n \bar{v}}{4 } ## where ## n ## is the number of particles per unit volume of the outside air. (## N ## is the number of particles of air inside the container). This ## n ## is constant and does change. One number you will need is ## \bar{v} ##. Average speed ## \bar{v} ## in a Maxwell-Boltzmann distribution is given by ## \bar{v}= (\frac{8}{\pi}) (\frac{kT}{M})^{1/2} ## , editing: ## \bar{v}=(\frac{8 kT}{\pi M})^{1/2} ##, where ## M ## is the (approximate) mass of a molecule of air. Since ## N_2 ## has M.W.=28, and ## O_2 ## has M.W.=32 , using an average M.W.=30 is an ok approximation, even though the air is 78% ##N_2 ## and 21% ##O_2 ##. [/QUOTE]
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How Long Does It Take for Pressure to Increase in a Punctured Container?
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