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Gas effusing through hole, working out time dependence
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[QUOTE="physconomic, post: 6442472, member: 683332"] [B]Homework Statement:[/B] Consider instead a thermally insulated container of volume V with a small hole of area A, containing a gas with molecular mass m. At time t = 0, the density is ##n_0## and temperature is ##T_0##. As gas effuses out through a small hole, both density and temperature inside the container will drop. Work out their time dependence, n(t) and T(t) in terms of the quantities given above. [B]Relevant Equations:[/B] ##N_L = \frac{1}{4} n A <u> = \frac{1}{4} \frac{N_0}{v} A \sqrt{\frac{8kT}{\pi m}}## Consider instead a thermally insulated container of volume V with a small hole of area A, containing a gas with molecular mass m. At time t = 0, the density is ##n_0## and temperature is ##T_0##. As gas effuses out through a small hole, both density and temperature inside the container will drop. Work out their time dependence, n(t) and T(t) in terms of the quantities given above. I know that ##N_L = \frac{1}{4} n A <u> = \frac{1}{4} \frac{N_0}{v} A \sqrt{\frac{8kT}{\pi m}}##, but not sure how to use this to find n(t) and T(t). I think I need to find the flux of the energy to know if the temperature is decreasing and then find n and t from that but not sure exactly how to do this. Any help greatly appreciated. [/QUOTE]
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Gas effusing through hole, working out time dependence
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