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 Homework Statement:

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.
 Relevant Equations:
 ##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.
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.