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amcca064

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Assume that the Earth's atmosphere has a uniform temperature of 20ºC and uniform composition, with an effective molar mass of 28.9 g/mol. a) show that the number density of molecules depends on height according to:

nv (y) = (n0) e^ -(mgy)/kBT

b) commercial jetliners typically cruise at an altitude of 11.0 km. Find the ratio of the atmospheric density there to the density at sea level.

Ok, so I really am kind of stuck here, for the normal Boltzmann distribution equation, where nv(E) = (n0) e^-E/kBT is it possible just to say that since the atmosphere is assumed to have uniform temperature and composition that (assuming no heat loss or gain through interaction with the ground or space) all the molecules have the same kinetic energy and therefore the only change in E would occur through a change in potential energy, therefore the E in the Boltzmann distribution eq can be subsituted for U and U can be substituted for mgy?? Seems far too easy this way. Help anyone?

Correct title should have been Bolztmann distribution law

nv (y) = (n0) e^ -(mgy)/kBT

b) commercial jetliners typically cruise at an altitude of 11.0 km. Find the ratio of the atmospheric density there to the density at sea level.

Ok, so I really am kind of stuck here, for the normal Boltzmann distribution equation, where nv(E) = (n0) e^-E/kBT is it possible just to say that since the atmosphere is assumed to have uniform temperature and composition that (assuming no heat loss or gain through interaction with the ground or space) all the molecules have the same kinetic energy and therefore the only change in E would occur through a change in potential energy, therefore the E in the Boltzmann distribution eq can be subsituted for U and U can be substituted for mgy?? Seems far too easy this way. Help anyone?

Correct title should have been Bolztmann distribution law

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