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27 Nov 2019
The law of atmospheres states that the number density ofmolecules in the atmosphere depends on height y above sea levelaccording to
nv (y) = n0 e^(-m0 gv/kg T)
where n0 is the number density at sea level (where y = 0). Theaverage height of a molecule in the Earthâs atmosphere is givenby
(a) Prove that this average height is equal to kBT/m0g. (b)Evaluate the average height, assuming the temperature is 10.0ï°C andthe molecular mass is 28.9 u, both uniform throughout theatmosphere.
The law of atmospheres states that the number density ofmolecules in the atmosphere depends on height y above sea levelaccording to
nv (y) = n0 e^(-m0 gv/kg T)
where n0 is the number density at sea level (where y = 0). Theaverage height of a molecule in the Earthâs atmosphere is givenby
(a) Prove that this average height is equal to kBT/m0g. (b)Evaluate the average height, assuming the temperature is 10.0ï°C andthe molecular mass is 28.9 u, both uniform throughout theatmosphere.
