The mean kinetic energy per molecule in a gas at temp. T is mv^2/2 = 3kT/2, wher

Question

The mean kinetic energy per molecule in a gas at temp. T is mv^2/2 = 3kT/2, where k=1.380 *10^.23 J/K.  A particle with a vertical speed v at the Earth's surface will rise to a height h=v^2/2g before it falls back to the Earth.

a) Show that the characteristic height for a molecule of mass m at temperature T is h= 3kT/2mg.

b) At T-250K, compute the characteristic heights for nitrogen(N2), oxygen(o2), carbon dioxide(CO2) and hydrogen(H2). What does this tell you about the compositional structure of the Earths atmosphere?

c) How does this calculation differ from that of the schale height done in the chapter?

Explanation / Answer

a) h = v^2/2g bug v^2 = 3 k T/m

so

h = 3 k T/m/(2g) = 2k T/(2m g)

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