Boltzmann distribution of two different gases

[oguz]

hi everyone,

consider two different masses of ideal gases with different molar masses, we're putting them in a uniform gravitational field and wait until they come to their equilibrium states. how would the density distribution change with height in this case?

( i came out with this question while working on a problem in "problems on general physics" by irodov. the answer to the problem seemed to be merely superposing two different distributions but doesn't this imply that molecules of both gases do not interact? if they don't, I'm asking should not they be stressing pressure on each other?)

 

[bbbeard]

hi everyone,

consider two different masses of ideal gases with different molar masses, we're putting them in a uniform gravitational field and wait until they come to their equilibrium states. how would the density distribution change with height in this case?

( i came out with this question while working on a problem in "problems on general physics" by irodov. the answer to the problem seemed to be merely superposing two different distributions but doesn't this imply that molecules of both gases do not interact? if they don't, I'm asking should not they be stressing pressure on each other?)

ISTR this problem is discussed in the Feynman lectures, where it is stated that the density in equilibrium is proportional to the Boltzmann probability, i.e. exp(-m*g*h/T), where m is the molecular mass (T is in energy units; use k_B for unit conversion). (This is assuming an isothermal atmosphere, which is not in mechanical equilibrium.) There will be a normalization factor that depends on the total amount of has. The higher molecular weight gas has a higher rate of density change with height.

BBB