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Kilian Stenning
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Homework Statement
A circular cylinder of height H is filled with monatomic gas molecules at temperature T. The cylinder stands on the surface of the Earth so that the gas molecules are subject to the gravitational field g.
(a) Find the average height, z , of the molecules in the cylinder as a function of temperature. (Hint: The probability of finding a molecule at height z is governed by the Boltzmann distribution). Show that for
T → 0, z = 0 , and for T → ∞ , z = H/2 .
Homework Equations
f(z) = Cexp(-mgh/kt)
<z> =∫ z fz dz/∫ fz dz
The Attempt at a Solution
let B=mg/kT
Ive got an answer for <z> to be (1/B)*(1-(e^(-BH))*(BH+1))/(1-e^(-BH))
To get the limits I've tried to use l'hopitals rule w.r.t T but I can't seem to get the right answer