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## Homework Statement

Let a box of height h be filled with classical ideal gas molecules of mass m in a constant gravitational filed g. As will be shown later, the distribution molecular height z obeys:

f(z) = C exp (-mgz/KT)

Where C is the normalization constant

a) find the average height z, of molecules in the box

b) find the limiting value of z when h->0

c) find the limiting value of z when h->infinitiy

## The Attempt at a Solution

I am a little confused as to where to begin, should i start with determining C?

I started with:

Area * Height * average_density = number of molecules

= Area * integral (z = 0, H [constant*exp(-mgz/(kT))] dz

= Area*constant*(kT/(mg))*integral(0,mgH)/(kT) [exp(-u)]du

= Area*constant*(kT/(mg))*(1-exp(-mgH/(kT))

Therefore,

number = N = Area*constant*(kT/(mg))*(1-e^(-mgH/(kT))

So:

Constant = N*(mg/(kT))/(Area*(1-e^(-mgH/(kT))

Am i on the right track? thanks in advance