A gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. A gas column under gravity, for example, does not have uniform density (and pressure). As you might expect, its density decreases with height. The precise dependence is given by the so-called law of atmospheres
`n_(2)= n_(1) "exp"[-mg(h_(2)-h_(1))//k_(B)T]`
where `n_(2), n_(1)` refer to number density at heights `h_(2)` and `h_(1)` respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
`n_(2)= n_(1)"exp"[ -mgN_(A)(rho-rho')(h_(2)-h_(1))//rhoRT)]` where `rho` is the density of the suspended particle, and `rho'`, that of surrounding medium. [`N_(A)` is Avogadro's number, and R the universal gas constant.] [Hint : Use Archimedes principle to find the apparent weight of the suspended particle.]