A very tall vertical cylinder contains carbon dioxide at a certain temperature `T`. Assuming the gravitational field to be uniform, find how the gas pressure on the bottom of the vessel will change when the gas temperature increases `eta` times.

Explanation

At a temperature `T` the concentration `n(Ƶ)` varies with height according to
`n (Ƶ) = n_0 e^(-mgz//kT)`
Thuis means that the cylinder contains `int _0^oo n(Ƶ) d Ƶ`
=`int_0^oo n_0 e^(-mg//kT) d Ƶ = (n_0 kT)/(mg)`
Particles per unit area of the base. Clearly this cannot change. Thus `n_0 kT = p_0` = pressure at the bottom of the cylinder must not change with change of temperature.