So I'm trying to calculate the concentration of an ideal gas in an adiabatic container as a function of position where the top and bottom plates of the container are fixed at temperatures T1 and T2, respectively, with T2 > T1.  Thus, there is a temperature gradient from bottom to top, ie. $T(z) = T_2 - (T_2-T_1)\frac{z}{h}$, where h is the height of the container.  How do I calculate the concentration of the gas, $n(z)$, which I expect to be smaller at the bottom (near the hot plate) and larger at the top?