A plane wall $($see schematic$)$ is composed of a material having a temperature dependent thermal conductivity given by kw $=$ BT where B$=5$ W$/$m$^2$ K$^2.$ The thickness of the wall is L$=0\mathrm{.}5$ m and it has a cross$-$sectional area of Ac $=1$ m$^2.$ The temperature on the wall's far left extreme is Th$=300$ K and on its far right Tc$=20$ K$.$Assuming one$-$dimensional heat transfer through the wall, derive an expression for the spatial dependence of temperature along the x$-$direction. Your final answer should take the form of T$($x$)=$ f$($B$,$T$,$Ac $,$Th $,$Tc $,$L$,$x$)$