$2\mathrm{.}22$ The steady$-$state temperature distribution in a one$-$dimensional wall of thermal conductivity $50$ W$/$m K and thickness $50$ mm is observed to be $1(\backslash$deg C$)=$ a $+$bx$?,$ where a $=200\backslash$deg C$,$ b $=-2000\backslash$deg C$/$m$\text{'},$ and x is in meters.