Use the First Law to $1)$ derive a differential equation that describes how the

steady temperature varies inside a plane wall $($from one outer surface to the

other$).$ Recall the in$-$class practice problem for a plane wall that has a

constant thermal conductivity k and constant cross$-$sectional area Ac$.$ Then

$2)$ solve the equation completely using the boundary conditions at x$=0$ and at

x$=$L$.$ That is at x$=0$ T$=$T$1$ and at x$=$L T$=$T$2.$ Lastly $3),$ find the heat transfer

rate for this situation. Show all your steps. If you have trouble, refer to the

notes.$(5$pts$)$