$4)$ Consider the plane wall shown below with cross sectional area $\backslash ($ Z $\backslash ).$ The left side of the wall is perfectly insulated and the right side is exposed to the environment. The wall is composed of $3$ sections, A$,$ B$,$ and C$,$ each length L$.$ Section A experiences uniform internal heat generation $\backslash (\backslash$dot$\{$q$\}\backslash ).$ Sections A and B have contact resistance between them equal to $\backslash (\backslash$mathrm$\{$R$\}\_\{$A B$\}\backslash )$ and sections B and C have contact resistance between them equal to $\backslash (\backslash$mathrm$\{$R$\}\_\{$B C$\}\backslash ).$ Assuming $1$D conduction, steady state, and uniform thermal conductivity throughout the wall, answer the following:

a$)$ Using the plots below, plot the temperature distribution and heat rate for the wall. Be sure to mark where zero is on the heat rate plot. $(14$ pts$)$

b$)$ What is $\backslash (\backslash$Delta T$\_\{$B C$\}\backslash )$ equal to $($the temperature drop between sections B and C$)?(10$ pts$)$