P$1(50$ pts $.)$ Consider a long resistance wire of radius $r_1=0\mathrm{.}25cm$ and thermal conductivity $k_{\text{w}\text{i}\text{r}\text{e}}=25\frac{W}{m}*K$ in which heat is generated uniformly as a result of resistance heating at a constant rate of $e_{\text{g}\text{e}\text{n}}=65\frac{W}{c}{m}^3.$ The wire is embedded in a $0\mathrm{.}60-cm-$thick layer of ceramic whose thermal conductivity is $k_{\text{c}\text{e}\text{r}\text{a}\text{m}\text{i}\text{c}}=1\mathrm{.}5\frac{W}{m}*K.$ If the outer surface temperature of the ceramic layer is measured to be $T_3=40C.$ Determine the temperatures at the center of the resistance wire and the interface of the wire and the ceramic layer under steady conditions. $($Note: the temperature profile where heat is generated in the long cylinder is given by $\{$:$T(r)=-\frac{e_{er}}{4k}+C_1)$