Calculate the heat loss rate in watts from steam through an insulated pipe with minimal thickness. The pipe, with a length of L $=10$ m and an inner radius of r $=40$ mm$,$ features an $8$ mm insulation layer with a thermal conductivity of k $=0\mathrm{.}12$ W m$-1$ K$-1.$ The average temperatures of the inner and outer surfaces of the insulation are maintained at T$1=100\backslash$deg C and T$2=50\backslash$deg C$,$ respectively. Disregard interface thermal resistance and assume one$-$dimensional heat transfer.