$1\mathrm{.}4$ A concrete wall, which has a surface area of $20m^2$ and is $0\mathrm{.}30$ m thick, separates conditioned room air from ambient air. The temperature of the inner surface of the wall is maintained at $25C,$ and the thermal conductivity of the concrete is $1\frac{W}{m}*K.$

$($a$)$ Determine the rate of heat loss through the wall for outer surface temperatures ranging from $-15C$ to $38C,$ which correspond to winter and summer extremes, respectively. Display your results graphically.

$($b$)$ On your graph, also plot the rate of heat loss as a function of the outer surface temperature for wall materials having thermal conductivities of $0\mathrm{.}75$ and $1\mathrm{.}25\frac{W}{m}*K.$ Explain the family of curves you have obtained.