Question $1$:

$(30$ marks$)$

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 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 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.

$($Hint: Use IHT software$/$MS Excel and the Bergman textbook$)$

Note: Take 'full screen' screenshots $($of the whole desktop screen showing everything including date and time on your desktop$)$ showing of your results in IHT software and paste it in your answer.