$(22$ points$)$ A log cabin home has a $19[cm]$ thick pine wall that measures $3[m]$ by $6m,$ which includes two windows, each $1[m^2].$ One window is single$-$pane $0\mathrm{.}5[cm]$ plate glass, the other is double$-$pane with a $0\mathrm{.}5[cm]$ air gap. The outside air is $-20C$ on a cold winter night and provides a convection coefficient of $200[\frac{W}{m^2}-K].$ The inside air is $20[C]$ with a convection coefficient of $10[\frac{W}{m^2}-K].$

a$.$ Draw the thermal circuit through the entire wall including windows.

b$.$ Determine the total heat loss $[$W$].$

c$.$ Determine the heat loss $[$W$]$ through the wall, single$-$ and double$-$pane window.

d$.$ Determine the inside surface temperature $C$ of the wall, single$-$ and doublepane window. Which surface is likely to have frost, condensate or nothing on it$?$