$57$ A $12-$m$-$long and $5-$m$-$high wall is constructed of two layers of $1-$cm$-$thick sheetrock $($k $0\mathrm{.}17$ W$/$m $$ C$)$ spaced $16$ cm by wood studs $($k $0\mathrm{.}11$ W$/$m $$ C$)$ whose cross section is $12$ cm $5$ cm$.$ The studs are placed vertically $60$ cm apart, and the space between them is filled with fiberglass insulation $($k $0\mathrm{.}034$ W$/$m $$ C$).$ The house is maintained at $20$C and the ambient temperature outside is $9$C$.$ Taking the heat transfer coefficients at the inner and outer surfaces of the house to be $8\mathrm{.}3$ and $34$ W$/$m$2$ C$,$ respectively, determine $($a$)$ the thermal resistance of the wall considering a representa$-$ tive section of it and $($b$)$ the rate of heat transfer through the wall.