A wall separating two rooms is constructed of two layers of $0\mathrm{.}6-$inch thick sheetrock $($k $=0\mathrm{.}10$

Btu $/$ h ft $$F$),$ which is a plasterboard made of two layers of heavy paper separated by a layer

of gypsum, placed $5$ inches apart. The space between the sheetrock is filled with fiberglass

insulation $($k $=0\mathrm{.}020$ Btu $/$ h ft $$F$).$

a$)$ Determine the thermal resistance of the wall.

b$)$ The insulation of building materials is often specified as an $$R$-$value$,$ where R$-1=1$ ft$2$

$$F h $/$ Btu. What is the R$-$value of the wall?

c$)$ If one room is at $70$F and the other is at $60$F find the rate of heat transfer assuming:

i$.$ The wall surfaces are at the same temperature as the air $($i$.$e$.70$F and $60$F$)$

ii$.$ There is a convection coefficient on both sides of wall h $=10$ Btu $/$ h ft$2$F$,$ but

radiation is neglected.

iii. Radiation to the room is to be included for both surfaces, where emissivity $=0\mathrm{.}8$

and the Stefan$-$Boltzmann constant $=1\mathrm{.}71410-9$ Btu $/$ h ft$2$R$4$

$.$