Lecture #$5-$ Homework $($due by $1/31/2024$ before class$)$

A compound wall consisting of wood $($thermal conductivity $=0\mathrm{.}3222Btu{m}^{-1}h{r}^{-1}{R}^{-1})$ that is $2-$inches thick $($each layer$)$ and has an air gap of $6-$inches $($thermal conductivity $=0\mathrm{.}02W{m}^{-1}{K}^{-1})$ is used to maintain the interior house wall temperature at $65F$ at night as heat radiates outwards. The compound wall is laid out as wood:air$-$gap:wood. Given that the night air on a cold day $($no wind$)$ is $9F,$ assume the house emissivity is $0\mathrm{.}9$ and steady$-$state heat transfer:

a$)$ Indicate the unit conversions required to base SI units

b$)$ What are the temperatures throughout the wall at each junction $F$

c$)$ How much heat transfer is there per unit wall surface area $\frac{W}{m^2}$

d$)$ Over $8$ hours, how much total energy exits the house with a surface area of $2000f{t}^2$ in $[$J$]?$

You must show all calculations, unit conversions, etc. to receive full points. Simply putting down the answer is not sufficient; we need to see your work. Use the Engineering Solution Sheet.