Final answer:
The rate of heat flow through a wall is calculated by using the total R-value of all layers, the temperature difference between indoors and outdoors, and the wall's area.
Step-by-step explanation:
The question is about the rate of heat flow through a well-insulated exterior wall of a house under specific temperature conditions. To determine the heat flow rate, you need to consider the total R-value of the combined materials in the wall and apply the formula for heat transfer: Q = ΔT / R_total × area where ΔT is the difference in temperature between the inside and outside of the wall, R_total is the sum of the R-values of all the layers in the wall, and 'area' is the surface area of the wall.
(a) First we calculate the total R-value of the wall by adding the R-factors of drywall, fiberglass, and insulated siding. Next, we find the temperature difference (ΔT = 22°C - (-2°C) = 24°C). Finally, we apply the heat transfer formula using the total R-value and the area of the wall (3 m tall x 10 m wide = 30 m²).
(b) When considering the wood studs, the R-values will be different for the sections with studs compared to those without because wood has a different R-value. A more complex calculation is required where the wall is divided into sections, and the heat flow is calculated separately for the sections with and without studs before adding them together to get the total heat current.