Final answer:
The rate of heat flow through the wall without studs (part a) is calculated using the total R-value of the drywall and siding, resulting in 227.7 watts. For part b, introducing studs would alter the R-value, but the specific effect is not calculated as per the instructions.
Step-by-step explanation:
Calculation of Heat Flow Through a Wall
To calculate the rate of heat flow through a well-insulated wall, we can use the concept of thermal resistance or R-value. The rate of heat flow (Q) is given by the equation Q = ΔT / R_total, where ΔT is the temperature difference across the wall, and R_total is the total thermal resistance of the wall. In this case, ΔT is 22 °C - (-2 °C) = 24 °C, and R_total is the sum of the R-values of the individual layers since the wall has no air leaks.
For part (a), R_total equals the sum of the R-values for drywall (0.56) and insulated siding (2.6), giving us an R_total of 3.16. Using the equation for heat flow, we find Q = 24 °C / 3.16 = 7.59 watts per square meter. Assuming the wall is 3 m tall and 10 m wide, the total rate of heat flow through the wall is 7.59 W/m^2 * 30 m^2 = 227.7 watts.
For part (b), to account for the 2-by-4 studs, we would need to calculate the effective R-value of the wall, mixing the R-values of the fiberglass and wood since wood has a different R-value. However, based on the instruction, we will not make the complex calculation and instead conclude that the presence of studs will slightly lower the R-value and increase the rate of heat flow compared to the wall without studs.