Final answer:
The question relates to physics, specifically heat transfer through a wall. Gypsum board or Plasterboard is typically used for curved walls, but the physics problem calculates the rate of heat flow through an exterior wall with different layers providing thermal resistance.
Step-by-step explanation:
Heat Flow Through a Wall
The type of drywall that is typically installed as a double-layer system to cover curved interior walls is Gypsum board or Plasterboard. However, for the physics problem given, we are looking at the rate of heat flow through a well-insulated exterior wall that has different layers, each contributing to the wall's total thermal resistance (R-value).
To calculate the heat flow rate (also known as the heat current), we use the following formula derived from Fourier's law of heat conduction:
Heat flow rate (Q) = ΔT / R_total
Where ΔT is the temperature difference across the wall, and R_total is the total R-value of the wall. For part (a), we sum up the R-values of all layers:
- R_total = R_drywall + R_fiberglass + R_siding
- R_total = 0.56 + R_fiberglass + 2.6
The R-value for 3.5 inches of fiberglass is typically around 11. Therefore:
- R_total = 0.56 + 11 + 2.6 = 14.16
With ΔT = 22 °C - (-2 °C) = 24 °C, the heat flow rate is:
- Q = ΔT / R_total = 24 °C / 14.16 = approximately 1.695 W/m²
For part (b), we need to consider the thermal bridging effect of the 2-by-4 studs. Since they are less insulative than the fiberglass, they will change the overall R-value. However, the exact calculation of the new R-total including studs is not provided here. The principle is to use the proportion of the wall covered by studs to amend the R_total value.
In both cases, the rate of heat flow is proportional to the temperature difference and inversely proportional to the total R-value of the wall. Lower R-value results in higher heat flow, meaning more heat loss from inside to outside.